UBC Theses and Dissertations

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UBC Theses and Dissertations

Computer chess tactics and strategy Szabo, Alexander 1984

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COMPUTER CHESS TACTICS AND STRATEGY by ALEXANDER SZABO B. S c . , The U n i v e r s i t y o f B r i t i s h C o l u m b i a , 1978 M. S c . , The U n i v e r s i t y o f B r i t i s h C o l u m b i a , 1980 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF COMPUTER SCIENCE We a c c e p t t h i s t h e s i s a s c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA J u l y , 1984 © A l e x a n d e r S z a b o , 1984 I n p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r an a d v a n c e d d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by t h e h e a d o f my d e p a r t m e n t o r by h i s o r h e r r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . D e p a r t m e n t o f Computer S c i e n c e The U n i v e r s i t y o f B r i t i s h C o l u m b i a 1956 Main Mall V a n c o u v e r , Canada V6T 1Y3 D a t e August 8, 1984 i i A b s t r a c t The d e s i g n f o r a c h e s s p r o g r a m i s p r e s e n t e d . The n o t i o n s of t a c t i c s and s t r a t e g y a r e u s e d t o d e f i n e c o m p l e m e n t a r y ways of u n d e r s t a n d i n g any p o s i t i o n . An a s s o c i a t i o n i s made between t a c t i c s and b r u t e f o r c e t r e e s e a r c h i n g , and s t r a t e g y and knowledge e n c o d i n g . I t i s c l a i m e d t h a t knowledge i s b e s t a p p l i e d a t t h e t o p o f t h e t r e e a s e x e m p l i f i e d by TECH's p o s i t i o n a l p r e s o r t r a t h e r t h a n a t t h e " t e r m i n a l nodes u s i n g complex e v a l u a t i o n f u n c t i o n s . The t a c t i c s p a r t o f t h e d e s i g n i s i m p l e m e n t e d by t h e p r o g r a m TECH3 w h i c h i s d e s c r i b e d i n terms of r e f i n e m e n t s t o t h e minimax a l g o r i t h m . The r e f i n e m e n t s a r e t h e o,-p a l g o r i t h m , t h e q u i e s c e n c e s e a r c h , t h e t r a n s p o s i t i o n t a b l e , a~~P move o r d e r i n g , t h e s e a r c h d e p t h m e t r i c , t h e d e p t h i t e r a t i v e a-/3 t e c h n i q u e , and a s p i r a t i o n s e a r c h i n g o r w i n d o w i n g . The s i m p l e e v a l u a t i o n f u n c t i o n u s e d c a n a l s o be c o n s i d e r e d a s a r e f i n e m e n t t o minimax. TECH3's p e r f o r m a n c e on t h e p r o b l e m s i n R e i n f e l d (1958) i s 274/300 w h i c h , modulo mach i n e power, compares f a v o u r a b l y w i t h B E L L E ' s . A c o m p a r i s o n i s a l s o made w i t h t h e knowledge b a s e d t a c t i c s p r o g r a m , PARADISE. F i n a l l y , t h e t e c h n o l o g y c u r v e i s d e v e l o p e d a s a t o o l f o r m e a s u r i n g t h e e f f e c t i v e n e s s o f knowledge e n c o d i n g ( o r s t r a t e g y ) . In t h i s r e s p e c t NUCHESS i s i d e n t i f i e d a s t h e c u r r e n t b e s t c h e s s p r o g r a m . S u p e r v i s o r : D r . R.S. R o s e n b e r g i i i T a b l e o f C o n t e n t s Page A b s t r a c t i i L i s t Of T a b l e s i v L i s t Of F i g u r e s v Acknowledgements v i 1 . INTRODUCTION 1 2. PRELIMINARY DISCUSSION 3 3. TACTICS AND STRATEGY 8 3. 1 The B a s i c I d e a 8 3.2 How To S o l v e T a c t i c s 10 3.3 How To S o l v e S t r a t e g y 11 4. TECH3: A BRUTE FORCE TACTICS PROGRAM 14 4 . 1 O v e r v i e w , 14 4.2 The a-0 A l g o r i t h m 15 4.3 The Q u i e s c e n c e S e a r c h " 17 4.4 The T r a n s p o s i t i o n T a b l e 18 4.5 The R e m a i n i n g R e f i n e m e n t s 20 5. PERFORMANCE EVALUATION OF TECH3 25 6. THE TECHNOLOGY CURVE 31 7. CONCLUSIONS 38 B i b l i o g r a p h y And R e f e r e n c e s 40 A p p e n d i x 1: S o u r c e Code F o r TECH3 43 A p p e n d i x 2: T e s t P r o b l e m s And S o l u t i o n s 72 A p p e n d i x 3: R e s u l t s Of TECH3 On T e s t P r o b l e m s 84 i v L i s t o f T a b l e s T a b l e Page I - I n a c c u r a c i e s In The Book S o l u t i o n s 29 I I - The P r o b l e m s Not S o l v e d By TECH3 And BELLE 30 L i s t of F i g u r e s v F i g u r e Page 1 - A C l e a r Example Of T a c t i c s 13 2 - Human S t r a t e g y V e r s u s Computer T a c t i c s 13 3 - The I d e a B e h i n d The <x-|3 A l g o r i t h m 24 4 - The T r a n s p o s i t i o n T a b l e 24 5 - The E l o R a t i n g S ystem 36 6 - The T e c h n o l o g y C u r v e 37 7 - F u n d a m e n t a l D i v i s i o n Of The P r o b l e m 39 v i A c knowledgements I thank my t h e s i s s u p e r v i s o r , D r . R.S. R o s e n b e r g , f o r h i s s u g g e s t i o n s and p a t i e n t s u p p o r t o v e r t h e t h r e e y e a r p e r i o d o f t h i s p r o j e c t . I am e s p e c i a l l y g r a t e f u l f o r b e i n g a l l o w e d t h e f r e e d o m t o f o l l o w my n o s e , f o r b e t t e r o r f o r w o r s e . I t h a n k t h e Computing C e n t e r f o r s u p p o r t i n g t h i s p r o j e c t by making a v a i l a b l e a 0.2 r a t e f a c t o r a c c o u n t . I t h a n k my f e l l o w g r a d u a t e s t u d e n t , B a r r y Brachman, f o r t h e many d i s c u s s i o n s w h i c h h e l p e d shape t h e i d e a s p r e s e n t e d h e r e . I t h a n k D r . Hans B e r l i n e r f o r p r o v i d i n g a c o r r e c t i o n s l i s t t o t h e R e i n f e l d p r o b l e m s , and f o r h i s comments oh t h e 1st e d i t i o n o f t h i s t h e s i s . I t h a n k Ken Thompson f o r p r o v i d i n g t h e o u t p u t o f BELLE on t h e R e i n f e l d p r o b l e m s . I t hank P r o f e s s o r M a r s l a n d f o r h i s s u g g e s t i o n s and comments on t h e 1st e d i t i o n o f t h i s t h e s i s . F i n a l l y , I t h a n k my p a r e n t s f o r t h e i r e n couragement and s u p p o r t . 1 K_ INTRODUCTION Computer c h e s s i s a f r u i t f u l t e s t i n g g r o u n d f o r t h e i d e a s d e v e l o p e d i n t h e s t u d y o f A r t i f i c i a l I n t e l l i g e n c e ( A l ) . F o r example, t r e e s e a r c h i n g t e c h n i q u e s have b e n e f i t e d from e x t e n s i v e use i n c h e s s - p l a y i n g p r o g r a m s . I n d e e d , t h e c l a i m t h a t t h e s t a t e of t h e a r t i n t w o - p e r s o n t r e e s e a r c h i n g i s e x e m p l i f i e d by t h e modern c h e s s p r o g r a m i s j u s t i f i e d . Knowledge e n g i n e e r i n g , a n o t h e r n o t i o n o f i m p o r t a n c e t o A l , has a l s o been a p p l i e d t o computer c h e s s . A l t h o u g h s i g n i f i c a n t , t h e r e s u l t s t o d a t e have been s h o r t o f e x p e c t a t i o n s . The g o a l o f c r e a t i n g a m a s t e r s t r e n g t h p r o g r a m , u s i n g t o o l s o t h e r t h a n b r u t e f o r c e c o m p u t a t i o n a l power, has e l u d e d r e s e a r c h e r s . The p r o b l e m a d d r e s s e d by t h i s t h e s i s i s s i m p l y s t a t e d : how t o w r i t e a b e t t e r c h e s s p r o g r a m . How c a n a g i v e n amount o f c o m p u t a t i o n a l power be most e f f e c t i v e l y u t i l i s e d f o r t h e p u r p o s e s o f c h e s s - p l a y i n g ? T h i s i s t h e c e n t r a l q u e s t i o n e v e r y c h e s s - p r o g r a m w r i t e r g r a p p l e s w i t h . I n t h e f o l l o w i n g c h a p t e r s , t h e p l a n f o r w r i t i n g a b e t t e r c h e s s p r o g r a m b a s e d on t h i n k i n g o f c h e s s i n t e r m s o f t a c t i c s and s t r a t e g y i s p r e s e n t e d . C h a p t e r 4 d e s c r i b e s TECH3, a p r o g r a m i n t e n d e d t o s o l v e c h e s s t a c t i c s p r o b l e m s u s i n g t h e t e c h n i q u e s o f b r u t e f o r c e t r e e s e a r c h i n g . In C h a p t e r 5, t h e p e r f o r m a n c e o f TECH3 i s e v a l u a t e d on t h e 300 p r o b l e m s i n R e i n f e l d (1958) and compared w i t h o t h e r b r u t e f o r c e and knowledge b a s e d t a c t i c s p r o g r a m s , i n p a r t i c u l a r BELLE and PARADISE. The t e c h n o l o g y c u r v e , d e f i n e d a s t h e r e l a t i o n between c h e s s s t r e n g t h and machine power f o r a T E C H 3 - l i k e program, i s d e v e l o p e d i n C h a p t e r 6 a s a t o o l f o r m e a s u r i n g t h e e f f e c t i v e n e s s o f knowledge 2 e n c o d i n g . The f i n a l c h a p t e r summarises t h e major p o i n t s a l o n g w i t h p r o v i d i n g d i r e c t i o n s f o r f u r t h e r work. The B i b l i o g r a p h y and R e f e r e n c e s s e c t i o n c a n be u s e d f o r f u r t h e r o r i e n t a t i o n . R e a d e r s u n f a m i l i a r w i t h c h e s s a r e d i r e c t e d t o " L a s k e r ' s Manual of C h e s s " ( L a s k e r 1947). You a r e warned t h a t L a s k e r d e f i n e s c h e s s as an e x e r c i s e i n i n d e p e n d e n t t h i n k i n g . The g r o u n d work f o r computer c h e s s was s e t by Shannon ( 1 9 5 0 ) . The h i s t o r y of t h e f i e l d s i n c e t h e n c a n be o b t a i n e d from Newborn ( 1975, 1979). A t h e o r e t i c a l t r e a t m e n t o f t h e a-/3 a l g o r i t h m c a n be o b t a i n e d from P e a r l ( 1 9 8 0 ) . 3 2^ PRELIMINARY DISCUSSION The r e l e v a n t h i s t o r y o f computer c h e s s b e g i n s w i t h t h e c o n t r i b u t i o n of Shannon i n 1950. T h i s i s n o t t o say t h a t e a r l i e r d e v e l o p m e n t s were not i m p o r t a n t . In p a r t i c u l a r Z e r m e l o (1912) showed t h a t c h e s s , and as a c o n s e q u e n c e o t h e r s i m i l a r games, have a s i m p l e s t r u c t u r e . H i s r e s u l t s a r e c e n t r a l t o Game T h e o r y , a l t h o u g h much more work was r e q u i r e d b e f o r e t h i s became a p p a r e n t (Von Neumann and M o r g e n s t e r n , 1944). Shannon's c o n t r i b u t i o n l i e s i n b r i d g i n g t h e o r y and p r a c t i c e . Game T h e o r y c l a s s i f i e s c h e s s as a f i n i t e , two-person,, z e r o -sum game of p e r f e c t i n f o r m a t i o n and no c h a n c e . The t h e o r y i s t h a t c h e s s i s s o l v e d by t h e minimax a l g o r i t h m . The d i f f i c u l t y i s t h a t t h e c o m p u t a t i o n s t a k e a l o n g t i m e . Shannon's s o l u t i o n was t o t e r m i n a t e t h e a l g o r i t h m p r e m a t u r e l y by a p p l y i n g an e v a l u a t i o n f u n c t i o n w h i c h g u e s s e d a t t h e r e s u l t o f t h e t r u n c a t e d c o m p u t a t i o n . Some d i s c u s s i o n o f t e r m i n o l o g y may be h e l p f u l a t t h i s p o i n t . A c o n c e p t c a l l e d t h e game t r e e i s a u s e f u l way of u n d e r s t a n d i n g t h e s t r u c t u r e o f games l i k e c h e s s . E a c h b o a r d p o s i t i o n i s r e p r e s e n t e d by a node. D i f f e r e n t b o a r d p o s i t i o n s a r i s e f r o m t h e moves made by t h e p l a y e r s i n t h e c o u r s e of a game. Thus t h e b o a r d p o s i t i o n s a r e l o g i c a l l y c o n n e c t e d by moves w h i c h a r e r e p r e s e n t e d by d i r e c t e d a r c s c o n n e c t i n g t h e n o d e s . The e s s e n c e of t h e game i s c o n t a i n e d i n t h e game t r e e . C o n s i d e r some o f t h e p r o p e r t i e s o f t h e game t r e e . F i r s t n o t i c e t h a t many nodes a r e n o t c o n n e c t e d t o t h e b u l k o f t h e t r e e , w h i c h a r i s e s from t h e node r e p r e s e n t i n g t h e s t a r t i n g b o a r d p o s i t i o n . They f o r m i s l a n d s w h i c h a r e i n a c c e s s a b l e t o t h e 4 p l a y e r s . From t h i s p o i n t on we w i l l c o n s i d e r o n l y t h e main i s l a n d c o n t a i n i n g t h e s t a r t i n g node. S e c o n d n o t i c e t h a t some nodes have no a r c s l e a v i n g f r o m tham. T h e s e a r e c a l l e d l e a f n o d e s , and t h e y r e p r e s e n t mate p o s i t i o n s . T h e r e a r e t h r e e t y p e s o f l e a f nodes c o r r e s p o n d i n g t o t h e t h r e e p o s s i b l e outcomes of c h e s s , namely, w h i t e i s c h e c k m a t e d and b l a c k w i n s , b l a c k i s c h e c k m a t e d and w h i t e w i n s , o r w h i t e o r b l a c k a r e s t a l e m a t e d and t h e game i s a draw. The t h r e e outcomes a r e r e f e r r e d t o as t h e game t h e o r e t i c v a l u e s . T h i r d n o t i c e t h a t t h e r e a r e c y c l e s i n t h e game t r e e , whereby i t i s p o s s i b l e t o r e p e a t e d l y r e t u r n t o t h e same node. In f a c t some nodes f o r m g r o u p s from w h i c h l e a f nodes a r e i n a c c e s s a b l e . F i n a l l y n o t i c e t h a t i n g e n e r a l t h e r e a r e many p a t h s from one node t o a n o t h e r , e s p e c i a l l y i f t h e s h o r t e s t p a t h i s l o n g . A l l nodes c a n be l a b e l e d w i t h a u n i q u e game t h e o r e t i c v a l u e . I f f r o m a node w h i t e c a n , no m a t t e r how b l a c k p l a y s , a r r i v e a t a l e a f node where b l a c k i s c h e c k m a t e d , t h e n t h e v a l u e o f t h a t node i s , o f c o u r s e , t h a t w h i t e w i n s . C o n v e r s e l y , i f f r o m a node b l a c k c a n , no m a t t e r how w h i t e p l a y s , a r r i v e a t a l e a f node where w h i t e i s c h e c k m a t e d , t h e n t h e game t h e o r e t i c v a l u e o f t h a t node i s t h a t b l a c k w i n s . I f n e i t h e r w h i t e n o r b l a c k c a n f o r c e a win t h e n t h e node i s l a b e l e d a s a draw. A s y s t e m a t i c p r o c e d u r e f o r d e t e r m i n i n g t h e game t h e o r e t i c v a l u e o f a node i s t h e minimax a l g o r i t h m w h i c h i n negamax f o r m c a n be d e s c r i b e d a s f o l l o w s : 5 M i n i m a x ( node ) { i f LEAF( node ) t h e n r e t u r n ( GAMETHEORETICVALUE( node ) ) i f CYCLE( node ) t h e n r e t u r n ( 0 ) a := -°° l o o p : { node' := NEXTSUCCESSOR( node ) i f n o d e ' = n i l t h e n r e t u r n ( a ) a' := -Minimax( node' ) i f a'>a t h e n a := a' g o t o l o o p The i n p u t i s a c h e s s p o s i t i o n ( n o d e ) . The t o p l e v e l i n p u t i s r e f e r r e d t o - a s t h e r o o t p o s i t i o n or t h e r o o t node. The o u t p u t , a, i s t h e game t h e o r e t i c v a l u e of t h e p o s i t i o n . In t h e negamax f o r m a l i s m , i f w h i t e i s t o move and w h i t e w i n s o r b l a c k i s t o move and b l a c k w i n s t h e n a=+63 ( s a y ) , w h i l e i f w h i t e i s t o move but b l a c k wins o r b l a c k i s t o move but w h i t e wins t h e n a=-63. I f t h e game t h e o r e t i c v a l u e o f t h e p o s i t i o n i s a draw t h e n a=0. The negamax f o r m a l i s m removes t h e i m p o r t a n c e of s i d e - t o -move, e x c e p t a t t h e t o p l e v e l . The LEAF p r e d i c a t e i s t r u e i f i t s i n p u t i s a l e a f node. The CYCLE p r e d i c a t e i s t r u e i f i t s i n p u t has o c c u r r e d b e f o r e on t h i s v a r i a t i o n . (A v a r i a t i o n i s a p a t h from t h e r o o t node t o w a r d s a l e a f node.) The GAMETHEORETICVALUE f u n c t i o n r e t u r n s 0 (=draw) i f i t s i n p u t l e a f node i s a s t a l e m a t e , and -63 i f i t s i n p u t l e a f node i s a c h e c k m a t e . The NEXTSUCCESSOR g e n e r a t o r embodies t h e r u l e s of c h e s s . I t s u c c e s s i v e l y g e n e r a t e s s u c c e s s o r nodes t o i t s i n p u t node. The s p e c i a l v a l u e " n i l " i s r e t u r n e d a f t e r a l l s u c c e s s o r s have been g e n e r a t e d . In p r a c t i c e t h i s i s n o t e f f e c t i v e s i n c e most p o s i t i o n s r e q u i r e an u n r e a s o n a b l e amount o f c o m p u t a t i o n . Shannon's 6 s o l u t i o n i n v o l v e d m o d i f y i n g t h e LEAF p r e d i c a t e so t h a t many more nodes a r e "end p o i n t s " . T h e s e "end p o i n t s " o r p s e u d o - l e a f nodes a r e c a l l e d t e r m i n a l nodes and t h e m o d i f i e d LEAF p r e d i c a t e I w i l l r e f e r t o as t h e TERMINAL p r e d i c a t e . The GAMETHEORETICVALUE f u n c t i o n must a l s o be m o d i f i e d t o r e t u r n a p p r o x i m a t e v a l u e s f o r n o n - l e a f n o d e s . I w i l l r e f e r t o t h e new f u n c t i o n a s t h e EVALUATION f u n c t i o n . A n o t h e r i m p o r t a n t c o n t r i b u t i o n made by Shannon was r e c o g n i z i n g t h e p r o b l e m o f q u i e s c e n c e . Many p o s i t i o n s c a n n o t be e v a l u a t e d ( l o c a l l y ) by any f u n c t i o n of l e s s c o m p l e x i t y t h a n "minimax". C o n s e q u e n t l y i t i s s i m p l e s t t o c h o o s e TERMINAL s u c h t h a t t h e s e a r c h c o n t i n u e s t h r o u g h t h e s e n odes, i f p o s s i b l e . Shannon's i d e a s f o r m t h e b a s e s o f e v e r y s u c c e s s f u l c h e s s p r o g ram t o t h i s d a t e . P o s s i b i l i t i e s f o r t h e c h o i c e o f TERMINAL and EVALUATION a r e f a r f r o m b e i n g e x h a u s t e d , nor do we have any good i d e a o f what t h e l i m i t s o f t h e i r p o t e n t i a l m i g h t be. Computer c h e s s d i d not end w i t h Shannon, f a r f r o m i t . P r o g r e s s was however, s l o w . I t t o o k two d e c a d e s , t i l l t h e 1970's, b e f o r e t h e s t a t e of t h e a r t had a d v a n c e d t o t h e p o i n t where t o u r n a m e n t s between c h e s s - p l a y i n g p rograms became w o r t h w h i l e . E n t h u s i a s t s r u s h e d t o code t h e most complex TERMINAL-EVALUATION c o m b i n a t i o n s t h e y c o u l d . What can h a r d l y be c o n s i d e r e d s u r p r i s i n g , t h e e a r l y e x p e r i e n c e was t h a t a l l t h i n g s b e i n g e q u a l , s i m p l e r was b e t t e r . P rograms n o t b a s e d on t h e minimax p a r a d i g m d i d w o r s t o f a l l . T h r e e p r o g r a m s o f n o t e emerged d u r i n g t h i s p e r i o d . The f i r s t was CHESS 4.5, a c r e a t i o n o f S l a t e and A t k i n (1977) a t N o r t h w e s t e r n U n i v e r s i t y . T h i s p r o g r a m (and i t s a n c e s t o r s p r 7 d e s e n d a n t s ) won v i r t u a l l y e v e r y computer c h e s s c h a m p i o n s h i p i n t h e 7 0 ' s . T h r o u g h t h e i r p rogram, S l a t e and A t k i n r e f i n e d and d e v e l o p e d t h e t e c h n i q u e s o f e f f i c i e n t t r e e s e a r c h i n g ( s e e C h a p t e r 4 ) . They made t h e minimax a l g o r i t h m go. The s e c o n d p r o gram t o emerge d u r i n g t h i s p e r i o d was BELLE, a c r e a t i o n of Condon and Thompson (1982) a t B e l l L a b s . T a k i n g t h e b e s t s e a r c h i n g t e c h n i q u e s a v a i l a b l e , t h e y c o n s t r u c t e d s p e c i a l - p u r p o s e h a r d w a r e o f a t l e a s t an o r d e r o f m a g n i t u d e more c h e s s - s p e c i f i c c o m p u t a t i o n a l power t h a n any p r e v i o u s m a c h i n e . B o t h CHESS 4.5 and BELLE a r e c o m p l e t e l y i n t h e Shannon mo l d . E x c e p t f o r t e c h n i q u e (a-/3, t r a n s p o s i t i o n t a b l e s , e t c ) e v e r y t h i n g i s a c c o r d i n g t o Shannon. In my v i e w , t h e most i m p o r t a n t p r o g r a m t o emerge (and submerge') d u r i n g t h i s p e r i o d was TECH, a c r e a t i o n o f G i l l o g l y a t C a r n e g i e - M e l l o n U n i v e r s i t y . TECH has s i g n i f i c a n c e b e c a u s e i t h i n t s a t an e x t e n s i o n t o t h e Shannon p a r a d i g m . The e x t e n s i o n ( G i l l o g l y ' s p o s i t i o n a l p r e s o r t ) i s t h a t a few c o m p u t a t i o n s done a t o r n e a r t h e r o o t node may have a s much s i g n i f i c a n c e as t h e m u l t i t u d i n o u s c o m p u t a t i o n s done a t t h e t e r m i n a l n o d e s . The n e x t c h a p t e r , a f t e r making c l e a r t h e c e n t r a l t h e s i s o f t h i s p a p e r ( c o m p u t a t i o n s f o r t a c t i c s v s c o m p u t a t i o n s f o r s t r a t e g y ) , w i l l h o p e f u l l y e n l i g h t e n t h e r e a d e r a s t o t h e s i g n i f i c a n c e o f t e r m i n a l node v s r o o t node c o m p u t a t i o n s . 8 TACTICS AND STRATEGY 3.1 The B a s i c I d e a The b a s i c i d e a i s t o t h i n k o f c h e s s i n t e r m s of t a c t i c s and s t r a t e g y . T h i s p r o v i d e s two c o m p l e m e n t a r y , y e t c o m p l e t e , p o i n t s o f v i e w . From t h e p e r s p e c t i v e of t a c t i c s , t h e c o n s t r u c t i o n o f any p r o g r a m w i l l f o c u s on t h e l o c a l , d i r e c t c o n s e q u e n c e s o f t h e r u l e s o f c h e s s , w h i l e t h e c o m p l e m e n t a r y p e r s p e c t i v e o f s t r a t e g y w i l l n e c e s s i t a t e a g l o b a l f o c u s . The two a r e a s a r e a p p r o a c h e d w i t h d i f f e r e n t d e v i c e s . A c l e a r s e p a r a t i o n o f t h e s e d i f f e r e n t aims may p r o v i d e t h e b a s i s f o r t h e c o n s t r u c t i o n o f s u p e r i o r p r o g r a m s . O t h e r r e s e a r c h e r s i n c l u d i n g M o u s s o u r i s , H o l l o w a y , and G r e e n b l a t t (1979) have e x p r e s s e d s i m i l a r o p i n i o n s . C h e s s i s o f t e n t h o u g h t o f i n t e r m s of t a c t i c s and s t r a t e g y by human c h e s s p l a y e r s . F o r them t a c t i c s i s synonymous w i t h c o m b i n a t i o n s o r c a l c u l a t i n g v a r i a t i o n s w h i l e s t r a t e g y . i s more o f t e n r e f e r r e d t o as p o s i t i o n p l a y o r p l a n n i n g . The f o l l o w i n g t h r e e e x a m ples a r e p r o v i d e d t o c l a r i f y t h i s . (1) An example o f t a c t i c s i s i l l u s t r a t e d by F i g u r e 1 where b l a c k f o r c e s mate w i t h t h e c o m b i n a t i o n 1 1... Bh2+ 2. Kh1 Bg3+ 3. Kg1 Rh1+ 4. Kxh1 Qh4+ 1 C h e s s moves a r e g i v e n by s p e c i f y i n g t h e p i e c e t y p e w h i c h i s t o move and t h e s q u a r e t h e p i e c e i s t o move t o . The p i e c e t y p e s a r e P=pawn, K = k i n g , N = k n i g h t , B = b i s h o p , R=rook, and Q=queen. The s q u a r e s a r e l a b e l l e d by t h e i r column and row on t h e b o a r d . The 8 c o lumns ( f i l e s ) a r e c a l l e d , l e f t t o r i g h t ( f r o m t h e w h i t e s i d e of t h e b o a r d ) , a, b, c, d, e, f , g, and h. The 8 rows ( r a n k s ) a r e c a l l e d , b o t t o m t o t o p ( f r o m t h e w h i t e s i d e ) , 1, 2, 3, 4, 5, 6, 7, and 8. Thus t h e b o t t o m r i g h t c o r n e r s q u a r e i s h i . An "x" i n d i c a t e s a c a p t u r e . A "+" i n d i c a t e s t h a t t h e move g i v e s c h e c k , w h i l e "++" i n d i c a t e s c h e c k m a t e . In t h e f i g u r e s b l a c k p i e c e s , a r e p r e f i x e d w i t h 9 5. Kg 1 Qh2++. (2) An example o f s t r a t e g y c a n be g l e a n e d f r o m t h e endgame k i n g and rook v e r s u s k i n g . The s i d e w i t h k i n g and rook p l a n s t o manoeuvre t h e l o n e k i n g t o an edge o f t h e b o a r d . (2) The p o s i t i o n i n F i g u r e 2 was u s e d by B e r l i n e r (1973) t o show t h e need f o r s t r a t e g y i n computer c h e s s . A human c h e s s p l a y e r w o u l d r e a l i s e w i t h l i t t l e t r o u b l e t h a t t h e o n l y t h i n g t o do h e r e i s Kd2-c2-b2-a3-b4-c5 e t c ( o r Kd2-c1-b2 e t c ) . T h i s i s s t r a t e g i c a l l y o b v i o u s . The same c o n c l u s i o n , w i t h c o n s i d e r a b l e e f f o r t , c a n be d e r i v e d t a c t i c a l l y . In f a c t i t t a k e s TECH3 l e s s t h a n two s e c o n d s t o show t h a t w h i t e f o r c e s t h e win o f a t l e a s t a pawn w i t h Kd2-c l . T a c t i c s i s a d i r e c t c o n s e q u e n c e o f t h e r u l e s o f c h e s s . S t r a t e g y , on t h e o t h e r hand, i s what you do when n o t h i n g c a n be c a l c u l a t e d . I n p r a c t i c e t h i s d i s t i n c t i o n i s b l u r r e d . M a t e r i a l i s a s t r a t e g i c c o n c e p t w h i c h , b e c a u s e o f i t s u t i l i t y , has been t r a n s f e r r e d i n t o t h e domain o f t a c t i c s . C h e s s t a c t i c s p r o b l e m s a r e p r o b l e m s where t h e game t h e o r e t i c v a l u e s - win, l o s e , and draw - and t h e m a t e r i a l b a l a n c e p l a y t h e d e c i s i v e r o l e . A l l o t h e r s t r a t e g i c c o n s i d e r a t i o n s a r e i g n o r e d . S t r a t e g y means f o r m i n g a p l a n b a s e d on an a s s e s s m e n t o f t h e p o s i t i o n . The p l a n does n o t a r i s e f r o m t h e c r e a t i v e f a n c y o f a p l a y e r , b u t r a t h e r t h e p l a n i s b a s e d on t h e p o s i t i o n . The p r o b l e m o f s t r a t e g y i s t o f o r m u l a t e a mapping between p o s i t i o n s and p l a n s . T h i s may n o t be d i f f i c u l t i f t h e number o f p l a n s i s n o t l a r g e . S t r a t e g y i s an e a s i e r way o f d o i n g d e e p t a c t i c s . S t r a t e g y i s what c o m p l i c a t e d t a c t i c s becomes. In p r i n c i p l e e i t h e r one i s s u f f i c i e n t t o s o l v e c h e s s , g i v e n enough t i m e o r s p a c e . 10 The n a t u r e o f c h e s s i s s u c h t h a t t o win, a b a c k g r o u n d of n e a r p e r f e c t s h a l l o w t a c t i c s i s r e q u i r e d . The p r i m e r e a s o n f o r t h e l a c k o f s u c c e s s o f many c h e s s programming e f f o r t s has beer, due t o a d e f i c i e n c y on t h i s p o i n t , o r p e r h a p s i t i s more a c c u r a t e t o say t h a t t h e s u c c e s s of c h e s s p r o g r a m s ( l i k e CHESS 4.5) has been due t o t h e f a c t t h a t t h e y p l a y t a c t i c a l l y s o und c h e s s . 3.2 How t o S o l v e T a c t i c s I p r o p o s e t h a t t h e most e f f e c t i v e s o l u t i o n t o t a c t i c s i s p r o v i d e d by t h e b r u t e f o r c e a p p r o a c h . T h i s a p p r o a c h i s i l l u s t r a t e d and d e v e l o p e d by t h e p r o g r a m s TECH ( G i l l o g l y 1972, 1978), CHESS 4.5 ( S l a t e and A t k i n 1977), and BELLE (Condon and Thompson 1982, 1983). The c e n t r a l c o r e o f t h e b r u t e f o r c e a p p r o a c h i s a d i r e c t , head-on a t t a c k t o t h e p r o b l e m . T h i s c o n s i s t s o f t h e w e l l d e v e l o p e d t e c h n i q u e s o f t r e e s e a r c h i n g . T h e s e t e c h n i q u e s a r e f u l l y e x p l a i n e d i n C h a p t e r 4 where TECH3 i s d e s c r i b e d . A n o t h e r a p p r o a c h t o s o l v i n g t a c t i c s has been t r i e d w i t h some s u c c e s s . T h i s a p p r o a c h i s e x e m p l i f i e d by CAPS II ( B e r l i n e r 1974, 1977), P i t r a t ' s p r o g r a m ( P i t r a t 1977, 1980), and PARADISE ( W i l k i n s 1980, 1982). They have t h e common f e a t u r e o f u t i l i s i n g knowledge t o g u i d e and c o n t r o l t h e s e a r c h . T h e s e e f f o r t s a r e of g r e a t v a l u e t o t h e u n d e r s t a n d i n g o f t h e p r o b l e m s o f knowledge e n c o d i n g . However, a l t h o u g h i n p r i n c i p l e a knowledge b a s e d p r o g r a m c o u l d be c o n s t r u c t e d t o p e r f o r m w i t h t h e a c c u r a c y of an e x h a u s t i v e b r u t e f o r c e p rogram, s u c h l a b o r i s m i s d i r e c t e d . Knowledge i s p r o p e r l y u s e d by t h a t w h i c h r e q u i r e s i t ( i e 11 s t r a t e g y ) . 3.3 How t o S o l v e S t r a t e g y I p r o p o s e t h a t t h e most e f f e c t i v e s o l u t i o n t o s t r a t e g y i s p r o v i d e d by t h e knowledge a p p r o a c h . A major p a r t o f c u r r e n t e f f o r t s i n AI a r e d i r e c t e d t o w a r d s u n d e r s t a n d i n g (and d e f i n i n g ) t h i s a p p r o a c h . C h e s s programs w i l l c o n t i n u e t o p l a y s t r o n g e r as f a s t e r h a r d w a r e i s i n t r o d u c e d . In t h i s way t h e y w i l l i n e v i t a b l y s u r p a s s t h e b e s t humans ( s e e C h a p t e r 6 ) . To o b t a i n a b e t t e r c h e s s p r o g r a m , i n d e p e n d e n t of h a r d w a r e , t h e use o f human c h e s s knowledge i s e s s e n t i a l . The p r o b l e m o f c o u r s e i s how. One way o f u s i n g knowledge i n c h e s s - p l a y i n g p r o g r a m s i s by a p p l y i n g e v a l u a t i o n f u n c t i o n s t o t h e t e r m i n a l nodes of t h e s e a r c h t r e e . An e v a l u a t i o n f u n c t i o n a c c o m p l i s h e s i t s t a s k of e n c o d i n g knowledge t o s o l v e s t r a t e g y by a s s i g n i n g a s i n g l e n u m e r i c a l measure of g o o d n e s s t o a p o s i t i o n . In a d d i t i o n t o m a t e r i a l , an e v a l u a t i o n f u n c t i o n w i l l have t e r m s d e a l i n g w i t h pawn s t r u c t u r e , k i n g s a f e t y , p i e c e a c t i v i t y and o t h e r c o n c e p t s f r o m human c h e s s knowledge. Most p r o g r a m s , i n c l u d i n g BELLE, use e v a l u a t i o n f u n c t i o n s . S l a t e and A t k i n (1977) have d e s c r i b e d t h e e v a l u a t i o n f u n c t i o n u s e d by CHESS 4.5. The m a j o r drawback w i t h t h i s method o f e n c o d i n g knowledge i s t h a t t h e e v a l u a t i o n f u n c t i o n must r e m a i n c o m p u t a t i o n a l l y s i m p l e i f t h e b r u t e f o r c e component i s t o r e m a i n e f f e c t i v e . The p o s i t i o n a l p r e s o r t method o f TECH p r o v i d e s a way of. u s i n g knowledge and a v o i d i n g t h e t e r m i n a l node c o m p u t a t i o n a l b o t t l e n e c k . T h i s method c a n be v i e w e d i n two d i f f e r e n t ways. (1) An e v a l u a t i o n f u n c t i o n i s a p p l i e d t o t h e s u c c e s s o r s o f t h e r o o t 12 node. T h i s d e f i n e s t h e s t r a t e g i c v a l u e of t h e moves a v a i l a b l e a t t h e r o o t node. I n t h e l i k e l y e v e n t t h a t more t h a n one move i s a v a i l a b l e w i t h l a r g e s t t a c t i c a l v a l u e , t h e s t r a t e g i c v a l u e a c t s a s a t i e b r e a k e r . (2) The p o s i t i o n a l p r e s o r t d e f i n e s a mapping between p o s i t i o n s and p l a n s . The a p p r o p r i a t e p l a n g u i d e s t h e move s e l e c t i o n among t a c t i c a l l y e q u i v a l e n t moves. (A p l a n i s a method o r a r u l e o r a p r e s c r i p t i o n f o r what t o do o r how t o h a n d l e a c e r t a i n t y p e o f p o s i t i o n . ) T h e r e a r e many o t h e r ways o f u s i n g knowledge t o s o l v e s t r a t e g y . T h i s i s an u n e x p l o r e d a r e a f o r r e s e a r c h . 13 8 • • • -rt • - R -K • 7 -P • • • • -P -P • 6 • • -P -B • • • -p 5 • • • -P • • • • 4 • • • • • • P -R 3 • P N Q • • • 2 P • P B • P P • 1 • • • • R R K • a b c d e f g h B l a c k t o move F i g u r e 1 - A C l e a r Example o f T a c t i c s 8 7 6 5 4 3 2 1 •P P •K . -P •P P P • • K -P P W h i t e t o move F i g u r e 2 - Human S t r a t e g y V e r s u s Computer T a c t i c s 1 4 4^ TECH3: A.BRUTE FORCE TACTICS PROGRAM  4.1 O v e r v i e w The a l g o r i t h m d e s c r i b e d h e r e has much i n common w i t h t h e p r o g r a m TECH ( G i l l o g l y 1972, 1978). F o r t h i s r e a s o n t h e a l g o r i t h m has been named TECH3. TECH3 i s a b r u t e f o r c e p r o g r a m . I t s t a s k i s a c c o m p l i s h e d w i t h a l m o s t no c h e s s s p e c i f i c k n owledge. TECH3's I/O r e q u i r e m e n t s a r e as f o l l o w s . The i n p u t ( I ) c o n s i s t s o f a l e g a l c h e s s p o s i t i o n and a CPU t i m e r e s o u r c e c o n s t r a i n t . The o u t p u t (0) c o n s i s t s o f a l e g a l c h e s s move and a s c o r e . N a t u r a l l y , t h e o u t p u t move i s l e g a l (and b e s t ! ? ) i n t h e i n p u t p o s i t i o n . The s c o r e i s j u s t t h e 'minimaxed' v a l u e o f t h e EVALUATION f u n c t i o n a p p l i e d t o t h e t e r m i n a l nodes o f t h e t r e e d e f i n e d by t h e s e a r c h a l g o r i t h m (TECH3) and t h e i n p u t ( I ) . The EVALUATION f u n c t i o n u s e d i s s i m p l e . I f t h e t e r m i n a l node i s game t h e o r e t i c ( i e a l e a f node) t h e n t h e game t h e o r e t i c v a l u e i s r e t u r n e d . O t h e r w i s e t h e m a t e r i a l b a l a n c e i s r e t u r n e d . The game t h e o r e t i c v a l u e s a r e -63, 0, and 63 f o r s i d e - t o - m o v e l o s e s , draws, and w i n s , r e s p e c t i v e l y . The m a t e r i a l b a l a n c e i s g i v e n by t h e sum o f t h e v a l u e s o f a l l t h e p i e c e s on t h e b o a r d . The s i d e - t o - m o v e p i e c e v a l u e s a r e 1, 18, 3, 3, 5, and 9 f o r pawn, k i n g , k n i g h t , b i s h o p , r o o k , and queen, r e s p e c t i v e l y . The s i d e - n o t - t o - m o v e p i e c e v a l u e s a r e t h e n e g a t i v e s o f t h e s i d e - t o -move p i e c e v a l u e s . TECH3 c a n be v i e w e d a s a number of r e f i n e m e n t s o f t h e minimax a l g o r i t h m . The r e f i n e m e n t s a r e t h e a-/J a l g o r i t h m , t h e 15 q u i e s c e n c e s e a r c h , t h e t r a n s p o s i t i o n t a b l e , a-|3 move o r d e r i n g , t h e s e a r c h d e p t h m e t r i c , t h e d e p t h i t e r a t i v e a-/3 t e c h n i q u e , and a s p i r a t i o n s e a r c h i n g c r windo w i n g . The f o l l o w i n g s e c t i o n s w i l l f o c u s on e a c h of t h e s e c o n t r i b u t i o n s i n d e t a i l . 4.2 The a-ft A l g o r i t h m The c e n t r a l i d e a b e h i n d t h e a-/3 a l g o r i t h m i s t h a t o n l y one r e f u t a t i o n p e r p o s i t i o n i s n e c e s s a r y . To u n d e r s t a n d t h i s c o n s i d e r t h e f o l l o w i n g ( s e e F i g u r e 3 ) . L e t A be a p o s i t i o n , Aa and Ab be s u c c e s s o r p o s i t i o n s t o A, and AbA be a s u c c e s s o r p o s i t i o n t o Ab. Suppose t h a t t h e EVALUATION f u n c t i o n a p p l i e d t o Aa y i e l d s -x. T h i s i m p l i e s (minimax) t h a t t h e s c o r e o f A i s >x. ( I n t h e negamax f o r m a l i s m t h e s i g n c h a n g e s w i t h e v e r y l e v e l , t h u s -x a t Aa goes t o x a t A. The s c o r e o f A i s >x b e c a u s e t h e p l a y e r , a l w a y s t r y i n g t o maximize h i s s c o r e , has o t h e r c h o i c e s (Ab) w h i c h may y i e l d a l a r g e r s c o r e . ) Suppose t h a t t h e EVALUATION f u n c t i o n a p p l i e d t o AbA y i e l d s y. T h i s i m p l i e s t h a t t h e s c o r e o f Ab i s £-y (by t h e same r e a s o n i n g a s b e f o r e ) . The w o r s t c a s e c o n d i t i o n f o r t h e p l a y e r a t Ab i s t h a t t h e s c o r e of Ab e q u a l s -y i n w h i c h c a s e t h e s c o r e o f A i s >y. F i n a l l y , s u p p o s e t h a t x>y. C l e a r l y , e x a m i n i n g o t h e r s u c c e s s o r s t o Ab w i l l n o t change t h e s c o r e o f A. (Why? B e c a u s e s u c c e s s o r s t o Ab c a n o n l y i m prove Ab's s c o r e w h i c h a t A makes y s m a l l e r s t i l l t h a n x.) AbA has r e f u t e d Ab ( r e l a t i v e t o A a ) . The s u b t r e e w i t h r o o t Ab c a n be c u t o f f . As a m o d i f i c a t i o n t o t h e minimax a l g o r i t h m t h e a-ft a l g o r i t h m c a n be d e s c r i b e d a s f o l l o w s : 16 a/3( a, /3, node ) { i f TERMINAL( node ) t h e n r e t u r n ( E VALUATION node ) ) l o o p : {• node' :-~ NEXTSUCCES30R( node ) i f n o d e ' = n i l t h e n r e t u r n ( a ) a' := -a/3( -/3, - a , node' ) i f a'>a t h e n a := a' i f a>/3 t h e n r e t u r n ( a ) g o t o l o o p } } The two p a r a m e t e r s a and /3 a r e u s e d t o keep t r a c k of t h e b e s t s c o r e f o r t h e c u r r e n t node and t h e s c o r e n e c e s s a r y t o r e f u t e t h e c u r r e n t node, r e s p e c t i v e l y . I f a becomes >/3 t h e n t h e c u r r e n t node has been r e f u t e d and a i s r e t u r n e d t o t h e n e x t h i g h e r l e v e l . T h i s i s r e f e r r e d t o as a / 3 - c u t o f f . I f t h e s c o r e o f t h e c u r r e n t node i s n o t g r e a t e r t h a n t h e o r i g i n a l a t h e n a i s r e t u r n e d anyway. T h i s i s r e f e r r e d t o as an a - c u t o f f even t h o u g h none of t h e t r e e i s c u t o f f a t t h i s l e v e l . An a - c u t o f f g u a r a n t e e s a /3- c u t o f f a t t h e n e x t h i g h e r l e v e l . A t an a - c u t o f f t h e s c o r e r e t u r n e d i s <a. A t a /3- c u t o f f t h e s c o r e r e t u r n e d i s >/3. I f n e i t h e r c u t o f f o c c u r s t h e n a i s l e s s t h a n t h e s c o r e r e t u r n e d w h i c h i s l e s s t h a n /3. The p r e d i c a t e CYCLE has been removed s i n c e i t s p u r p o s e w i l l be f u l f i l l e d by t h e t r a n s p o s i t i o n t a b l e . The f u n c t i o n s M inimax (node) and a/3 (-»,+», node) have i d e n t i c a l I/O b e h a v i o r (modulo CYCLE, TERMINAL, and EVALUATION). 1 7 4 . 3 The, Q u i e s c e n c e S e a r c h From a p r a c t i c a l p o i n t o f v i e w t h e most i m p o r t a n t t h i n g t o e v a l u a t e a c c u r a t e l y i s t h e m a t e r i a l b a l a n c e . The q u i e s c e n c e s e a r c h ( S l a t e and A t k i n 1977) i s an e f f i c i e n t way of d o i n g t h i s . E s s e n t i a l l y an a-/3 s e a r c h i s done on t h e t r e e , e x t e n d i n g f r o m t e r m i n a l n o d e s , o f a l l moves w h i c h i m m e d i a t e l y change t h e m a t e r i a l b a l a n c e . The q u i e s c e n c e s e a r c h c a n be d e s c r i b e d a s f o l l o w s : Q s e a r c h ( a, 0 , node ) { a' : = EVALUATION( node ) l o o p : { i f a'>a t h e n a := a' i f a>/3 t h e n r e t u r n ( a ) node' := NEXTCAPTURE( node ) i f n o d e ' = n i l t h e n r e t u r n ( a ) a' := - Q s e a r c h ( -/?, - a , node' ) g o t o l o o p } } The NEXTCAPTURE g e n e r a t o r o n l y g e n e r a t e s s u c c e s s o r s w h i c h have a d i f f e r e n t m a t e r i a l b a l a n c e than, t h e i r p a r e n t node. O t h e r w i s e i t i s i d e n t i c a l t o t h e NEXTSUCCESSOR g e n e r a t o r . The o r d e r o f t h e s t e p s has been c h a n g e d t o r e f l e c t t h e p o s s i b i l i t y o f e a r l y t e r m i n a t i o n ( v i a t h e n u l l move). I f a t any p o i n t t h e s i d e - t o - m o v e i s s a t i s f i e d ( a > 0 ) w i t h t h e immediate EVALUATION t h e n i t i s assumed t h a t a s u c c e s s o r ( t h e n u l l move) e x i s t s w h i c h a t w o r s t p r e s e r v e s t h i s EVALUATION. O t h e r w i s e t h e s e a r c h c o n t i n u e s u n t i l a node has no NEXTCAPTURE s u c c e s s o r s . The q u i e s c e n c e s e a r c h i s i n t e g r a t e d w i t h t h e a - 0 a l g o r i t h m by r e p l a c i n g EVALUATION (node) w i t h Q s e a r c h ( a , / 3 , n o d e ) . 18 4.4 The T r a n s p o s i t i o n T a b l e I t i s p o s s i b l e t o a r r i v e a t t h e same c h e s s p o s i t i o n f r o m many d i f f e r e n t move s e q u e n c e s . F o r example t h e move s e q u e n c e s 1. Ke2 Ke7 2. Ke3, 1. K f 2 Ke7 2. Ke3 and 1. Kd2 Ke7 2. Ke3 a l l l e a d t o t h e same p o s i t i o n . I t i s w o r t h w h i l e s u p p l e m e n t i n g t h e a-j3 a l g o r i t h m w i t h a mechanism w h i c h e l i m i n a t e s r e - s e a r c h i n g p o s i t i o n s a r r i v e d a t t h r o u g h a t r a n s p o s i t i o n o f moves ( S l a t e and A t k i n 1977, Condon and Thompson 1982). The b a s i c p r o b l e m h e r e c o m p u t a t i o n a l l y i s t h e d e t e c t i o n o f d u p l i c a t e p o s i t i o n s . T h i s i s s o l v e d e l e g a n t l y by t h e f o l l o w i n g scheme. A s s i g n 12 ( 6 4 - b i t ) random numbers t o e a c h o f t h e 64 s q u a r e s on t h e c h e s s b o a r d . The 12 random numbers a r e a s s o c i a t e d , one t o one, w i t h t h e 12 t y p e s of p i e c e s ( w h i t e and b l a c k pawn, k i n g , k n i g h t , b i s h o p , r o o k and q u e e n ) . The h a s h code o f a p o s i t i o n i s t h e e x c l u s i v e o r (XOR) o f t h e random numbers a s s o c i a t e d w i t h t h e p i e c e s on t h e b o a r d . What makes t h i s c o m p u t a t i o n a l l y e f f i c i e n t i s t h a t once we have t h e h a s h code f o r a p o s i t i o n , t h e h a s h c o d e f o r s u c c e s s o r p o s i t i o n s can be e a s i l y d e t e r m i n e d by XORing j u s t t h e p i e c e s w h i c h c h a n g e . F o r example, a f t e r t h e move Bc1-d2 t h e h a s h code f o r t h e new p o s i t i o n i s j u s t t h e h a s h c o d e f o r t h e o l d p o s i t i o n XORed w i t h t h e random number f o r Be 1 XORed w i t h t h e random number f o r Bd2. To d i s t i n g u i s h between p o s i t i o n s w h i c h a r e d i f f e r e n t i n s i d e - t o - m o v e t h e h a s h code i s f u r t h e r XORed e a c h t i m e t h e move ph a s e c h a n g e s ( i e e v e r y move) w i t h t h e move p h a s e random number. P o s i t i o n s w h i c h a r e i d e n t i c a l e x c e p t f o r c a s t l i n g s t a t u s o r en p a s s a n t s t a t u s a r e n o t d i s t i n g u i s h e d . The a s s u m p t i o n i s made t h a t i d e n t i c a l h a s h c o d e s c o r r e s p o n d t o i d e n t i c a l p o s i t i o n s . 19 P a r t o f t h e h a s h c o d e (16 b i t s , maximum of 32 b i t s ) i s u s e d a s an a r r a y i n d e x i n t o t h e t r a n s p o s i t i o n t a b l e w h i l e t h e r e s t (32 b i t s ) i s u s e d as a h a s h code c h e c k . The t a b l e c o n s i s t s of ( 6 4 - b i t ) e n t r i e s d i v i d e d i n t o two p a r t s . The f i r s t p a r t (32 b i t s ) o f e a c h t a b l e e n t r y i s t h e h a s h c o d e c h e c k w h i l e t h e s e c o n d p a r t (32 b i t s ) s t o r e s i n f o r m a t i o n r e l e v a n t t o t h e a-/3 a l g o r i t h m . The i n f o r m a t i o n s t o r e d i n c l u d e s (1) (5 b i t s ) t h e d e p t h t o w h i c h t h i s p o s i t i o n has been s e a r c h e d , (2) (6 b i t s ) t h e b e s t move t o be p l a y e d f r o m t h i s p o s i t i o n , (3) (2 b i t s ) a f l a g i n d i c a t i n g t h e s t a t u s o f t h i s node ( a - c u t o f f , / 3 - c u t o f f o r no c u t o f f ) , a nd (4) (16 b i t s ) t h e s c o r e f o r t h i s p o s i t i o n ( s e e F i g u r e k). E a c h t i m e a node i s e n t e r e d i n t h e s e a r c h p r o c e s s a c h e c k i s made t o see i f i t i s i n t h e t r a n s p o s i t i o n t a b l e . I f i t i s , and t h e s e a r c h d e p t h r e q u i r e d i s l e s s t h a n o r e q u a l t o t h e s e a r c h d e p t h s t o r e d , t h e n one of t h e f o l l o w i n g t h r e e c o n d i t i o n s h o l d s . (1) The node i s an a - c u t o f f i n w h i c h c a s e t h e c u r r e n t j3 p a r a m e t e r i s s e t t o t h e minimum o f t h e s t o r e d s c o r e and t h e c u r r e n t 0 p a r a m e t e r . (2) The node i s a |3- c u t o f f i n w h i c h c a s e t h e c u r r e n t a p a r a m e t e r i s s e t t o t h e maximum o f t h e s t o r e d s c o r e and t h e c u r r e n t a p a r a m e t e r . I n e i t h e r c a s e i f a>/3 t h e n f u r t h e r p r o c e s s i n g i s n o t n e c e s s a r y and t h e s c o r e r e t u r n e d i s t h e s t o r e d s c o r e . O t h e r w i s e p r o c e s s i n g c o n t i n u e s n o r m a l l y . (3) The node i s not a c u t o f f i n w h i c h c a s e t h e s c o r e r e t u r n e d i s t h e s t o r e d s c o r e . E a c h t i m e a node i s e x i t e d by t h e s e a r c h p r o c e s s a c h e c k i s made t o see i f i t s h o u l d be w r i t t e n i n t h e t a b l e . T h i s i s done i f t h e d e p t h t h i s node has been s e a r c h e d t o i s g r e a t e r t h a n o r 20 e q u a l t o t h e d e p t h s t o r e d i n t h e t a b l e a t t h e w r i t e l o c a t i o n . Thus t h e t a b l e has a p r i o r i t y s t r u c t u r e f a v o u r i n g p o s i t i o n s c l o s e t o t h e r o o t o v e r p o s i t i o n s d eep i n t h e t r e e . N o r m a l l y t h e t a b l e i s ' z e r o e d ' b e f o r e e a c h t o p l e v e l a-/3 i n v o c a t i o n . N o t i c e t h a t t h e t a b l e c a n be u s e d t o d e t e c t draws by r e p e t i t i o n . T h i s i s done t r i v i a l l y by w r i t i n g draw s c o r e s (=0) t o t h e t a b l e f o r e a c h node on t h e way down t h e t r e e . ( T h i s i s o n l y done i f t h e s e a r c h d e p t h i s g r e a t e r t h a n o r e q u a l t o t h e d e p t h s t o r e d i n t h e t a b l e . ) The node, i f e n c o u n t e r e d l o w e r i n t h e t r e e , w i l l n e c e s s a r i l y c a u s e t h e s e a r c h t o b a c k u p . The draw s c o r e i s u n f a i l i n g l y o v e r w r i t t e n w i t h t h e c o r r e c t s c o r e on b a c k i n g up t h r o u g h t h e o r i g i n a l node. The t a b l e a l s o m a i n t a i n s t h e p r i n c i p a l v a r i a t i o n by k e e p i n g t r a c k o f b e s t moves. From t h e p o i n t o f v i e w o f Game T h e o r y t h e t r a n s p o s i t i o n t a b l e e n c o d e s t h e b e s t s t r a t e g y f o r b o t h s i d e s . The p r o b a b i l i t y o f o b t a i n i n g f a l s e d a t a f r o m t h e t a b l e on a s i n g l e p r o b e i s a b o u t one c h a n c e i n 2 t o t h e N, where N i s t h e number of b i t s i n t h e h a s h code c h e c k . T h i s e r r o r r a t e , f r o m p r a c t i c a l e x p e r i e n c e , i s a c c e p t a b l e even f o r s m a l l N (N=14). 4.5 The R e m a i n i n g R e f i n e m e n t s (1) a-/3 move o r d e r i n g : The e f f i c i e n c y o f t h e a-/3 a l g o r i t h m i s d e p e n d e n t on t h e o r d e r i n w h i c h s u c c e s s o r p o s i t i o n s ( o r moves) a r e s e a r c h e d . In t h e w o r s t c a s e a-/3 e x a m i n e s e x a c t l y t h e same nodes as minimax and t h u s i s o f no b e n e f i t a t a l l . The b e s t c a s e , however, a l l o w s a-/3 t o examine o n l y on t h e o r d e r o f t h e s q u a r e r o o t o f t h e 21 number o f nodes examined by minimax and y e t s t i l l y i e l d t h e same r e s u l t . In p r a c t i c e i t has been d i s c o v e r e d t h a t a s i m p l e o r d e r i n g works w e l l h e r e . F i r s t , t h e b e s t move f r o m t h e t r a n s p o s i t i o n t a b l e e n t r y f o r t h i s node i s s e a r c h e d . S e c o n d , t h e moves w h i c h change t h e m a t e r i a l b a l a n c e a r e s e a r c h e d i n t h e o r d e r o f l a r g e s t c h a n g e s f i r s t . F i n a l l y , t h e r e m a i n i n g moves a r e s e a r c h e d . The NEXTSUCCESSOR and NEXTCAPTURE g e n e r a t o r s have t h i s r e s p o n s i b i l i t y . (2) t h e s e a r c h d e p t h m e t r i c : I t s h o u l d be c l e a r t h a t t h e TERMINAL p r e d i c a t e does an enormous j o b i n d e f i n i n g t h e c h a r a c t e r o f t h e s e a r c h a l g o r i t h m . TERMINAL d e f i n e s t h e s e a r c h d e p t h m e t r i c . A common m e t r i c , known as f u l l w i d t h d - p l y s e a r c h i n g , i s t o d e c l a r e l e a f nodes and a l l nodes >d l e v e l s from t h e r o o t node t e r m i n a l . A v a r i a n t o f t h i s w h i c h t a k e s i n t o a c c o u n t t h e t a c t i c a l i m p o r t a n c e of moves w h i c h g i v e c h e c k , i s t o not c o u n t moves w h i c h g i v e c h e c k when c o u n t i n g t h e d l e v e l s from t h e r o o t node ( i e moves w h i c h g i v e c h e c k c o u n t f o r z e r o w h i l e a l l o t h e r moves c o u n t f o r o n e ) . The v e r s i o n o f TECH3 d e s c r i b e d i n t h e 1st e d i t i o n o f t h i s t h e s i s employed t h i s m e t r i c . BELLE u s e s a s i m i l a r s e a r c h d e p t h m e t r i c , n ot c o u n t i n g r e p l i e s t o c h e c k i n s t e a d o f t h e c h e c k i n g moves t h e m s e l v e s . The m e t r i c u s e d by t h e v e r s i o n o f TECH3 d e s c r i b e d h e r e i s a v a r i a n t o f f u l l w i d t h d - p l y s e a r c h i n g where c h e c k i n g moves c o u n t f o r z e r o , r e p l i e s t o c h e c k ( i f n o t c h e c k i n g moves t h e m s e l v e s ) c o u n t f o r one, and a l l o t h e r moves n o t o f t h e above two t y p e s have a w e i g h t o f one o r two d e p e n d i n g on a c o m p a r i s o n w i t h t h e 22 c u r r e n t a p a r a m e t e r . I f t h e m a t e r i a l b a l a n c e a f t e r t h e move i s p l a y e d i s g r e a t e r t h a n a t h e n t h e move c o u n t s f o r one, o t h e r w i s e ( m a t e r i a l b a l a n c e < a) t h e move c o u n t s f o r two. The j u s t i f i c a t i o n f o r t h i s new m e t r i c i s t h a t i t works ( s e e C h a p t e r 5 ) . (3) t h e d e p t h i t e r a t i v e a-/3 t e c h n i q u e : A c r i t i c a l p r o b l e m f o r c h e s s p r o g r a m s i s t h a t o f t i m e c o n t r o l . C h e s s i s p l a y e d i n a f i n i t e t i m e e n v i r o n m e n t . The s e a r c h a l g o r i t h m must r e t u r n w i t h i t s r e s u l t s a f t e r a p r e d i c t a b l e t i m e i n t e r v a l . Because' of t h e h i g h l y v a r i a b l e n a t u r e o f c h e s s s e a r c h t r e e s , t h e r e i s some d i f f i c u l t y i n a c c o m p l i s h i n g t h i s . The d e p t h i t e r a t i v e a-/3 t e c h n i q u e was i n t r o d u c e d t o d e a l w i t h t h i s p r o b l e m ( S l a t e and A t k i n 1977). T h i s t e c h n i q u e c a n be d e s c r i b e d a s f o l l o w s : I t e r a t i v e a / 3 ( node ) { d := 1 l o o p : { d := d + 1 s c o r e := a|3( +=>, node ) /* d i s p a s s e d t o TERMINAL */ i f NOMORETIME t h e n r e t u r n ( s c o r e ) g o t o l o o p } } NOMORETIME i s a p r e d i c a t e w h i c h i s t r u e i f a p r e d e f i n e d t i m e t h r e s h o l d i s e x c e e d e d . The t r a n s p o s i t i o n t a b l e ( w i t h b e s t move s t o r e d ) g e n e r a l l y a l l o w s t h e i t e r a t i v e v e r s i o n t o c o m p l e t e a d - p l y s e a r c h i n l e s s t i m e t h a n t h e n o n - i t e r a t i v e v e r s i o n . 23 (4) a s p i r a t i o n s e a r c h i n g o r w i n d o w i n g : A s p i r a t i o n s e a r c h i n g o r windowing r e f e r s t o t h e c h o i c e o f v a l u e s f o r a and ft i n t h e t o p l e v e l c a l l of t h e a-ft a l g o r i t h m . The s m a l l e r t h e d i f f e r e n c e between a and ft, t h e s m a l l e r t h e window. G e n e r a l l y , s m a l l e r windows l e a d t o f a s t e r s e a r c h e s . T h e r e a r e a number of ways t h i s c h o i c e c a n be made ( M a r s l a n d and C a m p b e l l 1982). The f o l l o w i n g i s r e a s o n a b l e : S e a r c h ( node ) { d := .1 s c o r e := EVALUATION( node ) l o o p : { d := d + 1 s c o r e ' := aft( s c o r e - 1 , s c o r e + 1 , node ) /* d i s p a s s e d t o TERMINAL */ i f s c o r e V s c o r e t h e n s c o r e := aft( +°°, node ) i f NOMORETIME t h e n r e t u r n ( s c o r e ) g o t o l o o p } } The window i s made as s m a l l a s p o s s i b l e a r o u n d t h e s c o r e r e t u r n e d by t h e p r e v i o u s s e a r c h i t e r a t i o n on t h e a s s u m p t i o n t h a t t h i s i t e r a t i o n w i l l r e t u r n t h e same s c o r e . I f i t does not t h e n t h e s e a r c h i s r e p e a t e d w i t h a w i d e r window ( i e a=-<», ft=+°°) . The t r a n s p o s i t i o n t a b l e a s s i s t s i n t h e r e p e a t e d s e a r c h . 24 A (>x,>y) I f x>y t h e n e x a m i n i n g o t h e r s u c c e s s o r s t o Ab w i l l n o t ch a n g e t h e s c o r e o f A. AbA (=y) F i g u r e 3 - The I d e a b e h i n d t h e a-)3 A l g o r i t h m h a s h c h e c k a r r a y i n d e x / HASH CODE h a s h c h e c k a-/3 i n f o = ( f l a g , s c o r e , move , d e p t h ) TRANSPOSITION TABLE V • • • • • F i g u r e 4 - The T r a n s p o s i t i o n T a b l e 25 5^ PERFORMANCE EVALUATION OF TECH3 TECH3, r u n n i n g on an Amdahl 470 V/8, was t e s t e d on t h e p o s i t i o n s i n t h e book "Win a t C h e s s " ( R e i n f e l d 1958). T h i s book c o n t a i n s 300 c h e s s t a c t i c s p r o b l e m s and t h e i r s o l u t i o n s . O t h e r p r o g r a m s , i n c l u d i n g PARADISE and BELLE, have been t e s t e d on t h e s e p r o b l e m s and t h u s i t i s p o s s i b l e t o compare t h e i r p e r f o r m a n c e w i t h TECH3's. The c o m p l e t e F o r t r a n and 370 A s s e m b l e r s o u r c e c o d e f o r t h e v e r s i o n o f TECH3 w h i c h was t e s t e d i s g i v e n i n A p p e n d i x 1. TECH3 was g i v e n c r e d i t f o r s o l v i n g a p r o b l e m i f (1) t h e CPU t i m e u s e d d i d n o t e x c e e d 5 m i n u t e s and (2) t h e move r e t u r n e d was t h e same a s one o f t h e book s o l u t i o n s . In some c a s e s more t h a n one s o l u t i o n (move) was c o n s i d e r e d v a l i d . No c o n s i d e r a t i o n was g i v e n f o r whether TECH3 u n d e r s t o o d 1 t h e r e a s o n b e h i n d t h e i n i t i a l move. C r e d i t was g i v e n f o r v a l i d moves t e n d e r e d f o r s p u r i o u s r e a s o n s . T h i s d e c i s i o n was made t o make t h e c r e d i t s c o r i n g as o b j e c t i v e (and a u t o m a t a b l e ) as p o s s i b l e . The book s o l u t i o n s were f o u n d w i t h t h e a i d o f TECH3 and i n c o m m u n i c a t i o n s w i t h B e r l i n e r (1984) t o have 12 i n a c c u r a c i e s . T h e s e a r e l i s t e d i n T a b l e I . The 300 p o s i t i o n s f r o m "Win a t C h e s s " i n p s e u d o - f o r s y t h e n o t a t i o n a s t h e y were i n p u t t o TECH3 a l o n g w i t h t h e i r a c c e p t e d s o l u t i o n s a r e l i s t e d i n A p p e n d i x 2. G i v e n t h e s e c o r r e c t i o n s TECH3 o b t a i n e d a s c o r e o f 274/300. 1 I f a p r o g r a m " s e e s " i n i t s s e a r c h t r e e a l l t h e r e l e v a n t f a c t o r s b e h i n d a move t h e n i t u n d e r s t a n d s t h e p r o b l e m . I t i s n o t a l w a y s e a s y t o see i f t h e p r o g r a m s e e s . Would y o u g i v e c r e d i t t o TECH3 f o r #9 a t D=3 ( s e e A p p e n d i x 3) f o r s e e i n g t h e draw by r e p e t i t i o n ? 26 The 26 p r o b l e m s not s o l v e d a r e l i s t e d i n T a b l e I I . The u n s o l v e d p r o b l e m s were due t o e x c e e d i n g t h e 5 m i n u t e CPU t i m e l i m i t ( o r a t l e a s t g e t t i n g v e r y c l o s e t o i t ) . Merc d e t a i l s zz~ be o b t a i n e d f r o m A p p e n d i x 3 where t h e a c t u a l o u t p u t o f TECH3, i n summarized fo r m , i s l i s t e d . PARADISE was t e s t e d on 92 o f t h e s e p r o b l e m s ( W i l k i n s 1980, 1 982). T h e s e were #1,...,#100 no t i n c l u d i n g #2, #18, #33, #41, #43, #86, #87, and #100. On t h e s e 92 p r o b l e m s PARADISE g o t c r e d i t f o r 89. PARADISE f a i l e d t o s o l v e #31, #71, and #91. On t h e s e same 92 p r o b l e m s TECH3 g o t c r e d i t f o r 90, f a i l i n g t o s o l v e #71 a n d #92. I would be i n t e r e s t e d t o know how PARADISE p e r f o r m e d on #92 s i n c e t h e s o l u t i o n g i v e n by R e i n f e l d i s i n c o r r e c t and W i l k i n s makes no m e n t i o n o f t h i s i n h i s p a p e r s . B e r l i n e r (1981) gave BELLE c r e d i t f o r 280.5 on t h e f u l l s e t o f p r o b l e m s . I have e x a m i n e d t h e o u t p u t o f a more r e c e n t v e r s i o n o f BELLE (Thompson 1984). U s i n g t h e same s c o r i n g c r i t e r i o n o u t l i n e d above f o r TECH3, BELLE o b t a i n e d a s c o r e o f 282/300. The 18 p r o b l e m s not s o l v e d by BELLE a r e l i s t e d i n T a b l e I I where t h e y c a n be compared w i t h t h e 26 p r o b l e m s n o t s o l v e d by TECH3. I t i s c l e a r t h a t BELLE i s s u p e r i o r , i n r e a l t i m e , t o TECH3 r u n n i n g on an Amdahl V/8. A more a p p r o p r i a t e measure o f p e r f o r m a n c e f o r a T E C H 3 - l i k e ( o r B E L L E - l i k e ) p r o g r a m i s t o c o n s i d e r t h e b a s i c c o m p u t a t i o n a l s t e p i n h e r e n t i n t h e d e s i g n . T h i s b a s i c u n i t of c o m p u t a t i o n I w i l l c a l l t h e " a r c " . An a r c i s t h e c o m p u t a t i o n n e c e s s a r y t o go f r o m one node t o i t s s u c c e s s o r node and l a t e r , a f t e r p o s s i b l y o t h e r a r c s , r e t u r n t o t h e o r i g i n a l node. The s e a r c h t r e e c o n t a i n s o n l y l e g a l c h e s s p o s i t i o n s . C o n s e q u e n t l y a r c s w h i c h 27 v i s i t p s e u d o - l e g a l p o s i t i o n s ( i e k i n g l e f t i n c h e c k ) a r e n e v e r c o u n t e d . A l l e x t r a n e o u s c o m p u t a t i o n i s c o n s i d e r e d a r c o v e r h e a d . To o b t a i n some i d e a o f t h e c o m p l e x i t y of an a r c c o n s i d e r t h e f o l l o w i n g . On an Amdahl 470 V/8, TECH3 p r o c e e d s a t an a v e r a g e of 21,000 a r c s p e r s e c o n d . The V/8 hums a l o n g a t 40 c y c l e s p e r m i c r o s e c o n d . The machine i n s t r u c t i o n s f o r m i n g TECH3 r e q u i r e , on a v e r a g e , 2.5 machine c y c l e s p e r i n s t r u c t i o n t o e x e c u t e . C o n s e q u e n t l y e a c h a r c c o n s i s t s of t h e e x e c u t i o n o f a b o u t 760 machine i n s t r u c t i o n s . B E L L E ' s measure o f p e r f o r m a n c e i n t h i s r e s p e c t i s 120,000 a r c s p e r s e c o n d (Thompson 1984). A r e t h e a l g o r i t h m s e q u i v a l e n t i n t h e s e n s e t h a t t h e y a c c o m p l i s h i d e n t i c a l r e s u l t s g i v e n t h e same number o f a r c s ? How c a n two p r o g r a m s be compared a l g o r i t h m i c a l l y , o r i n d e p e n d e n t of t h e d i f f e r e n t h ardware t h e y may be u s i n g ? T h e r e a r e two t h i n g s w h i c h must be d e f i n e d (and m e a s u r e d ) . F i r s t i s t h e d i f f e r e n c e i n h a r d w a r e , t h e d i f f e r e n c e i n c h e s s -s p e c i f i c c o m p u t i n g power. S e c o n d i s t h e r e a l - t i m e p e r f o r m a n c e , t h e t i m e t a k e n t o s o l v e a c h e s s p r o b l e m . To d e f i n e t h e c h e s s -s p e c i f i c c o m p u t i n g power assume a v e r y s i m p l e b r u t e f o r c e t r e e s e a r c h i n g a l g o r i t h m ( l i k e TECH3) i s i m p l e m e n t e d on b o t h m a c h i n e s . The d i f f e r e n c e i n h a r d w a r e i s t h e n t h e r a t i o o f a r c s p e r s e c o n d p e r f o r m a n c e o f t h e same a l g o r i t h m on t h e two m a c h i n e s . I e s t i m a t e t h e d i f f e r e n c e between t h e c h e s s - s p e c i f i c c o m p u t i n g power of t h e BELLE har d w a r e and an Amdahl V/8 as a f a c t o r o f 8. N o t i c e t h a t t h i s i s n o t t h e r a t i o BELLE/TECH3 a r c s p e r s e c o n d p e r f o r m a n c e s i n c e BELLE and TECH3 a r e n o t i d e n t i c a l a l g o r i t h m s . Removing t h e slow e v a l u a t i o n component from BELLE, 28 f o r example, s h o u l d i n c r e a s e B E L L E ' s a r c s p e r s e c o n d p e r f o r m a n c e and a t t h e same t i m e move t h e a l g o r i t h m s " c l o s e r " . The r e a l - t i m e p e r f c r r . a r . c s of t h e t w o a l g o r i t h m s can be d e t e r m i n e d by c o m p a r i n g t h e i r p e r f o r m a n c e on t h e "Win a t C h e s s " p r o b l e m s . S i n c e t h e r e i s a h i g h v a r i a n c e of p e r f o r m a n c e on any s i n g l e p r o b l e m , t h e c o m p a r i s o n i s done by c o n s i d e r i n g t h e amount of t i m e r e q u i r e d t o s o l v e N p r o b l e m s , where N c a n v a r y anywhere from 1 t o 300. Put a n o t h e r way, we know t h a t TECH3 s o l v e s 274 p r o b l e m s i n l e s s t h a n 5 m i n u t e s p e r p r o b l e m . Compare t h i s number (5 m i n u t e s ) w i t h t h e amount of t i m e BELLE r e q u i r e s t o s o l v e 274 p r o b l e m s . R e p e a t t h i s c o m p a r i s o n f o r 273 p r o b l e m s s o l v e d , t h e n 272 p r o b l e m s s o l v e d , and so on. The a v e r a g e of t h e r a t i o of t h e t i m e f o r TECH3 t o s o l v e N p r o b l e m s t o t h e t i m e f o r BELLE t o s o l v e N p r o b l e m s (N=230 t o 268) i s more t h a n 2 but l e s s t h an 3 (2.5±.5) . A l g o r i t h m i c a l l y , TECH3 i s b e t t e r t h a n BELLE by a f a c t o r o f 8/2.5 o r a b o u t 3 (±1 a l l t h i n g s c o n s i d e r e d ) . 29 T a b i c I - I r . c c c u r a c i s s i r . the Bock S o l u t i o n s # 33 Qe4-f4 (1) # 92 Be6xg4 (2) #123 Re7-c7 (1 ) #130 Qg7-h8 (1) #152 Nc3-e4 (1 ) #157 Nd5-e7 (2) #210 Rd1-hi (2) #224 e5-e4 (1 ) #264 Ra8-b8 (1 ) #277 Rg8xg2 (1 ) #294 Bd6-f8 (1 ) #296 Bc6-d7, B c 6 x f 3 (1) E x p l a n a t i o n s : (1) T h i s move(s) i s e q u i v a l e n t t o t h e book s o l u t i o n . C o u nt t h e move(s) as a v a l i d s o l u t i o n . (2) T h i s move i s b e t t e r t h a n t h e book s o l u t i o n . Count t h e move as a v a l i d s o l u t i o n . The book s o l u t i o n i s n o t v a l i d . 30 T a b i c II - The P r o b l e m s n o t S o l v e d by TECH3 and BELLE # 2 # 2 #180 #180 #248 # 71 # 71 #196 #249 # 86 #213 #262 # 87 # 87 #222 #222 #265 #265 # 92 # 92 #229 #229 #269 #269 #100 #100 #230 #230 #270 #141 #141 #235 #235 #275 #275 #150 #239 #293 #155 #241 #297 #297 #163 #243 E x p l a n a t i o n : The f i r s t o f e a c h p a i r o f col u m n s l i s t s t h e 18 p r o b l e m s not s o l v e d by BELLE, w h i l e t h e s e c o n d l i s t s t h e 26 p r o b l e m s n o t s o l v e d by TECH3. The p r o b l e m s a r e l i s t e d s u c h t h a t i t i s c l e a r t h a t 3 p r o b l e m s (#150, #213, and #241) a r e s o l v e d by TECH3 but n o t by BELLE, 11 p r o b l e m s a r e s o l v e d by BELLE b ut n o t by TECH3, and 15 p r o b l e m s a r e n o t s o l v e d by b o t h p r o g r a m s . 31 THE TECHNOLOGY CURVE The t e c h n o l o g y c u r v e i s a g r a p h of c h e s s s t r e n g t h v e r s u s m a c h i n e power ( s e e F i g u r e 6 ) . I t d e l i n e a t e s t o what e x t e n t s u c c e s s i s due t o h a r d w a r e . The Y - a x i s r e p r e s e n t s t h e c h e s s s t r e n g t h o f a p r o gram i n E l o r a t i n g p o i n t s . The E l o r a t i n g s y s t e m i s d e s c r i b e d by E l o ( 1 9 7 8 ) . F i g u r e 5 shows t h e c o r r e s p o n d e n c e between r a t i n g s and d e s c r i p t i v e t i t l e s i n t h i s s y s t e m . I t i s s u f f i c i e n t t o know t h a t a s a l i n e a r a p p r o x i m a t i o n t h e r a t i n g d i f f e r e n c e between two p l a y e r s i n a match i s g i v e n by 400*(W-L)/N where W i s t h e number o f games won, L t h e number l o s t , and N t h e t o t a l number p l a y e d . The X - a x i s r e p r e s e n t s t h e m a c h i n e power i n t e r m s of t h e s p e e d a t w h i c h an e f f i c i e n t i m p l e m e n t a t i o n of a v e r y s i m p l e b r u t e f o r c e t r e e s e a r c h i n g a l g o r i t h m ( l i k e TECH3) i s e x e c u t e d . The e x e c u t i o n s p e e d i s m e a s u r e d by c o u n t i n g t h e number o f a r c s t r a v e r s e d i n t h e s e a r c h t r e e p e r u n i t t i m e (one way o n l y ) . A r c s a r e c o u n t e d a t a l l l e v e l s o f t h e t r e e i n c l u d i n g t h e q u i e s c e n c e p a r t . A r c s t r a v e r s e d more t h a n o n c e , b e c a u s e o f i t e r a t i o n o r w i n d o w i n g f o r example, a r e c o u n t e d once f o r e a c h t r a v e r s e . T h i s i s i d e n t i c a l t o t h e a r c s p e r s e c o n d p e r f o r m a n c e measure i n t r o d u c e d i n t h e l a s t c h a p t e r . The machine power i s e x p r e s s e d a s t h e l o g a r i t h m t o t h e b a s e 2 o f t h e a r c s p e r s e c o n d p e r f o r m a n c e m easure. The machine power o f t h e Amdahl 470 V/8 i s 32 assumed t o be l o g 2 ( l 6 , 0 0 0 a r c s / s e c o n d ) w h i c h i s a b o u t 1 4 1 . T h e r e a r e a number o f ways t h e X - a x i s c a n be i n t e r p r e t e d . S i n c e c h e s s games a r a n o r m a l l y p l a y e d under t o u r n a m e n t c o n d i t i o n s o f 40 moves i n 2 h o u r s , t h e a v e r a g e number o f nodes v i s i t e d p e r move c a n be d e t e r m i n e d . C h a n g i n g t h e r a t e a t w h i c h p l a y p r o c e e d s i s e q u i v a l e n t t o c h a n g i n g t h e machine power. Tournament c h e s s p r o c e e d s a t an a v e r a g e r a t e o f 2 7 s e c o n d s p e r move w h i l e s p e e d c h e s s i s p l a y e d a t an a v e r a g e r a t e o f 2 2 s e c o n d s p e r move. A machine power d i f f e r e n c e o f 5 c a n be s i m u l a t e d by c h a n g i n g from t o u r n a m e n t t o s p e e d c h e s s . A n o t h e r u s e f u l measure o f m a c h i n e power i s t h e a v e r a g e maximum f u l l w i d t h d e p t h s e a r c h e d a t t o u r n a m e n t s p e e d s . A f a c t o r o f a b o u t 32=2 5 a d d i t i o n a l e f f o r t i s r e q u i r e d t o e x t e n d t h e s e a r c h by 2 - p l y . To do a 7 - p l y s e a r c h r e q u i r e s a machine power of about 15. A 9 - p l y s e a r c h i n t h e same t i m e w o u l d r e q u i r e a machine power o f 20. The BELLE d a t a i n F i g u r e 6 was computed f r o m d a t a p r e s e n t e d i n Thompson (1982) and Condon and Thompson ( 1 9 8 3 ) . A s e r i e s o f B E L L E - l i k e p r o g r a m s P3, P4, ... P9 r e s t r i c t e d i n t h e i r s e a r c h d e p t h were d e f i n e d . M a t c h e s were p l a y e d between t h e p r o g r a m s t o d e t e r m i n e t h e i r r e l a t i v e r a t i n g s . An a b s o l u t e r a t i n g f o r t h e p r o g r a m s was o b t a i n e d by a s s u m i n g BELLE = (17,2200) ( i e t h e machine power o f t h e BELLE hardware i s 17 and t h e c h e s s s t r e n g t h 1 T h i s i s b a s e d on an e a r l i e r v e r s i o n o f TECH3 d e s c r i b e d i n t h e 1st e d i t i o n o f t h i s t h e s i s . S i n c e t h e V/8 has n o t c h a n g e d between e d i t i o n s , i t seems r e a s o n a b l e t h a t i t s machine power s h o u l d r e m a i n a t 14. My p o s i t i o n i s now t h a t t h e V/8 (=14) i s t h e s t a n d a r d and any p i e c e of c o d e w h i c h c a n be c o n s i d e r e d as t y p i f y i n g c h e s s - s p e c i f i c c o m p u t a t i o n s c a n be u s e d f o r c o m p a r i s o n t o t h e V/8. 33 Of BELLE i s 2200) . A s i m i l a r e x p e r i m e n t had been p e r f o r m e d e a r l i e r by G i l l o g l y (1272) u s i n g TECH. F o r c o m p a r i s o n t h e TECH d a t a i s a l s o p l o t t e d on F i g u r e 6. The r a t i n g c o m p u t a t i o n s have been done a s s u m i n g TECH = (9,1250) (machine power f o r a PDP-10 + KA10 (0.34 m ips) i s assumed t o be 9 ) . Newborn (1979) has p u b l i s h e d h i s own v e r s i o n o f t h e " t e c h n o l o g y c u r v e " . F o r c o m p a r i s o n h i s r e s u l t s a r e shown i n F i g u r e 6 as w e l l . The s o l i d l i n e i n F i g u r e 6 i s t h e t e c h n o l o g y c u r v e . T h i s l i n e r e p r e s e n t s t h e p l a y i n g s t r e n g t h of t h e t a c t i c s a l g o r i t h m , TECH3, p r e s e n t e d i n C h a p t e r 4. No i n d e p e n d e n t d a t a i s g i v e n t o s u p p o r t t h e c l a i m t h a t t h e s o l i d l i n e i n f a c t r e p r e s e n t s t h i s . The s l o p e of t h e s o l i d l i n e i s b a s e d on an a v e r a g e o f t h e s l o p e s o f t h e 3 d a s h e d l i n e s . The o f f s e t o f t h e s o l i d l i n e ' i s b a s e d on t h e o b s e r v a t i o n by G i l l o g l y (1978) t h a t t h e p o s i t i o n a l p r e s o r t i m p r o v e s TECH by a b o u t 1 - p l y (=250 r a t i n g p o i n t s ) and my e s t i m a t e t h a t TECH3 i s two t i m e s b e t t e r t h a n TECH a t s p e n d i n g a r c s 2 . ( T h i s e s t i m a t e i s s u p p o r t e d by c o m p a r i n g TECH's p e r f o r m a n c e w i t h TECH3's on p r o b l e m s #19, #29, #30, and #48.) Thus t h e s o l i d l i n e i s f i x e d a t ( 9 , 1250 - 250 + 100 = 1100). U n t i l a d d i t i o n a l s u p p o r t i n g d a t a i s p r o v i d e d t h e t e c h n o l o g y c u r v e i s o n l y q u a l i t a t i v e l y d e f i n e d . U s i n g t h e t e c h n o l o g y c u r v e i t i s p o s s i b l e t o measure t h e 2 A g a i n t h i s r e f e r s t o t h e 1st e d i t i o n v e r s i o n o f TECH3. The v e r s i o n i n t h i s t h e s i s i s e s t i m a t e d t o be two t i m e s b e t t e r a g a i n . The e f f e c t of t h i s i s t h a t t h e t e c h n o l o g y c u r v e s h o u l d be r a i s e d by an a d d i t i o n a l 100 r a t i n g p o i n t s . 34 s u c c e s s w i t h w h i c h c h e s s knowledge has been e n c o d e d i n p r o g r a m s . T h i s i s done by c o m p a r i n g t h e e s t a b l i s h e d r a t i n g of programs l i k s .BELLE, CRAY BLITZ, NUCHESS, CHAOS, e t c . w i t h t h e r a t i n g g i v e n by t h e t e c h n o l o g y c u r v e a t t h e machin e power f o r t h e machine u s e d . F o r example BELLE has an e s t a b l i s h e d r a t i n g o f 2200. The machine power o f t h e BELLE h a r d w a r e i s e s t i m a t e d a t 17. The t e c h n o l o g y c u r v e a t 17 y i e l d s a r a t i n g o f 1900. Thus BELLE e n c o d e s a b o u t 2200-1900=300 r a t i n g p o i n t s w o r t h of c h e s s knowledge. As f u r t h e r e x a m p l e s , c o n s i d e r CRAY B L I T Z , NUCHESS and CHAOS w i t h e s t a b l i s h e d r a t i n g s o f 2200, 2100 and 1900 r e s p e c t i v e l y . CRAY BLITZ r u n s on a C r a y - I XMP, NUCHESS e s t a b l i s h e d i t s r a t i n g on a CDC C y b e r 175, w h i l e CHAOS u s e s an Amdahl 470 V/8. The machin e power f o r t h e s e c o m p u t e r s i s e s t i m a t e d a t 16, 14, and, o f c o u r s e , 14, r e s p e c t i v e l y . The t e c h n o l o g y c u r v e r a t i n g a t t h e s e machine powers i s 1800, 1600, and 1600, r e s p e c t i v e l y . Thus CRAY BLITZ e n c o d e s 2200-1800=400 r a t i n g p o i n t s w o r t h o f c h e s s knowledge, w h i l e NUCHESS e n c o d e s 2100-1600=500 r a t i n g p o i n t s w o r t h , and CHAOS e n c o d e s 1900-1600=300 r a t i n g p o i n t s w o r t h . The t h r e e s o u r c e s o f e r r o r i n t h i s measurement a r e t h e d e t e r m i n a t i o n o f t h e e s t a b l i s h e d r a t i n g , t h e d e t e r m i n a t i o n o f t h e machin e power, and t h e d e t e r m i n a t i o n of t h e t e c h n o l o g y r a t i n g . j The main p o i n t s we c a n d e r i v e f r o m t h e t e c h n o l o g y c u r v e a r e a s f o l l o w s . (1) F o r e v e r y f a c t o r o f two i n c r e a s e i n machine power, b r u t e f o r c e c h e s s p r o g r a m s improve by 100 r a t i n g p o i n t s . (2) The amount o f c h e s s knowledge e n c o d e d i n c o m p e t i t i o n p r o g r a m s r a n g e s from 500 p o i n t s f o r NUCHESS t o 300 p o i n t s f o r BELLE and CHAOS. A l l c h e s s - p l a y i n g p r o g r a m s , i n c l u d i n g t h e 35 c u r r e n t w o r l d champion CRAY B L I T Z , and c o m m e r c i a l c h e s s c o m p u t e r s 3 , p r o b a b l y f a l l w i t h i n t h i s narrow r a n g e . (3) Hardware improvements o v e r t h e h i s t o r y o f computer c h e s s have i n c r e a s e d c o m p u t i n g power by a f a c t o r o f 1000 ( = 2 1 0 ) . T h i s c o r r e s p o n d s t o a r a t i n g improvement o f 1000 p o i n t s . A f u r t h e r i n c r e a s e i n c o m p u t i n g power by a f a c t o r o f 32 (500 r a t i n g p o i n t s ) i s r e q u i r e d b e f o r e c o m p u t e r s w i l l be a b l e t o compete on p a r w i t h humans f o r t h e w o r l d c h a m p i o n s h i p . 3 T h e r e i s e v i d e n c e t o s u g g e s t t h a t some c o m m e r c i a l c h e s s c o m p u t e r s a r e p u s h i n g t h e t o p of t h i s r a n g e . F o r example t h e F i d e l i t y E l i t e b a s e d on t h e 6502 m i c r o p r o c e s s o r ( a t 4MHz) has a r a t i n g o f p e r h a p s 1800. The machine power of t h e 6502 ( a t 4MHz) i s o p t i m i s t i c a l l y 10. ( I t ' s h a r d t o b e l i e v e t h a t an 8 - b i t m i c r o p r o c e s s o r i s 1/16 an Amdahl V/8.) Thus t h e E l i t e e n c o d e s 1800-1200=600 p o i n t s o f knowledge. 36 28C0 2600 2400 2200 2000 1800 1 600 1 400 1200 1000 800 W o r l d Champion - K a r p o v G r a n d m a s t e r I n t e r n a t i o n a l M a s t e r M a s t e r - BELLE (1982) E x p e r t - A u t h o r A - c l a s s B - c l a s s C - c l a s s ( A v e r a g e t o u r n a m e n t p l a y e r ) D - c l a s s E - c l a s s B e g i n n e r TECH (1972) F i g u r e 5 - The E l o r a t i n g s y s t e m 37 THE TECHNOLOGY CURVE: C h e s s S t r e n g t h V S r i a c h i n e P o w e r o o 3 n • BELLE data O Newborn CO 21 tv • — * Q a. C3 •z. cr Q -Q — I U J X (JD I d r r CO-* CO CO UJ X o aa » TECH data Chess Strength -100 * Machine Power + 20Q 1 1 T 1 1 MRCHINE POWER - L0G2\5RRCS/SECOND) * Figure 6 - The Technoiogy Curve 38 CONCLUSIONS A framework f o r u n d e r s t a n d i n g computer c h e s s has been p r e s e n t e d . The b a s i c p o i n t s a r e : (1) I t i s u s e f u l t o i l l u m i n a t e c omputer c h e s s from t h e p o i n t o f view o f t a c t i c s and s t r a t e g y . T a c t i c s i s e s s e n t i a l t o p l a y i n g c h e s s w e l l . (2) B r u t e f o r c e p r o g r a m s a r e an e f f i c i e n t method o f d e a l i n g w i t h c h e s s t a c t i c s . They a r e a v a i l a b l e o f f t h e s h e l f . (3) The t e c h n o l o g y c u r v e p r o v i d e s t h e means t o measure t h e s u c c e s s w i t h w h i c h knowledge has been e n c o d e d . Thus t h e e f f e c t s o f h a r d w a r e and t r e e s e a r c h i n g t e c h n i q u e s a r e d e c o u p l e d from computer s t r a t e g y . (4) E f f o r t s s h o u l d now be d i r e c t e d t o w a r d s d i s c o v e r i n g an e f f e c t i v e c omputer c h e s s s t r a t e g y . The p o s i t i o n a l p r e s o r t t e c h n i q u e m e r i t s f u r t h e r i n v e s t i g a t i o n . A t t h e t o p l e v e l our p r o b l e m i s t o c o n s t r u c t a p r o g r a m w h i c h p l a y s c h e s s w e l l . A f u n d a m e n t a l s t e p t o w a r d s a s o l u t i o n i s t h e d i v i s i o n o f t h e p r o b l e m i n t o two p a r t s - s t r a t e g y and t a c t i c s ( s e e F i g u r e 7 ) . The s t r a t e g y p a r t i s r e s p o n s i b l e f o r t h e g l o b a l f e a t u r e s of t h e game. T h i s i n v o l v e s p l a n n i n g . The t a c t i c s p a r t i s r e s p o n s i b l e f o r g i v i n g good a d v i c e on l o c a l f e a t u r e s o f t h e game t o t h e s t r a t e g i c p a r t . T h i s i n v o l v e s c a l c u l a t i n g v a r i a t i o n s . An a t t e m p t t o p r o c e e d a l o n g t h e s e l i n e s has been made. 39 STRATEGY MOVES OF A GAME TACTICS F i g u r e 7 - F u n d a m e n t a l D i v i s i o n of t h e P r o b l e m 40 B i b l i o g r a p h y and R e f e r e n c e s A d e l s o n - V e l s k i i , G.M., A r l a z a r o v , V .L., B i t m a n , A.R., Z h i v o t o v s k i i , A.A., and Uskov, A.V. ( 1 9 6 9 ) , "Programming a Computer t o P l a y C h e s s " , M a t h e m a t i c s S u r v e y s 25, pp221-262. B e r l i n e r , H.J. ( 1 9 7 3 ) , "Some N e c e s s a r y C o n d i t i o n s f o r a M a s t e r C h e s s Program", P r o c e e d i n g s 3 r d I n t e r n a t i o n a l J o i n t C o n f e r e n c e  on A r t i f i c i a l I n t e l l i g e n c e , pp77-85. B e r l i n e r , H.J. ( 1 9 7 4 ) , "Chess as P r o b l e m S o l v i n g : t h e Development o f a T a c t i c s A n a l y z e r " , Ph.D. T h e s i s , C a r n e g i e -M e l l o n U n i v e r s i t y . B e r l i n e r , H.J. ( 1 9 7 7 ) , "A R e p r e s e n t a t i o n and Some Mechanisms f o r a P r o b l e m - S o l v i n g C h e s s Program", A d v a n c e s i n Computer C h e s s J_, e d i t o r M.R.B C l a r k e , pp7-29, E d i n b u r g h . B e r l i n e r . H.J. ( 1 9 8 1 ) , "An E x a m i n a t i o n o f B r u t e F o r c e I n t e l l i g e n c e " , P r o c e e d i n g s 7 t h I n t e r n a t i o n a l J o i n t C o n f e r e n c e on A r t i f i c i a l I n t e l l i g e n c e , pp581-587. B e r l i n e r , H.J. ( 1 9 8 4 ) , P r i v a t e C o m m u n i c a t i o n s . Condon, J.H. and Thompson, K. ( 1 9 8 2 ) , " B e l l e C h e s s Hardware", A d v a n c e s i n Computer C h e s s 3, e d i t o r M.R.B. C l a r k e , pp45-54, Pergamon. Condon, J.H. and Thompson, K. ( 1 9 8 3 ) , " B e l l e " , C h e s s S k i l l i n  Man and M a c h i n e , 2nd e d i t i o n , e d i t o r P.W. F r e y , p p 2 0 l - 2 l 0 , S p r i n g e r - V e r l a g . E l o , A.E. ( 1 9 7 8 ) , The R a t i n g o f C h e s s p l a y e r s , B a t s f o r d . F r e y , P. ( 1 9 8 0 ) , "Machine P r o b l e m S o l v i n g P a r t 3: The A l p h a - B e t a P r o c e d u r e " , BYTE 5 (November), pp244-264. <? — G i l l o g l y , J . J . ( 1 9 7 2 ) , "The T e c h n o l o g y C h e s s Program", A r t i f i c i a l I n t e l l i g e n c e 3, pp145-163. 41 G i l l o g l y , J . J . ( 1 9 7 8 ) , " P e r f o r m a n c e A n a l y s i s o f t h e T e c h n o l o g y C h e s s Program", Ph.D. T h e s i s , C a r n e g i e - M e l l o n U n i v e r s i t y . L a s k e r , Emanual ( 1 9 4 7 ) , L a s k e r ' s Manual of C h e s s , D o v e r . M a r s l a n d , T.A. and C a m p b e l l , M. ( 1 9 8 2 ) , " P a r a l l e l S e a r c h o f S t r o n g l y O r d e r e d Game T r e e s " , C o mputing S u r v e y s 14, p p 5 3 3 - 5 5 l . M i c h i e , D. ( 1 9 8 2 a ) , " G a m e - P l a y i n g Programs and t h e C o n c e p t u a l I n t e r f a c e " , S i g a r t N e w s l e t t e r 80, pp64-70. M i c h i e , D. (1 9 8 2 b ) , "Computer C h e s s and t h e H u m a n i z a t i o n of T e c h n o l o g y " , Nature- 299, pp391-394. M o u s s o u r i s , J . , H o l l o w a y , J . , and G r e e n b l a t t , R. ( 1 9 7 9 ) , "CHEOPS: A C h e s s - O r i e n t e d P r o c e s s i n g System", M a c h i n e  I n t e l l i g e n c e 9, e d i t o r s J . E . Hayes, D. M i c h i e , and L . I . M i k u l i c h , pp351-360, W i l e y . Newborn, M.M. ( 1 9 7 5 ) , Computer C h e s s , Academic P r e s s . Newborn, M.M. ( 1 9 7 9 ) , "Recent P r o g r e s s i n Computer C h e s s " , A d v a n c e s i n Computers 18, e d i t o r M. Y o v i t s , pp59-117, Academic P r e s s . N e w e l l , A., Shaw, J . C . and Simon, H.A. ( 1 9 6 3 ) , " C h e s s - P l a y i n g P rograms and t h e P r o b l e m o f C o m p l e x i t y " , Computers and T h o u g h t , e d i t o r s E.A. Feigenbaum and J . Feldman, pp39-70, M c G r a w - H i l l . P e a r l , J . ( 1 9 8 0 ) , " A s y m p t o t i c P r o p e r t i e s o f Minimax T r e e s and G a m e - S e a r c h i n g P r o c e d u r e s " , A r t i f i c i a l I n t e l l i g e n c e 14, p p 1 l 3 -138. P i t r a t , J . ( 1 9 7 7 ) , "A C h e s s C o m b i n a t i o n P r o g r a m Which Uses P l a n s " , A r t i f i c i a l I n t e l l i g e n c e 8, pp275-321. P i t r a t , J . ( 1 9 8 0 ) , "The B e h a v i o r o f a C h e s s C o m b i n a t i o n s Program Which U s e s P l a n s " , A d v a n c e s i n Computer C h e s s 2, e d i t o r M.R.B. C l a r k e , pp110-121, E d i n b u r g h . 42 R e i n f e l d , F. ( 1 9 5 8 ) , Win a t C h e s s , D o v e r . Shannon, C.E. ( 1 9 5 0 ) , "Programming a Computer f o r P l a y i n g C h e s s " , P h i l o s o p h i c a l M a g a z i n e 41, pp25S~275. S l a t e , D . J . and A t k i n , L.R. ( 1 9 7 7 ) , "CHESS 4.5 - The N o r t h w e s t e r n U n i v e r s i t y C h e s s Program", C h e s s S k i l l i n Man and  M a c h i n e , e d i t o r P.W. F r e y , p p 8 2 - 1 l 8 , S p r i n g e r - V e r l a g . Thompson, K. ( 1 9 8 2 ) , "Computer C h e s s S t r e n g t h " , A d v a n c e s i n  Computer C h e s s 3, e d i t o r M.R.B. C l a r k e , pp55-56, Pergamon. Thompson, K. ( 1 9 8 4 ) , P r i v a t e C o m m u n i c a t i o n . Von Neumann, J . , and M o r g e n s t e r n , 0. ( 1 9 4 4 ) , T h e o r y of Games and  E c o n o m i c B e h a v i o r , P r i n c e t o n . W i l k i n s , D.E. ( 1 9 8 0 ) , " U s i n g P a t t e r n s and P l a n s i n C h e s s " , A r t i f i c i a l I n t e l l i g e n c e 14, p p l 6 5 - 2 0 3 . W i l k i n s , D.E. ( 1 9 8 2 ) , " U s i n g Knowledge t o C o n t r o l T r e e S e a r c h i n g " , A r t i f i c i a l I n t e l l i g e n c e 18, pp1-51. Z e r m e l o , E. ( 1 9 1 2 ) , "Uber E i n e Anwendung d e r M e n g e n l e h r e a u f d i e T h e o r i e d e s S c h a c h s p i e l s " ( i n German), 5 t h I n t e r n a t i o n a l  C o n g r e s s o f M a t h e m a t i c s , pp501-504. 43 A p p e n d i x 1: S o u r c e Code f o r TECH3 L i s t e d a r e 7 p a g e s o f F o r t r a n code f o l l o w e d by 20 pages o f 370 A s s e m b l e r c o d e . The F o r t r a n code i n c l u d e s t h e r o u t i n e s MAIN, BLOCK DATA, TACTIC, and DISPMV. The s u b r o u t i n e "TECH3", c a l l e d f rom TACTIC, i s t h e 370 A s s e m b l e r c o d e . C o l l e c t i v e l y , a l l t h i s c ode t o g e t h e r i s what i s r e f e r r e d t o as TECH3 i n t h e main t e x t . TACTIC and "TECH3" communicate v i a t h e 4 common b l o c k s SPACEO, SPACE 1, SPACE2, and SPACE3. The t r a n s p o s i t i o n t a b l e (TABLE) o c c u p i e s SPACEO, WEB o c c u p i e s SPACE 1, MIXED1 and MIXED2 o c c u p y SPACE3, w h i l e a l l t h e r e m a i n i n g d a t a s t r u c t u r e s a l o n g w i t h LISTMV (an a r e a where g e n e r a t e d moves a r e saved) a r e c o l l e c t e d t o g e t h e r i n SPACE2. MIXED1 and MIXED2 a r e b o t h a r r a y s o f 12x64 3 2 - b i t random i n t e g e r s u s e d i n t h e h a s h code c a l c u l a t i o n s . I t was g e n e r a t e d by t h e f o l l o w i n g p r o g r a m : INTEGER*4 MIXED1(768),MIXED2(768) INTEGER*4 I,J,K,X/-11/,MULT/781 25005/ INTEGER*2 I I ( 2 ) , J J ( 2 ) EQUIVALENCE ( I , I I ( 1 ) ) , ( J , J J ( 1 ) ) C DO 200 K=1,768 X=X*MULT I=X X=X*MULT J=X I I ( 2 ) = J J ( 1 ) MIXED1(K)=I X=X*MULT I=X X=X*MULT J=X I I ( 2 ) = J J ( 1 ) MIXED2(K)=I 200 CONTINUE C WRITE(1) MIXED1,MIXED2 STOP END 44 WEB i s an a r r a y o f 64x64 8 - b i t i n t e g e r s r e p r e s e n t i n g t h e r e l a t i o n s h i p o f e a c h s q u a r e (x) t o e v e r y o t h e r s q u a r e ( y ) . I f WEB(x,y) e q u a l s one o f (2, 4, 6, 8, 10, 12, 14, 16) t h e n i t i s p o s s i b l e t o go from x t o y by making D(WEB(x,y)/2) d i s p l a c e m e n t s ( i e y i s i n x's q u e en's web). I f i t i s p o s s i b l e t o go from x t o y i n a s i n g l e k n i g h t ' s move t h e n WEB(x,y) =1. In a l l o t h e r c a s e s WEB(x,y) =0. TABLE i s i n i t i a l i s e d t o z e r o f o r e v e r y i n v o c a t i o n of TACTIC. MIXED1, MIXED2, and WEB a r e r e a d i n from t h e f i l e "ZABO:TECH3*DATA" once o n l y . They a r e n e v e r c h a n g e d . The r e m a i n i n g d a t a s t r u c t u r e s ( a l l i n SPACE2) w h i c h r e q u i r e i n i t i a l i s a t i o n a r e s e t by BLOCK DATA. A r r a y s w i l l be e x c e e d e d i f t h e s e a r c h d e p t h p r o c e e d s beyond 4 8 - p l y . T h i s i s u n l i k e l y t o happen, b u t n o t as u n l i k e l y as you m i g h t t h i n k . LISTMV has s p a c e f o r 1025 moves. T h i s sometimes o v e r f l o w s on a d e p t h 10 s e a r c h o f a complex middle-game p o s i t i o n B o t h t h e s e e v e n t s a r e t e s t e d f o r and an o p e r a t i o n e x c e p t i o n i s c r e a t e d a t t h e a p p r o p r i a t e p l a c e i n t h e c o d e . 45 1 C***************************************************** 2 C 3 C MAIN 4 C 5 C 6 C 7 IMPLICIT INTEGER*4(A - Z) 8 C 9 INTEGER*4 BOARD(65), MAXLEN /I 28/ 10 C 1 1 LOGICAL*1 A(128) /128*' '/, SPOT(2) 12 INTEGER*2 11 / 0 / 13 EQUIVALENCE ( I 1 , S P O T ( l ) ) 1 4 C 1 5 INTEGER*2 PLUS /78/, MINUS /96 / 16 INTEGER*2 WPAWN /215/, WKING /210/, WNITE /213/ 1 7 INTEGER*2 WBSHP /I 94/, WROOK /217/, WQUEN /216/ 18 INTEGER*2 BPAWN /I 51/, BRING / l 4 6 / , BNITE /149/ 19 INTEGER*2 BBSHP /130/, BROOK / l 5 3 / , BQUEN / I 52/ 20 C 21 C 22 C 23 C c h e c k PAR= f o r TIME and DEPTH 24 C s e t d e f a u l t 25 C 26 TIMMAX = 500 27 DTHMAX = 31 28 C 29 CALL PARSTR(A, LEN, MAXLEN, 0, & 1020) 30 C 31 CALL FINDST( A, LEN, ' TIME=' , 5, 1, NF, £.1010) 32 NA = 4 33 CALL DTB(A(NF + 5 ) , TIME, NA, NB, ' ', & 1 01 0) 34 TIMMAX = TIME * 1000 35 1010 CONTINUE 36 CALL FINDST(A, LEN, 'DEPTH=', 6, 1, NF, &1020) 37 NA = 2 38 CALL DTB(A(NF + 6 ) , DTHMAX, NA, NB, ' ', £1 0 2 0 ) 39 c 40 c 41 c 42 C i n p u t a c h e s s p o s i t i o n i n f o r s y t h e n o t a t i o n 43 C 44 1020 CONTINUE 45 READ (5,1030,END=1100) ( A ( I ) , I = 1 , 1 2 8 ) 46 1 030 FORMAT (128A1) 47 C 48 C 49 C 50 C t r a n s l a t e t o i n t e r n a l b o a r d r e p r e s e n t a t i o n 51 C 52 SQ = 0 53 I = 0 54 1 040 1 = 1 + 1 55 SPOT(2) = A ( I ) 56 c 46 57 I F (11 .EQ. PLUS .OR. 11 .EQ. MINUS) 58 1 GO TO 1070 59 I F (11 .GT. 240) GO TO 1050 60 C 51 SQ = SQ + 1 62 I F (11 .EQ. WPAWN) BOARD(SQ) = 1 63 I F (11 .EQ. WKING) BOARD(SQ) = 2 64 I F (11 .EQ. WNITE) BOARD(SQ) = 3 65 I F (11 .EQ. WBSHP) BOARD(SQ) = 4 66 I F (11 .EQ. WROOK) BOARD(SQ) = 5 67 I F (11 .EQ. WQUEN) BOARD(SQ) = 6 68 C 69 I F (11 .EQ. BPAWN) BOARD(SQ) = -1 70 I F (11 .EQ. BRING) BOARD(SQ) = -2 71 I F (11 .EQ. BNITE) BOARD(SQ) = "3 72 I F (11 .EQ. BBSHP) BOARD(SQ) = -4 73 I F (11 .EQ. BROOK) BOARD(SQ) = -5 74 I F (11 .EQ. BQUEN) BOARD(SQ) = "6 75 C 76 GO TO 1040 77 1050 CONTINUE 78 NUM = 1 1 - 240 79 DO 1060 K = 1, NUM 80 SQ = SQ + 1 81 BOARD(SQ) = 0 82 1060 CONTINUE 83 C 84 GO TO 1040 85 1070 CONTINUE 86 I F (11 .EQ. PLUS) BOARD(65) = 1 87 I F (11 .EQ. MINUS) BOARD(65) = -1 88 1 = 1 + 1 89 C 90 C ==================== 91 C 92 C c a l l TACTIC t o s o l v e p r o b l e m 93 C 94 WRITE (6,1080) ( A ( J ) , J = I , 1 2 8 ) 95 1080 FORMAT ( ' ', 1 28A1 ) 96 C 97 CALL TACTIC(BOARD, TIMMAX, DTHMAX) 98 C 99 WRITE (6,1090) 100 1090 FORMAT ( ' ' ) 101 GO TO 1020 102 C 103 C ==================== 104 C 105 1100 CONTINUE 106 RETURN 107 END 108 c***************************************************** 109 C 110 BLOCK DATA 111 C 112 C ==================== 47 113 C 114 IMPLICIT INTEGER*4(A - Z) 115 C 116 LOGICAL*1 WEB 117 INTEGER*2 FINE, BESTCD, CASTLE, DEPTH, INCHK, 118 1 LBSAV, LSAV, LSSAV, MATER, MOVECD, SAVE, 119 2 SCORE, B, SQ, QSP, CHK1, CHK2, CHK4, D, 120 3 ROW, WT, WT2, D1, D4, D5, D5P, D6, 121 4 KINGSQ, KSQ, NITE, PAWN, ROOK, PLYP, 122 5 PLYQ, WHOMOV, PASSE, FRESH, M64, M63, 123 6 M4, N1, N2, N4, N6, N8, N10, N14, N16, 124 7 N63, N80, N128, N160, N252, FREE 125 C 126 COMMON /SPACE2/ F I N E ( 7 6 8 ) , BESTCD(48), C A S T L E ( 4 8 ) , 127 1 DEPTH(48), HASH1(48), HASH2(48), INCHK(48), 128 2 L B S A V ( 4 8 ) , L S A V ( 4 8 ) , L S S A V ( 4 8 ) , MATER(48), 129 3 MOVE(48), MOVECD(48), S A V E ( 4 8 ) , SCORE(48), 130 4 B ( 1 2 0 ) , S Q ( 7 8 ) , Q S P ( 6 4 ) , CHK1(42), 131 5 CHK2(42), CHK4(8), D ( 1 6 ) , R0W(13), WT(13), 132 6 WT2(4), D 1 ( 1 4 ) , D 4 ( 2 ) , D 5 ( 2 ) , D 5 P ( 2 ) , 133 7 D 6 ( 2 ) , KINGSQ(2), K S Q ( 2 ) , N I T E ( 2 ) , PAWN(2), 134 8 ROOK(2), PARCS, QARCS, MASK, PLYP, PLYQ, 135 9 WHOMOV, PASSE, NBIG, FRESH, M64, M63, M4, 136 * N1, N2, N4, N6, N8, N10, N14, N16, N63, 137 1 N80, N128, N160, N252, FREE, LISTMV(1025), 138 2 WEB(4096), MIXED1(768), MIXED2(768) 139 C 140 C ====================== 141 C 142 DATA FINE /768*0/ 143 DATA MASK / Z 0 0 0 0 F F F F / 144 DATA D /-22, -2, 18, 20, 22, 2, -18, -20, -42, 145 1 -24, 16, 38, 42, 24, -16, -38/ 146 DATA LSSAV(3) /0/, LBSAV(3) /4104/ 147 DATA SQ /0, 1, 2, 3, 4, 5, 6, 7, 2*0, 8, 9, 10, 148 1 11, 12, 13, 14, 15, 2*0, 16, 17, 18, 19, 20, 149 2 21, 22, 23, 2*0, 24, 25, 26, 27, 28, 29, 30, 150 3 31, 2*0, 32, 33, 34, 35, 36, 37, 38, 39, 2*0, 151 4 40, 41, 42, 43, 44, 45, 46, 47, 2*0, 48, 49, 152 5 50, 51, 52, 53, 54, 55, 2*0, 56, 57, 58, 59, 153 6 60, 61, 62, 63/ 154 DATA B /I 20*1 4 / 155 DATA ROW /2816, 2560, 2304, 2048, 1792, 0, -1, 156 1 1536, 256, 512, 768, 1024, 1280/ 157 DATA CHK1 / - I , -1, 0, 0, -1, 0, 0, 0, 1, 0, 0, 1, 158 1 1, 0, -1 , 0, -1, 0, -1, - 1 , 0, 0, 1, 0, 1, 0, 159 2 1, 0, -1, 0, -1, 0, -1, 0, 0, 1, 1, 0, 1, 0, 160 3 1 , 0 / 161 DATA CHK2 / - 1 , - 1, 9*0, 1, 1, 0, -1, 0, -1, 7*0, 162 1 1, 0, 1, 0, -1, 0, -1, 7*0, 1, 0, 1, 0/ 163 DATA NITE /-6, 6/, CHK4 /40, 12, 68, 12, 68, 12, 164 1 40, 12/ 165 DATA PAWN /-2, 2/, D5P /32, -32/ 166 DATA ROOK /-10, 10/ 167 DATA D1 /6*-1, 0, 6*1, 0/ 168 DATA D4 /22, -22/, D5 /20, -20/, D6 /18, -18/ 48 169 DATA KSQ /52, 192/ 170 DATA WT/9, 5, 3, 3, 18, 1, 0, 1, 18, 3, 3, 5, 9/ 171 DATA WT2 /2, 2, 4, 8/ 172 DATA M64 /~64/, M63 /~63/, M4 /~4/, N1 / 1 / , N2 / 2 / 173 1 , N4 /4/, N6 /6/, MS / £ / , N10 / I C / , N i l /14/, 174 2 N16 /16/, N63 /63/, N80 /80/, N128 /128/, 175 3 N160 /160/, N252 /252/, NBIG /Z12000000/ 176 DATA QSP /198, 196, 194, 192, 190, 188, 186, 184, 177 1 164, 144, 124, 104, 84, 64, 44, 46, 48, 50, 178 2 52, 54, 56, 58, 78, 98, 118, 138, 158, 178, 179 3 176, 174, 172, 170, 168, 166, 146, 126, 106, 180 4 86, 66, 68, 70, 72, 74, 76, 96, 116, 136, 181 5 156, 154, 152, 150, 148, 128, 108, 88, 90, 182 6 92, 94, 114, 134, 132, 130, 110, 112/ 183 C 184 C ===================== 185 END 186 £ * * * * * * * * * * * * * * * * * * * * * * * * * * * * 187 C 188 SUBROUTINE TACTIC(BOARD, TIMMAX, DTHMAX) 189 C 190 C ==================== 191 C 192 . IMPLICIT INTEGER*4(A - Z) 193 C 194 COMMON /SPACE0/ TABLE(131072) 195 C 196 LOGICAL*1 WEB 197 C* COMMON /SPACE1/ WEB(4096) 198 C 199 C* COMMON /SPACE3/ MIXED1(768), MIXED2(768) 200 C 201 INTEGER*2 FINE, BESTCD, CASTLE, DEPTH, INCHK, 202 1 LBSAV, LSAV, LSSAV, MATER, MOVECD, SAVE, 203 2 SCORE, B, SQ, QSP, CHK1, CHK2, CHK4, D, 204 3 ROW, WT, WT2, D1, D4, D5, D5P, D6, 205 4 KINGSQ, KSQ, NITE, PAWN, ROOK, PLYP, 206 5 PLYQ, WHOMOV, PASSE, FRESH, M64, M63, 207 6 M4, N1, N2, N4, N6, N8, N10, N14, N16, 208 7 N63, N80, N128, N160, N252, FREE 209 C 210 COMMON /SPACE2/ F I N E ( 7 6 8 ) , BESTCD(48), C A S T L E ( 4 8 ) , 211 1 DEPTH(48), HASH1(48), HASH2(48), INCHK(48), 212 2 L B S A V ( 4 8 ) , L S A V ( 4 8 ) , L S S A V ( 4 8 ) , MATER(48), 213 3 MOVE(48), MOVECD(48), S A V E ( 4 8 ) , SCORE(48), 214 4 B ( 1 2 0 ) , SQ(78)., Q S P ( 6 4 ) , CHK1(42), 215 5 CHK2(42), C H K 4 ( 8 ) , D ( 1 6 ) , R0W(13), WT(13), 216 6 WT2(4), D 1 ( 1 4 ) , D 4 ( 2 ) , D 5 ( 2 ) , D 5 P ( 2 ) , 217 7 D 6 ( 2 ) , KINGSQ(2), KSQ(2), N I T E ( 2 ) , PAWN(2), 218 8 ROOK(2), PARCS, QARCS, MASK, PLYP, PLYQ, 219 9 WHOMOV, PASSE, NBIG, FRESH, M64, M63, M4, 220 * N1, N2, N4, N6, N8, N10, N14, N16, N63, 221 1 N80, N128, N160, N252, FREE, L I S T M V ( 1 0 2 5 ) , 222 . 2 WEB(4096), MIXED1(768), MIXED2(768) 223 C 224 C 49 225 C 226 DIMENSION BOARD(65) 227 LOGICAL*1 CHAR(8), DELTA /Z26/, SECOND / .FALSE. / 228 C 229 QS(K) = K + 21 + (K - 1) / 8 * 2 230 C 231 C ===================== 232 C 233 I F (SECOND) GO TO 1010 234 CALL FTNCMD('ASSIGN 1=AZPG:TECH3*DATA;') 235 READ (1) WEB, MIXED1, MIXED2 236 SECOND = .TRUE. 237 1010 CONTINUE 238 C 239 C 240 C ' z e r o ' t r a n s p o s i t i o n t a b l e 241 KMAX = MASK * 2 + 2 242 DO 1020 K = 1, KMAX 243 1020 TABLE(K) = 0 244 C t r a n s l a t e p o s i t i o n i n t o common b l o c k r e p r e s e n t a t i o n 245 MATER(3) = 0 246 DO 1030 K = 1, 64 247 B ( Q S ( K ) ) = BOARD(K) * 2 248 X = BOARD(K) 249 I F (X .EQ. 0) GO TO 1030 250 I F (X .EQ. 2) KINGSQ(2) = QS(K) * 2 251 I F (X .EQ. - 2) KINGSQO) = QS(K) * 2 252 I F (X .GT. 0) MATER(3) = MATER(3) + WT(X + 7) 253 I F (X .LT. 0) MATER(3) = MATER(3) - WT(X + 7) 254 1030 CONTINUE 255 C 256 WHOMOV = BOARD(65) 257 MATER(3) = MATER(3) * WHOMOV 258 CASTLE(2) = 3 259 CASTLE(3) = 3 260 PASSE = 0 261 PLYP = 6 262 HASH1(3) = MIXED1(2) 263 HASH2(3) = MIXED2(2) 264 C 265 C ==================== 266 C i n i t i a l i z e a l p h a - b e t a i t e r a t i o n l o o p 267 1040 CONTINUE 268 CALL TIME(1, 0, TIM0) 269 PARCS = 0 270 QARCS = 0 271 DEPTH(3) = 1 272 VALUE = MATER(3) 273 C 274 C 275 C 276 1050 CONTINUE 277 C i n c r e m e n t maximum s e a r c h d e p t h 278 DEPTH(3) = DEPTH(3) + 1 279 C s e t window 280 SCORE(1) = VALUE - 1 50 281 SCORE(2) = -VALUE - 1 282 C 283 CALL TECH3 284 C 285 IF (SCORE(3) .EQ. VALUE) CO TO 1Q£0 286 C s c o r e was o u t s i d e window 287 C open window and r e p e a t s e a r c h 288 SCORE(1) = -63 289 SCORE(2) = -63 290 C 291 CALL TECH3 292 C 293 VALUE = SCORE(3) 294 C 295 C 296 C 297 C end of i t e r a t i o n 298 C o u t p u t s t a t i s t i c s 299 1 060 CONTINUE 300 L = LSSAV(4) / 4 - BESTCD(3) 301 IF (L .GT. L S S A V ( 3 ) / 4 ) GO TO 1070 302 L = LBSAV(4) / 4 - BESTCD(3) + 63 303 IF (L .LT. L B S A V ( 3 ) / 4 ) GO TO 1070 304 BESTMV = 0 305 GO TO 1080 306 1 070 BESTMV = LISTMV(L) 307 IF (BESTMV .LT. 0) BESTMV - -BESTMV 308 1080 CONTINUE 309 C 310 CALL TIME(1, 0, TIM) DSCORE = SCORE(3) - MATER(3) 31 1 312 DTIME = TIM - TIM0 313 FOM = LAND(SHFTR(BESTMV,8),255) / 2 314 TOM = LAND(BESTMV,255) / 2 315 FLAG = LAND(SHFTR(BESTMV,16),255) / 2 316 C 317 IF (DTIME .EQ. 0) DTIME = 1 318 SPEED = (PARCS + QARCS + DTIME/2) / DTIME 319 BDF = B(FOM) / 2 320 BDT = B(TOM) / 2 321 CALL DISPMV(FOM, TOM, FLAG, BDF, BDT, CHAR) 322 C 323 WRITE (6,1090) DEPTH(3), DELTA, DSCORE, DTIME, 324 1PARCS, QARCS, SPEED, (CHAR(I),I=1,8) 325 1090 FORMAT C0D=', 12, A3, 'S=', 13, ' T=' , 17, 326 1 ' N=' f 18, 'p', 18, 'q N/T=', 12, 327 2 '. MV=' , 8A1 ) 328 C 329 C c o n t i n u e i t e r a t i n g a s l o n g as t i m e and d e p t h 330 C l i m i t s a r e n o t e x c e e d e d 331 IF (DEPTH(3) .LT. DTHMAX .AND. DTIME .LT. TIMMAX) 332 1 GO TO 1050 333 C 334 C 335 C 336 RETURN 51 337 END 338 Q***************************************************** 339 C 340 SUBROUTINE DISPMV(FROM, TO, FLAG, BDF, BDT, CHAR) 341 C 342 C ==================== 343 C 344 IMPLICIT INTEGER*4(A - Z) 345 C 346 LOGICAL*1 BIGO /'O'/r BLANK /' '/, CROSS /'x'/, 347 1 DASH /'-'/, EQUALS /'='/, 348 2 CP I E C E ( 6 ) /' ', 'K', 'N', 'B', 'R', 'Q'/ 349 3 , C F I L E ( 8 ) / ' a ' , ' b \ ' c ' , 'd', 'e', 350 4 ' f , 'g', 'h'/, CRANK(8) /'8', '7', '6', 351 5 '5', '4', '3', '2', T / , CHAR(8) 352 C 353 c = = = = = = = = = = = = = = = = = = = = = 354 C 355 C t r a n s l a t e move t o e x t e r n a l r e p r e s e n t a t i o n 356 C 357 DO 1010 K = 1, 8 358 1010 CHAR(K) = BLANK 359 I F (FROM .EQ. 0) GO TO 1030 360 I F (FLAG .EQ. 7) GO TO 1020 361 C 362 CHAR(1) = C P I E C E ( I A B S ( B D F ) ) 363 CHAR(2) = CFILE(FROM - FROM/10*10 - 1) 364 CHAR(3) = CRANK(FR0M/10 - 1) 365 CHAR(4) = DASH 366 I F (FLAG .EQ. 2 .OR. BDT .NE. 0) CHAR(4) = CROSS 367 CHAR(5) = C F I L E ( T O - TO/10*10 - 1) 368 CHAR(6) = CRANK(TO/10 - 1) 369 C 370 I F (FLAG .LT. 3 .OR. FLAG .GT. 7) GO TO 1030 371 CHAR(7) = EQUALS 372 CHAR(8) = CPIECE(FLAG) 373 GO TO 1030 374 C 375 1020 CONTINUE 376 CHAR(1) = BIGO 377 CHAR(2) = DASH 378 CHAR(3) = BIGO 379 I F (FROM .LT. TO) GO TO 1030 380 CHAR(4) = DASH 381 CHAR(5) = BIGO 382 C 383 1030 CONTINUE 384 RETURN 385 END 1 * 370 A s s e m b l e r code f o r TECH3 2 3 FINE EQU 0 4 5 BESTCD EQU 1534 6 CASTLE EQU 1630 7 DEPTH EQU 1726 8 HASH1 9 HASH2 10 INCHK 1 1 LBSAV 1 2 LSAV 1 3 LSSAV 1 4 MATER 1 5 MOVE 1 6 MOVECD 17 SAVE 18 SCORE 19 20 B 21 SQ 22 QSP 23 24 CHK1 25 CHK2 26 CHK4 27 D 28 ROW 29 WT 30 WT2 31 D1 32 D4 33 D5 34 D5P 35 D6 36 KINGSQ 37 KSQ 38 NITE 39 PAWN 40 ROOK 41 PARCS 42 QARCS 43 MASK 44 PLYP 45 PLYQ 46 WHOMOV 47 PASSE 48 49 NBIG 50 FRESH 51 M64 52 M63 53 N1 54 N2 55 N4 56 N6 57 N8 58 N1 0 59 N14 60 N63 61 N80 62 N1 60 63 EQU 1820 EQU 2012 EQU 2206 EQU 2302 EQU 2494 EQU 2590 EQU 2684 EQU 2878 EQU 2974 EQU 3070 EQU 31 66 EQU 3364 EQU 3562 EQU 3692 EQU 3776 EQU 3858 EQU 3874 EQU 3920 EQU 3946 EQU 3954 EQU 3980 EQU 3997 EQU 4001 EQU 4005 EQU 4009 EQU 401 3 EQU 401 7 EQU 4021 EQU 4025 EQU 4029 EQU 4032 EQU 4036 EQU 4040 EQU 4044 EQU 4046 EQU 4048 EQU 4050 EQU 4052 EQU 4056 EQU 4058 EQU 4060 EQU 4064 EQU 4066 EQU 4068 EQU 4070 EQU 4072 EQU 4074 EQU 4076 EQU 4080 EQU 4082 EQU 4086 53 64 LISTMV EQU 4088 a r e a f o r move l i s t s 65 MIXED 1 EQU 0 numbers f o r h a s h c o d i n g 66 MIXED2 EQU 3072 67 WEB EQU 0 r e l a t i o n between s q u a r e s 68 T l » X3R T? EQU n t r a n s p o s i t i o n t a b l e 69 70 * The f o l l o w i n g r e f e r s t o r e g i s t e r s 71 72 * R e g i s t e r 15 = TECH3 = e n t r y p o i n t 73 * R e g i s t e r 14 = A(SPACE2) 74 * R e g i s t e r 13 = A(SPACEO) 75 * o r o f f s e t t o A(SPACE2) 76 * o r r e t u r n a d d r e s s 77 78 PLY EQU 12 79 WHO EQU 1 1 80 PLY 1 EQU 10 s h f t K p l y , 1 ) 81 NWHO EQU 9 not who 82 83 FOM EQU 8 84 TOM EQU 7 85 FLAG EQU 6 86 DELTA EQU 6 87 88 LB EQU 5 89 C EQU 5 90 L EQU 5 91 FOX EQU 5 92 INDEX EQU 5 93 LS EQU 4 94 LMAX EQU 4 95 DEPTH0 EQU 4 96 VEC EQU 4 97 PEACE EQU 4 98 S EQU 4 99 X EQU 3 1 00 MAX EQU 3 101 M EQU 2 102 MOSS EQU 2 1 03 MASS EQU 1 104 PIECE EQU 1 105 106 *ENTER 107 TECH3 108 109 110 * 1 1 1 112 * 113 1 14 1 15 116 RETURN 117 ASPACE0 118 ASPACE1 119 ASPACE2 CSECT USING *,15 r e g 15 n e v e r c h a n g e d EXTRN SPACE0 EXTRN SPACE 1 EXTRN SPACE2 EXTRN SPACE3 B A1000 DC X L I ' 0 7 1 DC CL7'TECH3 ' DC F 1 0 1DC A(SPACEO) DC A(SPACE2+8192) DC A(SPACE2) 54 120 ASPACE3 DC A(SPACE2+12288) 121 A1000 STM 14,12,12(13) s a v e r e g i s t e r s 122 ST 13,RETURN 123 121 L 14,ASPACE2 r e g 14 n e v e r c h a n g e d 125 126 LH PLY,PLYP(14) 127 LH WHO,WHOMOV(14) 128 LR PLY 1,PLY 129 SLL PLY1,1(0) 130 LCR NWHO,WHO 131 XR 0,0 r e g 0 (=0) n e v e r c h a n g e d 1 32 133 LR C,NWHO r o o t p o s i t i o n i n c h e c k ? 134 LH S,KINGSQ(WHO,14) 135 BAL 13,A2070 136 STH C,INCHK(PLY,14) 137 B A1120 i n i t i a l i z a t i o n o v e r 138 * g o t o i n i t i a l e n t r y p o i n t 1 39 140 *QSEARCH 141 A1020 LH 1,MATER(PLY,14) 142 STH 1,SCORE(PLY,14) 143 144 LCR 2,1 145 CH 2,SCORE-2(PLY,14) 146 BNH A1580 147 LA 2,17(0,0) 148 AR 2,1 149 CH 2,SCORE-4(PLY,14) 150 BNH A1580 151 STH PLY,PLYQ(14) 1 52 153 A1030 CH 1,SCORE-4(PLY,14) 154 BNL A1031 155 LH 2,SCORE-4(PLY,14) 156 STH 2,SCORE(PLY,14) 157 A1031 LA PLY,2(0,PLY) 158 LA 1,96(0,0) 159 CR 1,PLY 160 BL A1031+2-161 LA PLY1,4(0,PLY1) 162 LCR WHO,WHO i 163 LCR NWHO,NWHO 1 64 165 BAL 13,A1620 166 LH LB,LBSAV-2(PLY,14) 167 STH LB,LBSAV(PLY,14) 168 A1040 XR MAX,MAX 169 XR LMAX,LMAX 170 LH L,LSSAV-2(PLY,14) 171 A1050 LA L , 4 ( 0 , L ) 172 CH L,LSSAV(PLY,14) 173 BH A1060 174 C MAX,LISTMV(L,14) 175 BNL A1050 176 L 1 77 LR 1 78 B 179 180 A1 0 £ Q LTR 181 BZ 182 C 183 BL 184 185 L 186 SH 187 ST 188 SH 189 SH 190 LCR 191 LCR 192 BAL 1 93 B 1 94 195 A1 070 ST 196 ST 197 198 BAL 199 L 200 AH 201 ST 202 LH 203 STH 204 LCR 205 CH 206 BH 207 BAL 208 B 209 210 A1 090 BAL 21 1 LH 212 LCR 213 CH 214 BNH 215 STH 216 CH 217 BH 218 219 A1 1 1 0 SH 220 SH 221 LCR 222 LCR 223 CH 224 BH 225 B 226 227 *TABLE 228 A1 1 20 STH 229 L 230 N 231 SLL MAX,LISTMV(L,14) LMAX,L A1 050 LMAX,LMAX A1 1 1 0 MAX,NBIG(14) A1 070 1,QARCS(14) 1,N1(14) 1,QARCS(14) PLY,N2(14) PLY1,N4(14) WHO,WHO NWHO,NWHO 13,A2010 A1 040 MAX,MOVE(PLY 1,14) 0, LISTMV(LMAX,14) 13,A1950 1, QARCS(14) 1,N1(14) 1 ,QARCS(14) 1 ,MATER(PLY, 14) 1,SCORE(PLY,14) 2,1 2,SCORE-2(PLY,14) A1 030 13,A2010 A1 1 1 0 13,A2010 1,SCORE(PLY,14) 2,1 2,SCORE-2(PLY,14) A1040 2,SCORE-2(PLY,14) 1,SCORE-4(PLY,14) A1 040 PLY,N2(14) PLY1,N4(14) WHO,WHO NWHO,NWHO PLY,PLYQ(14) A1090 A1 580 WHO,FRESH(14) INDEX,HASH1(PLY1,14) INDEX,MASK(14) INDEX,3(0) 232 L 13,ASPACE0 233 234 L 1,HASH2(PLY1,14) 1,TABLE(INDEX,13) 235 C -> b O- w BNE A1 1 50 237 238 STH 0,FRESH(14) 239 L 2,TABLE+4(INDEX,13) 240 SRDA 2,6(0) 241 SRL 3,26(0) 242 LR DEPTHO,3 243 SRDA 2,2(0) 244 SRL 3,30(0) 245 LR FLAG,3 2,8(0) 246 SRDA 247 SRL 3,24(0) 248 STH 3,BESTCD(PLY,14) 249 STH 2,SCORE(PLY,14) 250 251 CH DEPTHO,DEPTH(PLY,14) 252 BL A1 1 60 253 CH FLAG,N1(14) 254 BL A1 61 0 255 BE A1 1 40 256 257 LH 1,SCORE(PLY,14) 258 LCR 2,1 259 CH 2,SCORE-2(PLY,14) 260 BNH A1 61 0 261 CH 1,SCORE-4(PLY,14) 262 BNL A1 170 263 LH 1,SCORE-4(PLY,14) 264 STH 1,SCORE(PLY,14) 265 B A1 1 70 266 267 A1 1 40 LH 1,SCORE(PLY,14) 268 CH 1 ,SCORE-4(PLY,14) 269 BNH A1 61 0 270 LCR 2,1 271 CH 2,SCORE-2(PLY,14) 272 BNH A1 1 60 273 STH 2,SCORE-2(PLY,14) 274 B A1 1 60 275 276 A1 1 50 STH 0,BESTCD(PLY,14) 277 LH 1 ,SCORE-4(PLY,14) 278 STH 1 , SCORE(PLY,14) 279 LA 1,63(0,0) 280 N 1,TABLE+4(INDEX,13) 281 CH 1,DEPTH(PLY,14) 282 BH A l 1 80 283 284 A1 1 60 LH 1,SCORE-4(PLY,14) 285 STH 1,SCORE(PLY,14) 286 287 A1 170 L 1,HASH2(PLY1,14) 288 ST 1,TABLE(INDEX,13) 289 LH 1,DEPTH(PLY,14) 290 ST 1,TABLE+4(INDEX,13) 291 292 *PSEARCH 293 A1180 LA PLY,2(0,PLY) 294 LA 1,96(0,0) 295 CR 1,PLY 296 BL A1180+2 297 LA PLY1,4(0,PLY1) 298 LCR WHO,WHO 299 LCR NWHO,NWHO 300 LH 1,M64(14) 301 STH 1,SCORE(PLY,14) 302 303 BAL 13,A1620 304 305 STH 0,LSAV(PLY,14) 306 CH 0,FRESH(14) 307 BNE A1220 308 LH 1,BESTCD-2(PLY,14) 309 STH 1,MOVECD(PLY,14) 310 SLL 1,2(0) 311 LH L,LSSAV(PLY,14) 312 SR L,1 313 CH L,LSSAV-2(PLY,14) 314 BH A1210 315 316 LH L,LBSAV(PLY,14) 317 SR L,1 318 LA L , 2 5 2 ( 0 , L ) 319 CH L,LBSAV-2(PLY,14) 320 BNL A1220 321 "322 A1210 L 1,LISTMV(L,14) 32 3 ST 1 ,MOVE(PLY 1 ,14) 324 LCR 1,1 325 ST 1,LISTMV(L,14) 326 B A1280 327 328 A1220 CH 0,LSAV(PLY,14) 329 BL A1260 330 XR MAX,MAX 331 XR LMAX,LMAX 332 LH L,LSSAV-2(PLY,14) 333 A1230 LA L , 4 ( 0 , L ) 334 CH L,LSSAV(PLY,14) 335 BH A1240 336 C MAX,LISTMV(L,14) 337 BNL A1230 338 L MAX,LISTMV(L,14) 339 LR LMAX,L 340 B A1230 341 342 A1240 LTR LMAX,LMAX 343 BP A1250 344 LH 345 STH 346 B 347 248- A1250 ST 349 LCR 350 ST 351 LH 352 SR 353 SRL 354 STH 355 B 356 357 A1260 LH 358 SH 359 CH 360 BL 361 STH 362 C 363 BH 364 L 365 ST 366 SH 367 LCR 368 LA 369 SRL 370 STH 371 B 372 373 A1270 LH 374 CH 375 BNE 376 LA 377 STH 378 A1271 LH-379 CH 380 BNE 381 CH 382 BNE 383 STH 384 A1272 XR 385 LH 386 CH 387 BH 388 LA 389 B 390 391 *LEGAL 392 A1280 BAL 393 394 L 395 XR 396 397 CH 398 BE 399 CH 1,LBSAV-2(PLY,14) 1,LSAV(PLY,14) A1260 MAX,MOVE(PLY 1,14) MAX,MAX MAX,LISTMV(LMAX,14) 1,LSSAV(PLY,14) 1,LMAX 1,2(0) 1,MOVECD(PLY,14) A1 280 1,LSAV(PLY,14) 1,N4(14) 1,LBSAV(PLY,14) A1270 1, LSAV(PLY,14) 0, LISTMV(1,14) A1 260 2, LISTMV(1,14) 2,MOVE(PLY1,14) 1, LBSAV(PLY,14) 1 , 1 1,252(0,1) 1,2(0) 1,MOVECD(PLY,14) A1 280 1,SCORE-2(PLY,14) 1, M63(14) A1 271 2,31(0,0) 2, DEPTH-2(PLY,14) 2,SCORE(PLY,14) 2,M64(14) A1272 0,INCHK-2(PLY,14) A1 272 0,SCORE-2(PLY,14) FLAG,FLAG 1,SCORE-2(PLY,14) 1,SCORE-6(PLY,14) A1 600 FLAG,1(0,0) A1600 13,A1950 13,ASPACE1 VEC,VEC FLAG,N4(14) A1 490 FLAG,N14(14) 400 BE A1 430 401 BH A1330 402 LH FOX,KINGSQ(NWHO,14) 403 CH 0,INCHK-2(PLY,14) 404 BNE A1 320 405 406 LH 1,SQ(FOM,14) 407 SLL 1,6(0) 408 AH 1,SQ(FOX,14) 409 IC VEC,WEB(1,13) 410 41 1 CH VEC,N1(14) 412 BNH A1350 413 414 A1300 AH FOX,D(VEC,14) 415 CH 0,B(FOX,14) 416 BE A1300 417 LH 1,CHK4(VEC,14) 418 AH 1,B(FOX,14) 419 CH WHO,CHK2(1,14) 420 BNE A1 350 421 B A1 520 422 423 A1 320 LH 1,SQ(TOM,14) 424 SLL 1,6(0) 425 AH 1,SQ(FOX,14) 426 IC VEC,WEB(1,13) 427 428 LTR VEC,VEC 429 BZ A1 520 430 431 A1 330 LR C,WHO 432 LH S,KINGSQ(NWHO,14) 433 BAL 13,A2070 434 LTR c,c 435 BNZ A1 520 436 L 13,ASPACE1 437 438 A1 350 LH FOX,KINGSQ(WHO,14) 439 LH 1,SQ(FOM,14) 440 SLL 1,6(0) 441 AH 1,SQ(FOX,14) 442 IC VEC,WEB(1,13) 443 444 CH VEC,N1(14) 445 BNH A1380 446 447 A1 360 AH FOX,D(VEC,14) 448 CH 0,B(FOX,14) 449 BE A1 360 450 LH 1,CHK4(VEC,14) 451 AH 1 ,B(FOX,14) 452 CH NWHO,CHK2( 1 ,14) 453 BNE A1380 454 455 A1370 STH WHO,INCHK(PLY, 14) 456 B A1 530 457 458 A1 380 LH FOX,KINGSQ(WHO,14) 459 LH 1,SQ(TOM,14) 460 SLL 1,6(0) 461 AH 1,SQ(FOX,14) 462 IC VEC,WEB(1,13) 463 464 CH VEC,N1(14) 465 BH A1 400 466 BL A1 390 467 468 LH 1,NITE(NWHO,14) 469 CH 1,B(TOM,14) 470 BE A1 370 471 472 A1390 STH 0,INCHK(PLY,14) 473 B A1 530 474 475 A1 400 AH FOX,D(VEC,14) 476 CH 0,B(FOX,14) 477 BE A1 420 478 LH 1,CHK4(VEC,14) 479 AH 1,B(FOX,14) 480 CH NWHO,CHK1(1,14) 481 BNE A1 390 482 B A1 370 483 484 A1 420 AH • FOX,D(VEC,14) 485 CH 0,B(FOX,14) 486 BE A1 420 487 LH 1,CHK4(VEC,14) 488 AH 1,B(FOX,14) 489 CH NWHO,CHK2(1,14) 490 BNE A1390 491 B A1 370 492 493 A1 430 CH 0,INCHK-2(PLY,14) 494 BNE A1 520 495 LR C,WHO 496 LR S,TOM 497 BAL 13,A2070 498 LTR c,c 499 BNZ A1 520 500 LR C,WHO 501 CR FOM,TOM 502 BH A1431 503 SH S,N2(14) 504 B A1 432 505 A1431 AH S,N2(14) 506 A1 432 BAL 13,A2070 507 LTR C,C 508 BNZ A1 520 509 B A1 501 510 51 1 A1 490 LR C,WHO 512 LH S,KINGSQ(NWHO,14) 513 BAL 13,A2070 514 LTR C, C 515 BNZ A1520 516 517 A1501 LR C,NWHO 518 LH S,KINGSQ(WHO,14) 519 BAL 13,A2070 520 STH C,INCHK(PLY,14) 521 B A1530 522 523 A1520 BAL 13,A2010 524 B A1220 525 526 A1530 L 1,PARCS(14) 527 AH 1,N1(14) 528 ST 1,PARCS(14)" 529 530 LH 1,DEPTH-2(PLY,14) 531 CH 0,INCHK(PLY,14) 532 BNE A1531 533 534 CH 0,INCHK-2(PLY,14) 535 BNE A15305 536 LH 2,MATER(PLY,14) 537 LCR 2,2 538 CH 2,SCORE-2(PLY,14) 539 BH A15305 540 SH 1,N1(14) 541 542 A15305 SH 1,N1(14) 543 A1531 STH 1,DEPTH(PLY,14) 544 LTR 1,1 545 BNP A1020 546 547 *ENCODE 548 L 13,ASPACE3 549 550 L 1,HASH1-4(PLY1,14) 551 L 2,HASH2-4(PLY1,14) 552 LH FOM,SQ(FOM,14) \:553 SLL FOM,2(0) J554 LH PEACE,B(TOM,14) 555 LH TOM,SQ(TOM,14) 556 SLL TOM,2(0) 557 558 LH X,ROW(PEACE,14) 559 AR X,FOM 560 X 1,MIXED1(X,13) 561 X 2,MIXED2(X,13) 562 563 LH X,ROW(PEACE,14) 564 AR X,TOM 565 X . 1,MIXED1(X,13) 566 X 2,MIXED2(X,13) 567 568 X 1, MIXED1(0,13) 2, MIXED2(0,13) 569 X 570 571 CH 0,SAVE(PLY,14) 572 BE A1532 573 LH X,SAVE(PLY,14) 574 LH X,ROW(X,14) 575 AR X,TOM 576 X 1, MIXED1(X,13) 2, MIXED2(X,13) 577 X 578 579 A1 532 CH FLAG,N2(14) 580 BNH A1 561 581 CH FLAG,N14(14) 582 BE A1 550 583 BH A1 561 584 CH FLAG,N4(14) 585 BH A1 540 586 587 LH X,PAWN(WHO,14) 588 LH X,ROW(X,14) 589 AR X,TOM 590 AH X,D5P(WHO,14) 591 X 1, MIXED1(X,13) 2, MIXED2(X,13) 592 X 593 B A1 561 594 595 A1 540 LH X,ROW(PEACE,14) 596 AR X,FOM 597 X 1, MIXED1(X,13) 2, MIXED2(X,13) 598 X 599 600 LH X,PAWN(NWHO,14) 601 LH X,ROW(X,14) 602 AR X,FOM 603 X 1, MIXED1(X,13) 2, MIXED2(X, 13) 604 X 605 B A1 561 606 607 A1 550 LH PEACE,ROOK(NWHO,14) 608 LH PEACE,ROW(PEACE,14) 609 AR PEACE,TOM 610 CR TOM,FOM 61 1 BL A1 560 612 613 LR X,PEACE X,N4(14) 614 SH 615 X 1,MIXED1(X,13) 616 X 2,MIXED2(X,13) 617 618 LR X,PEACE X,N4(14) 619 AH 620 X 1, MIXED1(X,13) 2, MIXED2(X,13) 621 X 622 B A1 561 623 63 624 A1 560 LR X,PEACE 625 AH X,N4(14) 626 X 1, MIXED1(X,13) 2, MIXED2(X,13) 627 X 628 629 LR X,PEACE 630 SH X,N8(14) 631 X 1, MIXED1(X,13) 2, MIXED2(X,13) 632 X 633 634 A1 561 ST 1,HASH1(PLY 1,14) 635 ST 2,HASH2(PLY1,14) 636 B A1 1 20 637 638 *PSEARCH c o n t i n u e d 639 A1 580 BAL 13,A2010 640 LH 1,SCORE(PLY,14) 641 LCR 1,1 642 CH 1 ,SCORE-2(PLY, 14) 643 BNH A1220 644 645 STH 1,SCORE-2(PLY,14) 646 LH 2,MOVECD(PLY,14) 647 STH 2,BESTCD-2(PLY,14) 648 649 LCR 2,1 650 CH 2,SCORE-4(PLY,14) 651 BH A1 220 652 CH 1,N63(14) 653 BNE A1 581 654 LA 2,31(0,0) 655 STH 2,DEPTH-2(PLY, 14) 656 A1 581 LA FLAG,2(0,0) 657 658 A1 600 SH PLY,N2(14) 659 SH PLY 1 ,N4(14) 660 LCR WHO,WHO 661 LCR NWHO,NWHO 662 663 L 13,ASPACE0 664 L INDEX,HASH1(PLY1,14) 665 N INDEX,MASK(14) 666 SLL INDEX,3(0) 667 LA 1,63(0,0) 668 N 1,TABLE+4(INDEX, 13) 669 CH 1,DEPTH(PLY,14) 670 BH A1 61 0 671 672 L 1,HASH2(PLY1,14) 673 ST 1,TABLE(INDEX,13) 674 LH 1,SCORE(PLY,14) 675 SLL 1,8(0) 676 AH 1,BESTCD(PLY,14) 677 SLL 1,2(0) 678 AR 1 , FLAG 1,6(0) 679 SLL 64 680 AH 1,DEPTH(PLY,14) 681 ST 1,TABLE+4(INDEX,13) 682 683 A1610 CH PLY,PLYP(14) 684 BH A1580 685 686 *EXIT 687 L 13, RETURN 688 LM 14,12,12(13) r e s t o r e r e g i s t e r s 689 XR 15,15 r e t u r n c o d e = 0 690 BR 14 r e t u r n t o c a l l e r 691 692 * p s e u d o - s u b r o u t i n e s 693 694 *MOVGEN 695 A1620 LH LS,LSSAV-2(PLY,14) 696 LH LB,LBSAV-2(PLY,14) 697 LA X,128(0,0) 698 699 A1630 LH FOM,QSP(X,14) 700 LH PIECE,B(FOM,14) 701 CH NWHO,D1(PIECE,14) 702 BE A1631 703 A1880 SH X,N2(14) 704 BP A1630 705 706 STH 0,PASSE(14) 707 LH X,CASTLE-4(PLY,14) 708 STH X,CASTLE(PLY,14) 709 LTR X,X 710 BZ A1940 711 LH FOM,KINGSQ(NWHO,14) 712 CH FOM,KSQ(NWHO,14) 713 BE A1890 714 STH 0,CASTLE(PLY,14) 715 B A1940 716 717 A1890 CH X,N2(14) 718 BE A1920 719 LH PIECE,ROOK(NWHO,14) 720 CH PIECE,B+6(FOM,14) 721 BE A1900 722 SH X,N1(14) 723 STH X,CASTLE(PLY,14) 724 B A1910 725 726 A1900 C 0,B+2(FOM,14) 727 BNE A1910 728 SH LB,N4(14) 729 LA FLAG,14(0,0) 730 LA TOM,4(0,FOM) 731 ST TOM,LISTMV(LB,14) 732 STC FOM,LISTMV+2(LB,14) 733 STC FLAG,LISTMV+1(LB,14) 734 735 A1910 CH X,N2(14) 736 BL A1 940 737 A1 920 LH PIECE,ROOK(NWHO,14) 738 CH PIECE,B-8(FOM,14) 739 BE A1930 740 SH X,CASTLE(PLY,14) 741 STH 742 B A1 940 743 744 A1930 CH 0,B-2(FOM,14) 745 BNE A1940 746 C 0,B-6(FOM,14) 747 BNE A1 940 748 SH LB,N4(14) 749 LA FLAG,14(0,0) 750 LR TOM,FOM 751 SH TOM,N4(14) 752 ST TOM,LISTMV(LB,14) 753 STC FOM,LISTMV+2(LB,14) 754 STC FLAG,LISTMV+1(LB,14) 755 756 A1 940 STH LS,LSSAV(PLY,14) 757 STH LB,LBSAV(PLY,14) 758 CR LS, LB 759 BNL A1940+2 760 BR 13 761 762 A1 631 LPR P I E C E , P I E C E 763 CH PIECE,N2(14) 764 BNE A1 632 765 766 LTR WHO,WHO 767 BP A1781 768 CH FOM,N80(14) 769 BL A1 820 770 B A1 782 771 772 A1 781 CH FOM,N160(14) 773 BH A1820 774 775 A1782 LR TOM,FOM 776 AH TOM,D5(NWHO,14) 777 CH 0,B(TOM,14) 778 BNE A1790 779 SH LB,N4(14) 780 ST TOM,LISTMV(LB,14) 781 STC FOM,LISTMV+2(LB,14) 782 783 LTR WHO,WHO 784 BP A1783 785 CH FOM,N160(14) 786 BL A1 790 787 B A1 784 788 789 A1783 CH FOM,N80( 1 4) 790 BH A1790 791 66 792 A1784 AH TOM,D5(NWHO,14) 793 CH 0,B(TOM,14) 794 BNE A1790 795 LA FLAG,2(0,0) 796 CT.I *• T> V 1 1 * 1 \ —" , " - \ • / 797 ST TOM,LISTMV(LB, 14) 798 STC FOM,LISTMV+2(LB, 14) 799 STC FLAG,LISTMV+1(LB,14) 800 801 A1 790 LR TOM,FOM 802 AH TOM,D4(NWHO,14) 803 LH PIECE,B(TOM,14) 804 CH WHO,D1(PIECE,14) 805 BNE A1800 806 LA L S , 4 ( 0 , L S ) 807 LH MOSS,WT(PIECE,14) 808 ST TOM,LISTMV(LS,14) 809 STC FOM,LISTMV+2(LS,14) 810 STC MOSS,LISTMV(LS,14) 811 812 A1 800 LR TOM,FOM 813 AH TOM,D6(NWHO,14) 814 LH PIECE,B(TOM,14) 815 CH WHO,D1(PIECE,14) 816 BNE A1810 817 LA L S , 4 ( 0 , L S ) 818 LH MOSS,WT(PIECE, 14) 819 ST TOM,LISTMV(LS,14) 820 STC FOM,LISTMV+2(LS,14) 821 STC MOSS,LISTMV(LS, 14) 822 823 A1 81 0 CH 0,PASSE(14) 824 BE A1880 825 CH TOM,PASSE(14) 826 BE A181 1 827 LR TOM,FOM 828 AH TOM,D4(NWHO,14) 829 CH TOM,PASSE(14) 830 BNE A1 880 831 832 A1 81 1 LA L S , 4 ( 0 , L S ) 833 LA MOSS,1(0,0) 834 LA FLAG,4(0,0) 835 ST TOM,LISTMV(LS, 14) 836 STC FOM,LISTMV+2(LS, 14) 837 STC FLAG,LISTMV+1(LS, 1 4) 838 STC MOSS,LISTMV(LS,14) 839 B A1 880 840 841 A1 820 LR TOM,FOM 842 AH TOM,D5(NWHO,14) 843 CH 0,B(TOM,14) 844 BNE A1840 845 LA FLAG,12(0,0) 846 847 A1830 LA L S , 4 ( 0 , L S ) 67 848 LH MOSS,WT2(FLAG,14) 849 ST TOM,LISTMV(LS,14) 850 STC FOM,LISTMV+2(LS,14) 851 STC FLAG,LISTMV+1(LS,14) 852 STC MOSS, L I STMV (LS,-14) 853 SH FLAG,N2(14) 854 CH FLAG,N6(14) 855 BNL A1830 856 857 A1840 LR TOM,FOM 858 AH TOM,D4(NWHO,14) 859 LH PIECE,B(TOM,14) 860 CH WHO,D1(PIECE,14) 861 BNE A1860 862 LA FLAG,12(0,0) 863 864 A1850 LA L S , 4 ( 0 , L S ) 865 LH MOSS,WT(PIECE,14) 866 AH MOSS,WT2(FLAG,14) 867 ST TOM,LISTMV(LS,14) 868 STC FOM,LISTMV+2(LS,14) 869 STC FLAG,LISTMV+1(LS,14) 870 STC MOSS,LISTMV(LS,14) 871 SH FLAG,N2(14) 872 CH FLAG,N6(14) 873 BNL A1850 874 875 A1860 LR TOM,FOM 876 AH TOM,D6(NWHO,14) 877 LH PIECE,B(TOM,14) 878 CH WHO,D1(PIECE,14) 879 BNE A1880 880 LA FLAG,12(0,0) 881 882 A1870 LA L S , 4 ( 0 , L S ) 883 LH MOSS,WT(PIECE,14) 884 AH MOSS,WT2(FLAG,14) 885 ST TOM,LISTMV(LS,14) 886 STC FOM,LISTMV+2(LS,14) 887 STC FLAG,LISTMV+1(LS,14) 888 STC MOSS,LISTMV(LS,14) 889 SH FLAG,N2(14) 890 CH FLAG,N6(14) 891 BNL A1870 892 B A1880 893 894 A1632 CH PIECE,N6(14) 895 BNH A1633 896 897 LA M,14 ( 0,0) 898 LA DELTA,4(0,0) 899 CH PIECE,N10(14) 900 BE A1650 901 BL A1660 902 LA D E L T A , 2 ( 0 , 0 ) 903 904 A1 650 LA M,16(0,0) 905 A1 660 LR TOM,FOM 906 A1670 AH TOM,D(M,14) 907 CH 0,B(TOM,14) ono T>xtn i>ii ill 7.1580 909 SH LB,N4(14) 910 ST TOM,LISTMV(LB,14) 91 1 STC FOM,LISTMV+2(LB,14) 912 B A1 670 913 914 A1 680 LH PIECE,B(TOM,14) 915 CH WHO,D1(PIECE,14) 916 BNE A1 690 917 LA L S , 4 ( 0 , L S ) 918 LH MASS,WT(PIECE,14) 919 ST TOM,LISTMV(LS,14) 920 STC FOM,LISTMV+2(LS,14) 921 STC MASS,LISTMV(LS,14) 922 923 A1 690 SR M,DELTA 924 BP A1 660 925 B A1880 926 927 A1 633 BL A1 634 928 929 LA M,16(0,0) 930 A1 71 0 LR TOM,FOM 931 AH TOM,D+16(M,14) 932 CH 0,B(TOM,14) 933 BNE A1 720 934 SH LB,N4(14) 935 ST TOM,LISTMV(LB,14) 936 STC FOM,LISTMV+2(LB, 14) 937 B A1 730 938 939 A1720 LH PIECE,B(TOM,14) 940 CH WHO,D1(PIECE,14). 941 BNE A1730 942 LA L S , 4 ( 0 , L S ) 943 LH MASS,WT(PIECE,14) 944 ST TOM,LISTMV(LS,14) 945 STC FOM,LISTMV+2(LS,14) 946 STC MASS,LISTMV(LS,14) 947 948 A1 730 SH M,N2(14) 949 BP A1 71 0 950 B A1880 951 952 A1634 LA M,16(0,0) 953 LA FLAG,16(0,0) 954 A1750 LR TOM,FOM TOM,D(M,14) 955 AH 956 CH 0,B(TOM,14) 957 BNE A1760 958 SH LB,N4(14) 959 ST TOM,LISTMV(LB,14) 960 STC FOM,LISTMV+2(LB,14) 961 STC FLAG,LISTMV+1(LB,14) 962 B A1 770 963 961 A176C LH PIECE,B(TOM,14) 965 CH WHO,D1(PIECE,14) 966 BNE A1 770 967 LA L S , 4 ( 0 , L S ) 968 LH MASS,WT(PIECE,14) 969 ST TOM,LISTMV(LS,14) 970 STC FOM,LISTMV+2(LS, 14) 971 STC FLAG,LISTMV+1(LS,14) MASS,LISTMV(LS,14) 972 STC 973 974 A1770 SH M,N2(14) 975 BP A1 750 976 B A1880 977 *MAKE 978 A1950 IC TOM,MOVE+3(PLY1,14) 979 IC FOM,MOVE+2(PLY1 , 14) FLAG,MOVE+1(PLY1,14) 980 IC 981 XR 2,2 982 IC 2,MOVE(PLY 1 ,14) 983 984 AH 2,MATER-2(PLY, 14) 985 LCR 2,2 986 STH 2,MATER(PLY,14) 987 988 LH 1,B(TOM,14) 989 STH 1,SAVE(PLY,14) 990 LH 1,B(FOM,14) 991 STH 1,B(TOM,14) 992 STH 0,B(FOM,14) 993 994 LTR FLAG,FLAG 995 BZR 1 3 996 CH FLAG,N14(14) 997 BNL A1980 998 CH FLAG,N4(14) 999 BH A1970 1000 BE A1960 1001 1 002 LR 1 , TOM 1,D5(WHO,14) 1003 AH 1 004 STH 1,PASSE(14) 1005 BR 1 3 1006 1007 A1960 LR 1 ,TOM 1,D5(WHO,14) 1008 AH 1009 STH 0,B(1,14) 1010 BR 13 1011 1012 A1 970 LR 1,FLAG 1013 LTR WHO,WHO 1014 BL A1971 1015 LCR 1,1 1016 A1971 STH 1017 BR 1013 1019 A1980 STH *, n r* T> o o i \J \S J J l i l \ 1021 CR 1022 BL 1023 LH 1024 STH 1025 STH 1026 BR 1027 A1990 LH 1028 STH 1029 STH 1030 BR 1031 1032 *UNMAKE 1033 A2010 IC 1034 IC 1035 IC 1036 1037 LH 1038 STH 1039 LH 1040 STH 1 041 1042 LTR 1043 BZR 1044 CH 1045 BNL 1046 CH 1047 BH 1048 BE 1049 1050 STH 1051 BR 1052 1053 A2020 LR 1054 AH 1055 LH 1056 STH 1057 BR 1058 1059 A2030 LH 1060 STH 1061 BR 1062 1063 A2040 STH 1064 BHR 1065 CR 1066 BL 1067 LH 1068 STH 1069 STH 1070 BR 1071 A2050 LH 1,B(T0M,14) 13 TOM,KINGSQ(NWHO,14) 1 3 TOM,FOM A1 990 1 ,B+2(TOM,14) 1,B-2(TOM,14) 0, B+2(TOM,14) 13 1, B-4(TOM,14) 1,B+2(TOM,14) 0,B-4(TOM,14) 1 3 TOM,MOVE+3(PLY1,14) FOM,MOVE+2(PLY1,14) FLAG,MOVE+1 (PLY 1 ,14) 1,B(TOM,14) 1,B(FOM,14) 1,SAVE(PLY,14) 1,B(TOM,14) FLAG,FLAG 1 3 FLAG,N14( 14) A2040 FLAG,N4(14) A2030 A2020 0, PASSE(14) 1 3 1 ,TOM 1, D5(WHO,14) 2, PAWN(WHO,14) 2,B(1,14) 1 3 1,PAWN(NWHO,14) 1,B(FOM,14) 13 FOM,KINGSQ(NWHO,14) 1 3 TOM,FOM A2050 1,B-2(TOM,14) 1,B+2(TOM,14) 0,B-2(TOM,14) 13 1 ,B+2(TOM,14) 072 STH 073 STH 074 BR 075 r f c w f W *CHECK 077 A2070 LA 078 A2080 LR 079 AH 080 CH 081 BE 082 LH 083 AH 084 CH 085 BER 086 B 087 088 A2090 AH 089 CH 090 BE 091 LH 092 AH 093 CH 094 BER 095 A21 00 SH 096 BP 097 098 LH 099 LA 100 A21 1 0 LR 101 AH 102 CH 1 03 BER 104 SH 105 BP 106 107 XR 108 BR 109 1 1 0 END 1 ,B-4(TOM,14) 0,B+2(TOM,14) 1 3 1 ,16(0,0) 2,S 2, D(1,14) 0,B(2,14) A2090 3, CHK4(1,14) 3,B(2,14) C C H K 1 (3,14) 1 3 A21 00 2, D(1,14) 0, B(2,14) A2090 3, CHK4(1,14) 3,B(2,14) C,CHK2(3,14) 13 1, N2(14) A2080 3,NITE(C,14) 1 ,16(0,0) 2,S 2, D+16(1,14) 3, B(2,14) 1 3 1,N2(14) A21 1 0 C,C 1 3 72 A p p e n d i x 2: T e s t P r o b l e m s and S o l u t i o n s The 300 p r o b l e m s f r o m R e i n f e l d (1958) a l o n g w i t h t h e i r a c c e p t e d s o l u t i o n s a r e l i s t e d on t h e n e x t 11 p a g e s . Two l i n e s a r e u s e d f o r e a c h p r o b l e m . The f i r s t l i n e i s t h e p s e u d o - f o r s y t h e n o t a t i o n f o r t h e p r o b l e m p o s i t i o n . T h i s i s i n p u t t o TECH3. The b o a r d p o s i t i o n c a n be r e c o n s t r u c t e d by t r a c i n g f r o m t h e t o p l e f t c o r n e r (a8) o f t h e b o a r d , as one w o u l d r e a d , t o t h e b o t t o m r i g h t c o r n e r ( h i ) p l a c i n g p i e c e s as i n d i c a t e d . Lower c a s e l e t t e r s a r e b l a c k p i e c e s w h i l e upper c a s e l e t t e r s a r e w h i t e p i e c e s . Numbers i n d i c a t e t h e number o f empty s q u a r e s between p i e c e s o r t h e edge of t h e b o a r d . A p l u s a t t h e end means t h a t w h i t e i s t o move i n t h e p o s i t i o n w h i l e a minus means t h a t b l a c k i s t o move. As e x a m p l e s , Win a t C h e s s #9 i s t h e p o s i t i o n shown i n F i g u r e 1, w h i l e F i g u r e 2 i s g i v e n by 83k44pPp13pP1P12pP42P53K48+ The s e c o n d l i n e , i n d e n t e d by 3 s p a c e s , g i v e s t h e p r o b l e m number and t h e p r o b l e m s o l u t i o n ( s ) . The p r o b l e m s o l u t i o n i s t h e move t o be p l a y e d w h i c h g i v e s t h e b e s t r e s u l t . Sometimes more t h a n one b e s t move i s a v a i l a b l e . The c o r r e c t i o n s o f T a b l e I have been i n c l u d e d . 2rr3kpp3pp11nnqbNIp3pN32pP42P3QlPPB4PR4RK1+ Win a t C h e s s #1 MV=Qg3-g6 87p5k25p2p1p2P2Pr1pPK21P1R3P8-Win a t C h e s s #2 MV=Rb3xb2 5rk11ppb3pp1pb46q13P1p1r2P1R2PPP1BQ1P15RKN+ Win a t C h e s s #3 MV=Re3-g3 r1bq2rkpp3pbp2p1p1pQ7P3P42PB1N2PP3PPR2KR4+ Win a t C h e s s #4 MV=Qh6xh7 5k26ppp1qN41p1p43P42PKP2QPP3r23R4-Win a t C h e s s #5 MV=Qc6-c4 7kp71R5K6r16p16P188+ Win a t C h e s s #6 MV=Rb6-b7 rnbqkblrpppplppp84P36n17PPPPNPPP1R1BQKBNR-Win a t C h e s s #7 MV=Ng4-e3 r4q1kp2bR1rp2p2Q1N5p25p22P5PP3PPPR5K1+ Win a t C h e s s #8 MV=Re7-f7 3q1rk1p4pp12pb3p3p46Pr1PNQ4P1PB1PP14RRK1 -Win a t C h e s s #9 MV=Bd6-h2 2br2k12q3rnp2NppQ12p1P3Pp5R4P31P3PPP3R2K1+ Win a t C h e s s #10 MV=Rh4xh7 r1b1kb1r3q1ppppBp1pn28Np3P25B2PPP3PPR2Q1RK1+ Win a t C h e s s #11 MV=Bf3xc6 4k1r12p3r11pR1p33pP2p3P2qPP4N21PQ4P5R1K-Win a t C h e s s #12 MV=Qg4xf3 5rk1pp4p12n1p2p2Npq32p56P1P3P1BPR4Q1K+ Win a t C h e s s #13 MV=Qf1xf8 r2rb1k1pp1q1p1p2n1p1p12bp45P2PP1BPR1Q1BPN2PPR5K1 Win a t C h e s s #14 MV=Qh3xh7 1R61brk2p14p2pp1P1Pp2P76P11P4P12R3K1+ Win a t C h e s s #15 MV=Rb8xb7 r 4 r k1ppp2ppp2n52bqp38P2PB31PP1NPPPR2Q1RK1 + Win a t C h e s s #16 MV=Ne2-c3 1 k5rpppbn1pp4q1r11P3p22NPp31QP5P4PPPR1B1R1K1 + Win a t C h e s s #17 MV=Nc4-e5 R7P4k28888r76K1+ Win a t C h e s s #18 MV=Ra8-h8 r1b2rk1ppbn1ppp4p31QP4q3P4N4N2 5PPPR1B2RK1 + Win a t C h e s s #19 MV= c 5 - c 6 r2qkb1r1ppblpppp74p3P1Q1P32P55PPPR1B2KNR-Win a t C h e s s #20 MV=Bd7-b5 5rk11b3p1ppp3p23n1N21P6P1qB1PP13Q3P4R1K1+ Win a t C h e s s #21 MV=Qd2-h6 r1bqk2rppp1nppp4p3n5N12BPp3P1P52P2PPPR1BQK2R+ Win a t C h e s s #22 MV=Ng5xf7 r3nrk12p2p1pp1p1b1p12NpPq23R4P1N1Q31PP2PPP4R1K1+ Win a t C h e s s #23 MV= g2-g4 6k11b1nqpbppp4p15P21PN54Q3P5PP1B2B1K1-Win a t C h e s s #24 MV=Bg7-d4 3R.1 rkl85Qpp2p52P1p1q1P3P31P2PK28-Win a t C h e s s #25 MV=Qg4-h4 3r2k11p1b1pp1pq5p83NR32PQ3PPP3PP16K1-Win a t C h e s s #26 MV=Bd7-f5 7kpp4np2p3p13pN1q13P4Q71r3rPP2R2RK1+ Win a t C h e s s #27 MV=Qa3-f8 1r1r2k14pp1p2p1b1p1p3R3RqBP44P31PQ2PPP6K1-Win a t C h e s s #28 MV=Qb4-e1 r2q2k1pp1rbppp4pn22P5lP3B26P1P3QPBP1R3RK1+ Win a t C h e s s #29 MV= c 5 - c 6 1r3r24q1kpb1pp2p15p2pPn1N36P1P3PPBP2QRR1K1+ Win a t C h e s s #30 MV=Ne4xd6 rb3qk1pQ3ppp4p33P481P3N21P3PPP3R2K1+ Win a t C h e s s #31 MV= d5-d6 o r MV=Qb7xa8 6k1p4p1p1p3np12q54p34P1N1PP3PPP3Q2K1+ Win a t C h e s s #32 MV=Qd1-d8 8p1q2pkp2Pr2pl8P3Q36P15P1P2R3K1+ Win a t C h e s s #33 MV=Qe4-e5 o r MV=Qe4-f4 7k1b1r2p1p6p1p2qN23bP33Q4P5PP1B1R3K-Win a t C h e s s #34 MV=Bd4-g1 r3r2k2R3pppp1q1p283P3R7PPP3PP13Q2K1+ Win a t C h e s s #35 MV=Rh4xh7 3r42p1rk2lpQq1pp17p1P1P4P4P26PPR1R3K1-Win a t C h e s s #36 MV=Re7-e1 2r52rk2pp1pn1pb2pN1p4P2P41N2B3nPR1KPPP3R4-Win a t C h e s s #37 MV=Nc6xd4 4k3p4prp1p62b582Q3P1P2R1PKP4q3+ Win a t C h e s s #38 MV=Rd2-d8 r1br2k1pp2bppp2nppn282P1PB22N2P2PqN1B1PPR2Q1R1K+ Win a t C h e s s #39 MV=Nc3-a4 3r1r1k1p4ppp4p281PQR46PqP3PP22R3K1-Win a t C h e s s #40 MV=Rd8-c8 1k65RP11P61K66r1888+ Win a t C h e s s #41 MV=Kb5~a5 r1b1r1k1pp1n1pbp1qp3p13p41B1P4Q3PN2PP2BPPPR4RK1+ Win a t C h e s s #42 MV=Bb4-a5 r 2q3kp2P3p1 p3p23QP1 r 1 8B7P5PP2R3K1'+ Win a t C h e s s #43 MV=Qd5xa8 o r MV=Ba3-e7 3rb1k1pq3pbp4n1p13p42N52P2QB1PP3PPP1B1R2K1-Win a t C h e s s #44 MV= d5xc4 7k2p1b1pp8lp2P31P3r22P3Q11P5PR4qBK-Win a t C h e s s #45 MV=Qf1xa1 r1bqr1k1pp1nb1p14p2p3p1p23P4P1N1PNP11PQ2PP13RKB1R+ Win a t C h e s s #46 MV=Nc3-b5 r1b2rk1pp2bppp2n1pn2q5B12BP42N2N2PP2QPPP2R2RK1 -Win a t C h e s s #47 MV=Nc6xd4 1rbqlrk1p1p1bppp2p2n28Q1BP42N5PP3PPPR1B2RK1-Win a t C h e s s #48 MV=Rb8-b4 2b3k14rrppp2p42pP2RQlpP1Pp1N1P3P1P1q66RK+ Win a t C h e s s #49 MV=Qh5xh7 k4r21R4pb1pQp1n1p3P45p1P3P2P1r1q1R2K8+ Win a t C h e s s #50 MV=Rb7xb6 r1bq1r2pp4k14p2p3pPp1Q3N1R1P2PB46P16K1+ Win a t C h e s s #51 MV=Rf4-g4 r1k5lp3q2lQpb43N1p25Pp13P2PpPPPK3P4R3+ Win a t C h e s s #52 MV=Re1-e7 6k16p1p73Pn35p24rBqPP4RP15QK1-Win a t C h e s s #53 MV=Re3-e1 r3kr21pp4p1p1p47q4P1n12PP2Q1PP4P1R1BB2K1 -Win a t C h e s s #54 MV=Qh5-h1 r3r1k1pp1q1pp14b1p13p2B13Q1R28PPP3PP4R1K1+ ' Win a t C h e s s #55 MV=Qd4xg7 r1bqk2rpppp1ppp5n22b1n34P31BP3Q1PP3PPPRNB1K1NR-Win a t C h e s s #56 MV=Bc5xf2 r3q1krppp53p2pQ83PP1b15R2PPP3P15RK1+ Win a t C h e s s #57 MV=Rf3-f8 882R51p2qp1k1P2r32PQ2P15K28+ Win a t C h e s s #58 MV=Qd3-d1 r1b2rk12p1qnbpplpp2p15p22PQP31PN2N1PPB3PP13R1RK1+ Win a t C h e s s #59 MV=Nc3-d5 rn1qr1k11p2np22p3p181pPb47QPB1P1PP12KR1B1R+ Win a t C h e s s #60 MV=Qh3-h8 3qrbk1ppp1r2n3pP2p3P42P4P1P3Q2PB6R4R1K+ Win a t C h e s s #61 MV=Qf3-f7 6r13Pn1qkp1p1P1rp2Q2p22P51P4P1P3R2P5RK1-Win a t C h e s s #62 MV=Rg6xg3 r1brnbk1ppq2pp14p2p4N33P4P1PB1Q23B1PPPR3R1K1+ Win a t C h e s s #63 MV=Ne5xf7 86pp3q1p23n1k21P63NQ2P5PP16K1+ Win a t C h e s s #64 MV= g2-g4 1r1r1qk1p2n1p1pbplPn1pQ2pNp32P2P1N1P5BP6P3R1RK1+ Win a t C h e s s #65 MV=Nd5-e7 1k1r2r1ppq51bp4p3pQ382P2N2PP4P1R4R1K-Win a t C h e s s #66 MV=Qc7xe5 3r2k1p2q41p4p13rRp1p5P1P6PKP3R33Q4+ Win a t C h e s s #67 MV=Re5xd5 6k15ppp1q62b582R1pPP11P2Q2P7K+ Win a t C h e s s #68 MV=Qe2xe3 2k5pppr44R34Q32pp2q18PPP2PPP6K1+ Win a t C h e s s #69 MV= f 2 - f 3 2kr3rpppq1ppp3p1n2bQ2p31n1PP31PN1BN1 PIPP2PP12KR3R-Win a t C h e s s #70 MV=Nb4-a2 2kr3rpp1q1ppp5n21Nb52Pp1B27QP4PPP1R3RK1+ Win a t C h e s s #71 MV=Nb5xa7 r3r1k1pp1n1ppp2p54Pb22B2P2B1P5P5PPR2R2K1+ Win a t C h e s s #72 MV= e5-e6 r1q3rk1ppbb1p14Np1pp3pP2P3P32N4R1PP1Q1PP3R2K1+ Win a t C h e s s #73 MV=Qe2-d2 5r1kpp4pp2p52b1P34Pq21PB1p3P3Q1PP3N2K1-Win a t C h e s s #74 MV=Qf4-f1 r3r1k1pppq1ppp88lQ4n17PPPP2PP1RNB1R1K1-Win a t C h e s s #75 MV=Qd7-d6 r 1 b 1 q r k12p2ppppb1pnn21p2pNB13PP31BP5PP2QPPPRN1R2K1 Win a t C h e s s #76 MV=Bg5xf6 3r2k1ppp2ppp6q1b4n23nQB22p5P4PPPRN3RK1-Win a t C h e s s #77 MV=Nf5-g3 r2q3rppp2k24nbp15Q1p2P1NB28PP3P1P3RR1K1+ Win a t C h e s s #78 MV=Ne4-g5 r3k2rpbp2pp13b1n21p63P3p1B2N1PqPP1PQP1PR1B2RK1-Win a t C h e s s #79 MV=Qh3xh2 r4rk1p1B1bpp11p2pn1p82PP43B1P2qP2QP1P3R1RK1+ Win a t C h e s s #80 MV=Rd1-a1 r4rk11bR1bppp4pn21p2N31P6P3P34BPPP3R2K1 -Win a t C h e s s #81 MV=Be7-d6 3rr1k1pp3pp14b382P1B2R6QPP3q1P15R1K+ Win a t C h e s s #82 MV=Be4-h7 3rr1k1ppqbRppp2p583Q1n22P3N1PPB2PPP3R2K1+ Win a t C h e s s #83 MV=Qd4xd7 r2q1r1k2p1b1ppp1n51p1Q1bN14n31BP1B3PP3PPPR4RK1+ Win a t C h e s s #84 MV=Qd5-g8 kr2R3p4r22pg42N2p1p3P2p1Q5P15P1P5BK1+ Win a t C h e s s #85 MV=Nc5-a6 8p71ppk1n25pppP1PP42P1K1P15N1 PS-Win a t C h e s s #86 MV=Nf6-g4 Sp3k1p14r32ppNpp1PP1P42P3KP5P28-Win a t C h e s s #87 MV=Re6xe5 r6kp1Q4p2p1b1 rq4p3B3P34P3PP.P3P1 4RRK1 -Win a t C h e s s #88 MV=Rg6xg2 1r3b1kp4rpp4pp23q42ppbPPQ6RKPP5P2B1NR2-Win a t C h e s s #89 MV= g7-g5 3qrrk11pp2pp11p2bn1p5N22P5P1P3B11P4PP2Q1RRK1+ Win a t C h e s s #90 MV=Nf5xg7 2qr2k14b1p12p2p1p1pP1p3p2nP3PbQNB1PP1P3PK14RB2 Win a t C h e s s #91 MV=Bb3-e6 r4rk11p2ppbpp2pbnp1q73BPPP12N2B2PPP4PR2Q1RK1-Win a t C h e s s #92 MV=Be6xg4 r1b1k1nrpp3pQp4pq23pn38P1P52P2PPPR1B1KBNR+ Win a t C h e s s #93 MV=Bc1-h6 8k7p7 3Qp2Pn1P53KP31q68-Win a t C h e s s #94 MV= e5-e4 2r5lr64pNpk3pP1qp82P1QP25PK1R7+ Win a t C h e s s #95 MV=Nf6-g4 r1b4kppp2Bb16Pp3pP31qnP1p1Q8PPP3P11K1R3R+ Win a t C h e s s #96 MV=Qh4-d8 6k15p2p5np4B33P41PP1q3P3r1QP6RK+ Win a t C h e s s #97 MV=Qg2-a8 1r3rkl5pb1p2p2p1Q1n1q2p1NP1P33p1P1BPP1R3P1K2R3 Win a t C h e s s #98 MV=Nc5xe4 o r MV=Nc5-b3 r1bq1r1k1pp1Np1pp2p2pQ4R3n78PPPP1PPPR1B3K1 + Win a t C h e s s #99 MV=Re5-h5 8k1b5P4p21Pp2p1pK1P2P1P83B48+ Win a t C h e s s #100 MV= b5-b6 5rk1p5pp882Pbp31P4P17P4RN1K-Win a t C h e s s #101 MV=Bd4-c3 2Q2n22R4p1p1qpp1k83P3P3B2P15PK1r7+ Win a t C h e s s #102 MV=Qc8xf8 6k12pb1r1p3p1PpQplnPp31q2P32N2P2PrB52K3RR+ Win a t C h e s s #103 MV=Qh6xg6 b4r1kpq2rp2lp1bpn1p3PN2n2P2P2P2B3K1B2Q2N3R2R1+ Win a t C h e s s #104 MV=Qe2xh5 r2r2k1pb3ppp1p1bp37q3n2nPPP1B2P11B1N1P2RQ2NRK1 Win a t C h e s s #105 MV=Qh5xh4 4rrk1pppb47p3P2pq3Qn3P5P11PP4PR3RNNK-Win a t C h e s s #106 MV=Ne4-f2 5n2pRrk2p1P4p1p4p33N45P26PP6K1+ Win a t C h e s s #107 MV=Nd4-b5 r5k11q4pp2p5p1Q52P55R24RKPPr7+ Win a t C h e s s #108 MV=Qc5-e5 rn2k1nrpbp2ppp3q41p2N32p5QP6PB1PPPPPR3KB1R-Win a t C h e s s #109 MV= c 4 - c 3 2kr4bp3p2p2p2b1P72q5lN4B11PPQ2P12KR4-Win a t C h e s s #110 MV=Ba7-e3 6k1p5p15p22P2Q23pN2p3PbK1P7P6q1-Win a t C h e s s #111 MV=Qg1-f1 r4kr1ppp54bq1b7B2PR1Q1p2N3P1PP3P1P2K1R3+ Win a t C h e s s #112 MV=Re1xe6 rnbqkblr1p3ppp5N2lp2p1B12P58PP2PPPPR2QKB1R-Win.at C h e s s #113 MV=Qd8xf6 r1b1rnk11p4ppp1p2p23pN2n3P1PPq2NBPR1PPPQ52R3K1 Win a t C h e s s #114 MV=Bd3xh7 4N2k5rpp1Q6p3q38P5P11P3P1P5K2+ Win a t C h e s s #115 MV=Ne8-d6 r2r2k12p2pppp71p2P1n1P6q5P21PB1QP1PR5RK-Win a t C h e s s #116 MV=Rd8-d2 3r1rk1q4pppp1Rnp381p61N3P2PP3QPP3R2K1-Win a t C h e s s #117 MV=Nd6-e4 r5k1pb2rpp11p62p4q5R22PB2Q1P1P3PP5R1K+ Win a t C h e s s #118 MV=Rf4-h4 r2qr1k1p1p2ppp2p52b54nPQ13B4PPP3PPR1B2R1K-Win a t C h e s s #119 MV=Qd8xd3 r4rk11bn2qnp3p1B1Qp2P1pP11pp55N1PPPB2P22KR3R+ Win a t C h e s s #120 MV= g5-g6 6k15p1p2bP2pb4p32P51p1pNPPP1P1QlBK11q6-Win a t C h e s s #121 MV=Bc6xf3 1k6ppp4p1n2pq21N2Rb22P2Q28P4KPP3r1B2-Win a t C h e s s #122 MV=Rd1xf1 6k11b2rp21p4p13P4PQ4P12N2q25P23R2K1-Win a t C h e s s #123 MV=Bb7xd5 o r MV=Re7-c7 6k13r42R5P5P11P4p184rB26K1-Win a t C h e s s #124 MV= g4-g3 r1bqr1k1pp3ppp1bp53n43B42N2P1PPPP1B1P1R2Q1RK1-Win a t C h e s s #125 MV=Bb6xd4 r5r1pQ5p1qp2R22k1p34P32PP4P1P3PP6K1+ Win a t C h e s s #126 MV=Rf6xc6 2k4r1pr1n3p1p1q2p5pp13P1P2P1P1P31R2Q1PP1RB3K1+ Win a t C h e s s #127 MV=Rb2xb7 6rk1pp2Qrp3p1B21pb1p2R3n1q23P4PPP3PPR6K+ Win a t C h e s s #128 MV=Qf7-g6 3r1r1k1b2b1p11p5p2p1Pp2q1B2P24P2P1BR1Q2K6R1-Win a t C h e s s #129 MV=Bb7-f3 6k11pp3q15r21PPp43P1pP13Qn2P3B44R1K1-Win a t C h e s s #130 MV=Qg7-h6 o r MV=Qg7-h8 2rq1bk1p4p1p1p4p13b43B1Q28P4PpP3RR1K1+ Win a t C h e s s #131 MV=Re1-e8 4r1k15bpp2p53pr381B3pPqPPR2P22R2QK1 -Win a t C h e s s #132 MV=Re5-e1 r1b1k2r1pp1q2pp1n3p13QPp281BP3B1P5PP3R1RK1+ Win a t C h e s s #133 MV=Bg3-h4 3r2k1p6p2Q3p14q32P1p3P3Pb21P3P1P2K2BR1-Win a t C h e s s #134 MV=Rd8-d1 3r1r1kN2qn1pp1p2np22p52Q1P2N3P4PP4PP3R1RK1-Win a t C h e s s #135 MV=Ne6-d4 6kr1q2r1p11p2N1Q15p21 PIp46R17P2R3K1 + Win a t C h e s s #136 MV=Rc1-c8 3b1rk11bq3pp5pn11p2rN22p1p32P1B2Q1PB2PPPR2R2K1 Win a t C h e s s #137 MV=Rd1-d7 r1bq3rppppR1p15n1k3P46pP3Q4PP1N1PP15K1R+ Win a t C h e s s #138 MV=. h4-h5 rnb3krppp2ppp1b63q43pN3Q4N2PPP2KPPR1B1R3+ Win a t C h e s s #139 MV=Ne4-f6 r2b1rk1pq4p14ppQP3pB1p13P42R5PP3PP15RK1+ Win a t C h e s s #140 MV=Rc3-c7 4r1klplqr1p22pb1Bp11p5p3P1n1R1B3P2PP3PK12Q4R+ Win a t C h e s s #141 MV=Qc1xf4 r2q3nppp2pk13p45Pr12NP1Qp12P2pP1PP3K24R2R+ Win a t C h e s s #142 MV=Re1-e8 5b2pp2r 1 pk2pp1 pRp4rP1 N2P1 P31 P4QPP3q1 P1. 5R1K+ Win a t C h e s s #143 MV=Rg6xh6 r2q1rk1pp3ppp2p2b28B2pPPb17PPPP1N1P1R2Q1RK1 -Win a t C h e s s #144 MV= d4-d3 r1bq41p4kp3p1n2p4pB12pQ481P4PP4RRK1+ Win a t C h e s s #145 MV=Re1-e8 882Kp43P1B22P2k25p288+ Win a t C h e s s #146 MV=Bf5-c8 r2r2k1ppqbppbp2n2npl2pp46P11P1PPNNPPBP2PB1R2QK2R-Win a t C h e s s #147 MV=Nf6xg4 2r1k36prp1nBP31p3p1p2q52P5P1R4PK2Q2R1+ Win a t C h e s s #148 MV=Rg1xg7 6k16p12p4p4Pp24b1qP2Br41P2RQPK8-Win a t C h e s s #149 MV=Be4xg2 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888lp5rp1p1k1pNP2pBpP11P1K1P28-Win a t C h e s s #229 MV= b5-b4 2b51r62kBp1p1p2pP1P12pP41pP3K11R3P28-Win a t C h e s s #230 MV=Rb7-b4 r4rk11b1nqp1pp5p11p2PQ22p55N2PP3PPPR1BR2K1+ Win a t C h e s s #231 MV=Bc1-g5 1R2rq1k2p3p1Q2p1pPp84P38P1r3PP1R4K1+ Win a t C h e s s #232 MV=Rb8xe8 5rk1p1p2r1p2pp2p14p3PPPnP33Pq1PI 1Q1R1R1P4NK2-Win a t C h e s s #233 MV=Nd4-b3 2kr1r2p6p5Pp12p5lqp2Q1P7RPP61KR5+ Win a t C h e s s #234 MV=Rh3-b3 5r21p1RRrk14Qq1p1PP3p184B31b3P1P6K1+ Win a t C h e s s #235 MV=Re7xf7 o r MV=Qe6xf7 1R6p5pk4p2p4P382r3qPP3R1b14Q1K1-Win a t C h e s s #236 MV=Rc3-c1 r5k1pQp2qpp84pbN13P46P1PPr4P1K1R3R-Win a t C h e s s #237 MV=Rc2-c1 1k1r4pp1r1pp14n1p12R52Pp1qP13P2QPP4PB11R4K1+ Win a t C h e s s #238 MV=Bg2xb7 86k15pp1Q6p5P26PKP4q1P8-Win a t C h e s s #239 MV=Qf2-f1 2b4kp1b2p22p2q23p1PNp3P2R13B4P1Q2PKP4r3+ Win a t C h e s s #240 MV=Qc2xc6 2rq1rk1pp3ppp2n2b24NR23P4PB5Q1P4PP3R2K1+ Win a t C h e s s #241 MV=Qh3xh7 r1b1r1k1pp1nqp22p1p1pp84N3P1Q1P3lP3PPP1BRR2K1+ Win a t C h e s s #242 MV=Rd1xd7 1r3r1k3p41p1Nn1R14Pp1qpP3P1pP75Q1P6RK+ Win a t C h e s s #243 MV=Qf2-e2 r6rpp3ppp3k1b22pb4B4Pq12P1Q3P5PP1RBR2K1+ Win a t C h e s s #244 MV=Qe3xc5 4rrn1ppq3bk3pPnpp2p52PB42NQ1RPBPP5P5R1K+ Win a t C h e s s #245 MV=Qd3xg6 6R14qp1pppr1n1pk8lP2P1QP6N1P4PP16K1+ Win a t C h e s s #246 MV=Qg4-h5 2k1r31p2Bq2p2Qp3Pb1p1p1P2pP1P22P52P2KP11R6+ Win a t C h e s s #247 MV=Rb1xb5 5r1k1p4pp3q43Pp1R188PP4PP4Q1K1 -Win a t C h e s s #248 MV=Qd6-c5 r4rk1pbq2pp11ppbpn1p82PP41P1Q1N2PBB2PPPR3R1K1+ Win a t C h e s s #249 MV= c 4 - c 5 1b5k7Pp1p2np12P2p2PP3P24RQ1Rq2r3P6K1+ Win a t C h e s s #250. MV=Re3-e8 k7p4p2P1q1b1p13p3p3Q47P5PP11R4K1+ Win a t C h e s s #251 MV=Qd4-e5 o r MV=Qd4-f4 1rb1r1k1p1p2ppp5n22pP45P22QB4qNP3PP2KRB2R-Win a t C h e s s #252 MV=Re8-e2 k5r1p4b22P55p23P1P24QBrqP5P14R1K1+ Win a t C h e s s #253 MV=Qe3-e8 r6kpp3p1p2p1bp1qb3p34Pnr12PP2NPPP1Q1PPNR2B2RK-Win a t C h e s s #254 MV=Nf4xh3 3r3rp4pk1 5Rp1. 2q41 piP2RQ5N2P1P4P2biK+ Win a t C h e s s #255 MV=Rf6xg6 3r1rk11pb1qp1p2p3p1p7P2Np2R1P5P1BP2PP13Q1BK1+ Win a t C h e s s #256 MV=Nd4-f5 4r1k1pq3p1p2p1r1pl2Qlp33nN1P11P6P1P2P1P3RR1K1+ Win a t C h e s s #257 MV=Rd1xd4 r3brkn1p5p2p2Ppq2Pp3B3Pp2Q4P1R16PP5R1K+ Win a t C h e s s #258 MV=Bh5xg6 r1bq1rk1ppp2ppp2np42bN1PN12B1P33p4PPP2nPPR1BQ1K1R+ Win a t C h e s s #259 MV=Qd1-h5 2r2b1rp1Nk2pp3p1p2N2Qn34P3q6PP4PP11R3K1R+ Win a t C h e s s #260 MV=Qd5-e6 r5k11bp3ppp2p41p65p21PBP1nqP1PP3Q1R4R1K-Win a t C h e s s #261 MV=Nf3-d4 6k1p1B1b2p2b3rf2p54p31PP1N1PqP2R1P23Q2K1-Win a t C h e s s #262 MV=Rg6-h6 rnbqr2kpppp1Qpp8b2NN32B1n38PPPP1PPPR1B1K2R+ Win a t C h e s s #263 MV=Qf7-g8 r2r2k11R2qp2p5pp2P5b1PN1b2P71Q3PPP1B1R2K1 -Win a t C h e s s #264 MV=Rd8xd4 o r MV=Ra8-b8 2r1k2r2pn1pp11p3n1pp3PP24q2BP1P52Q1N1PPR4RK1+ Win a t C h e s s #265 MV= e 5 x f 6 r3q2r2p1k1p1p5p11p2Nb21P2nB2P72PNQbPPR2R3K-Win a t C h e s s #266 MV=Rh8xh2 2 r1kb1rpp3ppp2n1b31q1N2B11P2Q38P4PPP3RK1NR+ Win a t C h e s s #267 MV=Nd5-c7 2r3krppp2n1p7B5q1N1bp52Pp4PP2RPPPR2Q2K1+ Win a t C h e s s #268 MV=Re2-e8 2kr2nrpp.1n1ppp2p1p3q7lb1P1B2P1N2Q1P1PP1BPP1R3K2R+ Win a t C h e s s #269 MV= a3xb4 2r1r1k1pp1q1ppp3p1b23P43Q45N2PP2RPPP4R1K1+ Win a t C h e s s #270 MV=Qd4-g4 2kr4ppp3Pp4RP1B2r55P21P6P2p43K4+ Win a t C h e s s #271 MV=Re6-d6 nrq4r2k1p31p1pPnp1pRpP1p2P1P2P22P1BB21R2Q1P16K1+ Win a t C h e s s #272 MV=Be3xc5 2k4Bbpp1qp2p1b57p1PN1n1p12Pr4P5PPR3QR1K-Win a t C h e s s #273 MV=Ne4-g3 8lp6p5R1k7Prpp4K71NP58+ Win a t C h e s s #274 MV=Rg6-b6 r1b2 r k 1 1 pin1pppplp2q24p3P1B1Pn21QN2N21P3PPP3R1RK1-Win a t C h e s s #275 MV=Nf4xg2 r5k1pp1RR1pp1b66r12p5B6PP4qPK3Q4+ Win a t C h e s s #276 MV=Qd1-d5 1r4r1p2kb2pbq2p33p1p25P22BB3QPP4PP3RKR2-Win a t C h e s s #277 MV=Rg8-g3 o r MV=Rg8xg2 r2qkb1rpppb2pp3p1n25pN12BQP32N5PPP2PPPR1B1K2R+ Win a t C h e s s #278 MV=Bc4-f7 r74b32p1r1k11p1pPp1q1P1P1P1pPR2NRpP2Q3K18+ Win a t C h e s s #279 MV=Ne3xf5 r1r2bk15p1ppn4p1N2b43Pp3B3P32q1BPPPRQ3RK1-Win a t C h e s s #280 MV=Bf8xa3 83 2R52R4p5p1k6n181P2QPPqr76K1+ Win a t C h e s s #281 MV=Rc7xh7 6k12p3p11p1p1nN11B1P44PK282r3b17R+ Win a t C h e s s #282 MV=Rh1-h8 3 q 1 r k l 4 b p 1 p i r.2?2Q3p1 p26r1Pp2R2N•34PP7K+ Win a t C h e s s #283 MV=Nh3-g5 3r3kpp4pp8lP63N4Pn2P1qb1B1Q2B12R3K1+ Win a t C h e s s #284 MV=Nd4-f5 2rr3k1b2bppPp2p1n2R73P41qB2P21P4Q11K5R+ Win a t C h e s s #285 MV=Qg2xg7 3r 1 k21p6p4P22pP2Qb81P1KB3P6r8-Win a t C h e s s #286 MV=Rd8xd5 rn3k1rpp2bBpp2p2n2q5N13P41P6P1P3PPR1BQ1RK1+ Win a t C h e s s #287 MV=Qd1-h5 r1b2rk1p4ppp1p1Qp34P2N1P68P3qPPP3R1RK1+ Win a t C h e s s #288 MV=Nh5-f6 2r3k15p1pp3q1p12n3P11p1QP2P1P4N1PK62R5-Win a t C h e s s #289 MV=Qe6-e5 2k2r22p51pq5p1p1n3P1P2n1B1R4Pp2QR46K1-Win a t C h e s s #290 MV=Nf4-e2 5r1k3b2p1p6p1pRpR31P1P2q1P4pP15QnP1B4K1+ Win a t C h e s s #291 MV= h2-h3 4r3lQ1qk2pp4pp13Pb3P76PP5P24R1K1+ Win a t C h e s s #292 MV= d5-d6 1nbq1r1k3rbp1pp1p1pp1Q1p6P1pPN35NP11P2PPBPR4RK1 + Win a t C h e s s #293 MV=Nf3-g5 3r3k1r3p1pp1pB1p28p1qNP1Q1P6P1P4P13R3K+ Win a t C h e s s #294 MV=Nd5-f5 o r MV=Bd6-f8 4r3p4r1pR1p2pp11p1bk34pNPP2P1K32P2P23R4+ Win a t C h e s s #295 MV=Rd1xd5 3r41p3k1pp1b1p1p14Q1Pn2B3KP4pP2PP2R1N16q1-Win a t C h e s s #296 MV=Rd8-d4 o r MV=Bc6-d7 o r MV=Bc6xf3 3r1rk1p3qp1p2bb2p12p53P41P6PBQN1PPP2R2RK1-Win a t C h e s s #297 MV=Bd6xh2 3Q4p3b1k12p2rPp2q54B3P2P47P6RK+ Win a t C h e s s #298 MV=Qd8-h8 1 n2rr21pk3pppNn2p22N1p386P1PP2PPKP2RR4 + Win a t C h e s s #299 MV=Nc5-a4 b2b1r1k3R1ppp4qP24p1PQ4P35B24N1K18+ Win a t C h e s s #300 MV= g5-g6 84 A p p e n d i x 3: R e s u l t s o f TECH3 on T e s t P r o b l e m s Summarized o u t p u t f r o m TECH3 on e a c h o f t h e t e s t p r o b l e m s i s l i s t e d on t h e n e x t 14 p a g e s . A f t e r e a c h i t e r a t i o n a l i n e i s p r i n t e d . The i n f o r m a t i o n on e a c h l i n e c o n s i s t s o f : (1) The i t e r a t i o n d e p t h . I f t h e i t e r a t i o n d e p t h e q u a l s 31 t h e n a f o r c e d m a t i n g c o m b i n a t i o n has been f o u n d and c l e a r l y i t i s n o t n e c e s s a r y t o s e a r c h f u r t h e r . (2) The change i n s c o r e . A p o s i t i v e change i s good f o r t h e s i d e -to-move. F o r example a change o f 5 means t h a t t h e s i d e - t o - m o v e c a n improve t h e m a t e r i a l b a l a n c e f r o m h i s p o i n t o f view by t h e e q u i v a l e n t o f a rook o v e r what i t i s i n t h e g i v e n p o s i t i o n . I f t h e i t e r a t i o n d e p t h i s 31 t h e n t h e change i n s c o r e i s l a r g e s i n c e t h e v a l u e of w i n n i n g i s 63. (3) The move TECH3 would p l a y . T h i s i s compared w i t h t h e p r o b l e m s o l u t i o n s t o d e t e r m i n e i f TECH3 g e t s c r e d i t . (4) The CPU t i m e , i n s e c o n d s , u s e d so f a r i n t h e c o m p u t a t i o n . The n o t a t i o n ">300." means t h a t t h e n e x t i t e r a t i o n c o u l d n o t be c o m p l e t e d i n l e s s t h a n 300 s e c o n d s . Win a t C h e s s # 1 2 0 Ne5xc6 .008 3 0 Ne5xc6 .057 31 65 Qg3-g6 .314 Win a t C h e s s # 2 2 0 K f 6 - f 7 .002 3 0 Kf 6- f7 .016 4 0 Kf 6- f 7 .047 5 0 Kf 6- f 7 .094 6 0 Kf 6- f 7 .209 7 0 Kf 6- f7 .550 8 0 Kf 6- f 7 1.17 9 0 Kf 6- f 7 2.44 10 0 Kf 6- f 7 6.56 1 1 0 K f 6 - f 7 12.2 1 2 0 Kf 6- f 7 24.5 13 0 Kf 6- f 7 58.3 14 0 Kf 6- f 7 1 49. >300. Win a t C h e s s # 3 2 1 Re3-g3 .036 3 1 Re3-g3 .0J1 4 1 Re3-g3 . 156 5 1 Re3-g3 .395 6 1 Re3-g3 1.15 Win a t C h e s s # 4 31 63 Qh6xh7 .006 Win a t C h e s s # 5 31 66 Qc6-c4 .006 Win a t C h e s s # 6 2 1 Kh6xg5 .002 3 1 Kh6xg5 .009 4 5 Rb6-b7 .029 5 5 Rb6-b7 .048 6 6 Rb6-b7 .086 7 6 Rb6-b7 .153 8 6 Rb6-b7 .257 9 6 Rb6-b7 .414 10 6 Rb6-b7 .676 Win a t C h e s s # 7 2 1 Ng4xe5 .002 3 1 Ng4xe5 .014 4 1 Ng4xe5 .052 5 6 Ng4-e3 .153 6 6 Ng4-e3 .400 7 6 Ng4-e3 1 .22 Win a t C h e s s # 8 2 1 Nh6-f7 .017 3 4 R e 7 - f 7 .055 4 4 R e 7 - f 7 . 1 39 5 5 Re7-f7 .361 6 5 R e 7 - f 7 .870 TV7 i .-, e, •;-• 1X11 hi l_ C h e s s # 9 2 1 Rh4xg4 .011 3 3 Bd6-h2 .044 4 3 Bd6-h2 .125 31 66 Bd6-h2 .139 Win a t C h e s s # 10 2 2 Rh4xh7 .023 3 2 Rh4xh7 .059 4 2 Rh4xh7 . 1 93 5 3 Rh4xh7 .495 6 3 Rh4xh7 1 .50 Win a t C h e s s # 1 1 2 0 Qd1xd7 .008 3 1 B f 3 x c 6 .043 4 2 B f 3 x c 6 .198 5 7 B f 3 x c 6 .599 Win a t C h e s s # 12 31 67 Qg4xf3 .003 Win a t C h e s s # 13 . 2 2 Q f 1 x f 8 .011 3 2 Q f 1 x f 8 .040 4 2 Q f 1 x f 8 .111 5 2 Q f 1 x f 8 .285 6 2 Q f 1 x f 8 .818 Win a t C h e s s # 14 2 0 Bd3-e2 .009 3 3 Qh3xh7 .070 4 3 Qh3xh7 .224 5 3 Qh3xh7 .838 Win a t C h e s s # 15 2 0 b2-b3 .007 3 2 Rb8xb7 .030 4 2 Rb8xb7 .089 5 2 Rb8xb7 .278 6 2 Rb8xb7 .726 Win a t C h e s s # 16 2 0 Be3xc5 .001 3 0 Be3xc5 .024 4 0 Be3xc5 .062 5 0 Be3xc5 .169 6 3 Ne2-c3 1 .02 Win a t C h e s s # 1 7 2 0 Nc4-e5 .005 3 0 Nc4-e5 .127 4 0 Nc4-e5 .182 5 0 Nc4-e5 .346 6 1 Nc4-e5 2.98 Win a t C h e s s # 18 2 0 Kg1-h1 .004 3 0 Kg1-h1 .01 1 4 0 Kg1-h1 .045 5 0 Kg1-h1 .102 6 0 Kg1-f1 .420 7 0 K g 1 - f l .639 8 4 Ra8-h8 1 .72 9 4 Ra8-h8 2.36 10 4 Ra8-h8 3.46 1 1 4 Ra8-h8 6.24 Win a t C h e s s # 19 2 0 c 5 - c 6 .005 3 0 c 5 - c 6 .151 4 1 c 5 ~ c 6 .239 5 0 c 5 - c 6 .407 6 2 c 5 - c 6 1 .96 Win a t C h e s s # 20 2 0 g7-g6 .003 3 0 f 7 - f 6 . 1 35 4 6 Bd7-b5 .273 5 7 Bd7-b5 .390 6 7 Bd7-b5 .985 Win a t C h e s s # 21 2 0 Qd2xc3 .009 3 0 Qd2xc3 .040 4 0 Qd2xc3 . 1 78 5 1 Qd2-h6 .785 Win a t C h e s s # 22 2 0 Bc4-e2 .012 3 1 Ng5xf7 .047 4 1 Ng5xf7 .107 5 1 Ng5xf7 .252 6 1 Ng5xf7 .835 Win a t C h e s s # 23 2 0 Nc5xe6 .004 3 0 Nc5xe6 .088 4 0 Nc5xe6 .187 5 0 Nc5xe6 .437 6 3 g2-g4 2.82 Win a t C h e s s # 24 2 0 Qe7xe3 .005 3 0 Qe7xe3 .026 4 6 Bg7-d4 .137 5 6 Bg7-d4 .247 6 6 Bg7-d4 .634 86 Win a t C h e s s # 25 2 9 Qg4-h4 .010 3 9 Qg4-h4 .025 A s r> c c; • \J o 5 9 Qg4-h4 . 1 52 6 9 Qg4-h4 .321 7 10 Qg4-h4 .782 Win a t C h e s s # 26 2 1 Qb6xb2 .002 3 2 B d 7 - f 5 .138 4 2 B d 7 - f 5 .195 5 2 B d 7 - f 5 .294 6 2 B d 7 - f 5 1 .43 Win a t C h e s s # 27 31 66 Qa3-f8 .028 Win a t C h e s s # 28 2 0 Qb4xb2 .008 3 0 Qb4xb2 .027 4 2 Qb4-e1 .135 5 2 Qb4-e1 .265 6 2 Qb4-e1 .713 Win a t C h e s s # 29 2 0 B f 4 - g 5 .010 3 0 B f 4 - g 5 .086 4 0 B f 4 - g 5 .161 5 0 B f 4 - g 5 .325 6 2 c 5 - c 6 1 .29 Win a t C h e s s # 30 2 0 Ne4-g5 .018 3 0 Ne4-g5 . 106 4 0 Ne4-g5 .345 5 1 Ne4xd6 .840 Win a t C h e s s # 31 2 1 d5xe6 .005 3 2 d5xe6 .065 4 2 d5xe6 .130 5 2 d5-d6 .295 6 2 d5-d6 .793 Win a t C h e s s # 32 2 0 Ng3-h1 .006 3 1 Qd1-d8 .073 4 1 Qd1-d8 .138 5 1 Qd1-d8 .272 6 1 Qd1-d8 .820 Win a t C h e s s # 33 2 0 Qe4-e5 .009 3 0 Qe4-e5 .059 4 0 Qe4-e5 .186 5 0 Qe4-e5 .486 6 3 Qe4-e5 2.95 Win a t C h e s s i l 34 2 -2 Bb7xe4 .060 3 2 Bd4-g1 .112 4 2 Bd4-g1 . 1 45 5 2 Bd4-g1 .248 6 2 Bd4-g1 .996 Win a t C h e s s # 35 2 0 R c 7 - f 7 .007 3 0 R c 7 - f 7 .036 31 62 Rh4xh7 .138 Win a t C h e s s # 36 2 4 Re7-e1 .007 3 4 Re7-e1 .033 4 4 Re7-e1 . 1 64 5 4 Re7-e1 .459 6 4 Re7-e1 1 .45 Win a t C h e s s # 37 2 1 Nc6xd4 .021 3 1 Nc6xd4 .063 4 1 Nc6xd4 .215 5 1 Nc6xd4 .621 Win a t C h e s s # 38 2 4 Rd2-d8 .010 3 4 Rd2-d8 .031 4 4 Rd2-d8 .113 5 4 Rd2-d8 .336 6 4 Rd2-d8 -.941 Win a t C h e s s # 39 2 0 Bf4-d2 .012 3 4 Nc3-a4 .063 4 4 Nc3-a4 .102 5 4 Nc3-a4 .159 6 4 Nc3-a4 .593 Win a t C h e s s # 40 2 0 Rd8xd4 .004 3 4 Rd8-c8 .038 4 4 Rd8-c8 .099 5 4 Rd8-c8 .215 6 4 Rd8-c8 .512 Win a t C h e s s # 41 2 4 R f 7 - f 8 .005 3 4 R f 7 - f 8 .013 4 3 R f 7 - f 8 .087 5 4 Rf7-e7 .270 6 4 R f 7 - e 7 .501 7 4 Kb5-a5 1 .26 Win a t Ches s # 42 2 0 Bb4-d6 .023 3 0 Bb4-d6 .210 4 0 Bb4-d6 .357 5 0 Bb4-d6 .525 6 3 Bb4-a5 2.84 7 3 Bb4-a5 4.37 Win a t C h e s s # 43 2 0 Ba3-d6 .024 3 2 Ba3-e7 .090 4 2 Ba3-e7 . 182 5 2 Ba3-e7 .340 6 5 Ba3-e7 .944 Win a t Ches s # 44 2 0 Ne6-f8 .021 3 3 d5xc4 .105 4 3 d5xc4 .160 5 3 d5xc4 .256 6 3 d5xc4 1 .02 Win a t Ches s # 45 2 1 Qf1xa1 .004 3 5 Qf1xa1 .026 4 5 Qf1xa1 .084 5 5 Qf1xa1 .292 6 5 Qf1xa1 .721 Win a t C h e s s # 46 2 0 Nc3-e2 .012 3 0 Nc3-e2 .193 4 0 Nc3-e2 .346 5 0 Nc3-e2 .923 6 0 Nc3-e2 5.92 7 1 Nc3-b5 12.2 8 1 Nc3-b5 15.7 9 2 Nc3-b5 42.4 Win a t C h e s s # 47 2 1 Nc6xd4 .005 3 1 Nc6xd4 .024 4 1 Nc6xd4 .094 5 1 Nc6xd4 .296 6 1 Nc6xd4 1.13 Win a t C h e s s # 48 2 0 Rb8-b7 .079 3 0 Rb8-b7 .092 4 0 Rb8-b7 .224 5 0 Rb8-b7 .435 6 1 Rb8-b4 1 .89 Win a t C h e s s # 49 87 2 -1 e4-e5 .067 3 -1 e4-e5 .128 4 -1 e4-e5 .345 5 0 Qh5-h6 .906 6 C Qh5-h6 1.61 7 6 Qh5xh7 8.50 Win a t C h e s s # 50 2 6 Rb7xb6 .024 31 70 Rb7xb6 .030 Win a t C h e s s # 51 2 0 Nd4-f3 .019 3 5 Rf4-g4 .120 4 6 Rf4-g4 .316 5 10 Rf4-g4 1.25 Win a t C h e s s # 52 2 0 Nd5-c3 .014 3 0 Nd5-c3 .049 4 0 Nd5-c3 .295 5 1 Re1-e7 .906 Win ac C h e s s # 53 2 0 Re3xf3 .009 3 0 Re3xf3 .109 4 4 Re3-e1 .213 5 4 Re3-e1 .423 6 4 Re3-e1 .955 Win a t C h e s s # 54 31 62 Qh5-h1 .01 1 Win a t C h e s s # 55 2 0 Qd4-e5 .007 3 0 Qd4-f2 .205 4 0 Qd4-f2 .441 5 0 Qd4-f2 .838 31 64 Qd4xg7 1.51 Win a t C h e s s # 56 2 5 B c 5 x f 2 .017 3 5 B c 5 x f 2 .064 4 5 B c 5 x f 2 .209 5 5 B c 5 x f 2 .743 Win a t C h e s s # 57 2 0 R f 3 - £ 8 .011 31 65 Rf3.-f8 .016 Win a t C h e s s # 58 2 0 Rc6-c8 .017 3 1 Rc6-c5 .168 4 1 Rc6-c5 .388 5 4 Qd3-d1 1.12 Win a t C h e s s # 59 2 1 Qd4xg7 .015 3 1 Qd4xg7 .039 4 3 Nc3-d5 . 1 42 5 4 Nc3-d5 .349 6 4 Nc3-d5 .980 Win a t C h e s s # 60 31 66 Qh3-h8 .008 Win a t C h e s s # 61 31 65 Q f 3 - f 7 .009 Win a t Ches s # 62 2 0 Rg6-g5 .017 3 1 Rg6xg3 .066 4 1 Rg6xg3 .185 5 1 Rg6xg3 .902 Win a t C h e s s # 63 2 0 Ne5-g4 .019 3 1 Ne5xf7 .180 4 1 Ne5xf7 .398 5 1 Ne5xf7 .805 Win a t C h e s s # 64 2 0 Qe3-f3 .027 31 62 g2-g4 .091 Win a t C h e s s # 65 2 0 Qh6xf8 .030 3 5 Nd5-e7 .083 4 9 Nd5-e7 .218 5 9 Nd5-e7 .593 Win a t C h e s s # 66 2 0 Qc7xe5 .002 3 0 Qc7xe5 .023 4 0 Qc7xe5 .099 5 0 Qc7xe5 .208 6 0 Qc7xe5 .481 7 0 Qc7xe5 1 .61 Win a t C h e s s # 67 2 0 Qd1xd5 .006 3 4 Re5xd5 .032 4 4 Re5xd5 .083 5 4 Re5xd5 .196 6 4 Re5xd5 .524 Win a t C h e s s # 68 2 0 Rc3-c4 .003 3 1 Qe2xe3 .019 4 2 Qe2xe3 .067 5 3 Qe2xe3 . 1 22 6 3 Qe2xe3 .319 7 3 Qe2xe3 1.18 Win a t C h e s s # 69 2 0 Qe5-h8 .009 3 1 Re6-e8 .056 4 1 Re6-e8 . 1 56 5 1 f 2 - f 3 .504 Win a t Ches s # 70 2 6 Nb4-a2 .033 3 6 Nb4-a2 .070 4 6 Nb4-a2 .191 5 6 Nb4-a2 .534 Win a t C h e s s # 71 2 0 Qh3xd7 .006 3 0 Qh3xd7 .039 4 0 Qh3xd7 .165 5 0 Qh3xd7 .415 6 0 Qh3xd7 1 .89 7 0 Qh3xd7 6.70 8 0 Qh3xd7 25.5 9 0 Qh3xd7 78.6 1 0 0 Qh3xd7 210. >300. Win a t Ches s # 72 2 1 e5-e6 .013 3 1 e5-e6 .042 4 2 e5-e6 . 102 5 2 e5-e6 .219 6 2 e5-e6 .656 Win a t . Ch e s s # 73 2 0 Nc3-d5 .010 3 0 Nc3-d5 .031 4 0 Nc3-d5 .181 5 3 Qe2-d2 .535 Win a t ; C h e s s # 74 2 2 Q f 4 - f 1 .009 3 2 Q f 4 - f 1 .027 4 3 Q f 4 - f 1 .126 5 3 Q f 4 - f 1 .331 6 3 Q f 4 - f 1 1 .07 Win a t ; C h e s s # 75 2 0 Re8xe1 .003 3 0 Re8xe1 .031 4 0 Re8xe1 . 1 22 5 0 Re8xe1 .378 6 6 Qd7-d6 1.18 Win at : C h e s s # 76 2 0 Bb3xe6 .017 3 0 Bb3xe6 .068 4 0 Bb3xe6 .220 5 0 Bb3xe6 .613 6 2 B g 5 x f 6 2.33 7 2 B g 5 x f 6 7.38 Win a t C h e s s # 77 2 0 Nd4-e6 .008 3 0 Nd4-e6 .094 4 5 Nf5-g3 .320 5 6 Nf5-g3 .634 Win a t C h e s s # 78 2 1 Ne4-g5 .034 3 2 Ne4-g5 .121 4 2 Ne4-g5 .412 5 2 Ne4-g5 1 .42 Win a t C h e s s # 79 2 - 1 Nf6-d7 .330 31 64 Qh3xh2 .380 Win a t C h e s s # 80 2 0 d4-d5 .011 3 0 d4-d5 .083 4 0 d4-d5 .199 5 0 d4-d5 .580 6 0 d4-d5 '3.34 7 0 d4-d5 7.45 8 0 d4-d5 21 .8 9 0 d4-d5 1 03. 10 4 Rd1-a1 230. >300. Win a t C h e s s # 81 2 -2 Ra8xa3 .029 3 -2 Ra8xa3 .059 4 -2 Ra8xa3 .111 5 - 1 Be7-d6 .593 Win a t C h e s s # 82 2 0 Be4-h7 .035 3 0 Be4-h7 .110 4 0 Be4-h7 .335 5 0 Be4-h7 .976 Win a t C h e s s # 83 2 3 Re7xe8 .009 3 3 Re7xe8 .045 4 3 Qd4xd7 .211 5 3 Qd4xd7 .700 Win a t C h e s s # 84 31 65 Qd5-g8 .007 Win a t C h e s s # 85 2 0 Re8xb8 .007 3 0 Re8xb8 .029 4 3 Nc5-a6 . 1 45 5 4 Nc5-a6 .287 6 4 Nc5-a6 .752 Win a t C h e s s # 86 2 0 Nf6-g8 .004 3 0 Nf6-g8 .024 4 0 Nf6-g8 .071 5 0 Nf6-g8 .195 6 0 Nf6-g8 .538 7 0 Nf6-g8 1 .40 8 0 Nf6-g8 3.56 9 0 Nf6-g8 8.68 10 0 Nf6-g8 20.7 1 1 0 Nf6-g8 49.5 12 0 Nf6-g8 117. 1 3 0 Nf6-g8 287. Win a t C h e s s # 87 2 0 c5xd4 .004 3 0 c5xd4 .018 4 0 c5xd4 .056 5 0 c5xd4 .138 6 0 c5xd4 .356 7 0 c5xd4 .939 8 0 c5xd4 2.29 9 0 c5xd4 5.42 10 0 c5xd4 11.8 1 1 0 c5xd4 26.9 1 2 0 c5xd4 62. 1 1 3 0 c5xd4 143. >300. Win a t C h e s s # 88 2 0 Be6xa2 .012 3 0 Be6xa2 .083 31 65 Rg6xg2 .277 Win a t C h e s s # 89 2 0 Qd5-d6 .007 3 0 Qd5-d6 .188 4 0 Qd5-d6 .344 5 0 Qd5-d6 .657 6 3 g7-g5 3.90 7 3 g7-g5 8.45 Win a t C h e s s # 90 2 0 Nf5-e3 .014 3 0 Nf5-e3 .075 4 0 N f 5 - e 3 .426 5 0 Nf5-e3 .772 6 1 Nf5xg7 1.67 7 1 Nf5xg7 3.52 8 1 Nf5xg7 8.08 Win a t C h e s s # 91 2 0 Nd4-e6 .012 3 0 Nd4-e6 .050 4 0 Nd4-e6 .341 5 0 Nd4-e6 .580 6 0 Nd4-e6 1 .59 7 0 Nd4-e6 5.91 8 0 Nd4-e6 13.1 9 0 Nd4-e6 38.9 10 1 Bb3-e6 141 . 1 1 1 Bb3-e6 261 . Win a t C h e s s # 92 2 0 Nf6-d7 .011 3 0 Nf6-d7 .038 4 0 Nf6-d7 .137 5 0 Nf6-d7 .663 6 0 Nf6-d7 2.44 7 0 Nf6-d7 8.88 8 0 Nf6-d7 23.5 9 0 Nf6-d7 74.7 10 0 Nf6-d7 273. Win a t C h e s s # 93 2 0 Qg7xf6 .009 3 0 Qg7xf6 .032 4 0 Qg7xf6 . 1 30 5 0 Qg7xf6 .405 6 0 Qg7xf6 1 .30 7 0 Qg7xf6 3.69 8 0 Qg7xf6 10.8 9 2 Bc1-h6 33.4 Win a t . C h e s s # 94 2 5 e5-e4 .038 3 5 e5-e4 .098 4 5 e5-e4 .283 5 5 e5-e4 .833 Win a t . C h e s s # 95 2 5 Nf6-g4 .015 3 5 Nf6-g4 .029 4 5 Nf6-g4 .064 5 5 Nf6-g4 .250 6 5 Nf6-g4 .753 Win a t . C h e s s # 96 2 1 Qh4-d8 .025 3 1 Qh4-d8 .051 4 1 Qh4-d8 .155 5 1 Qh4-d8 .466 6 1 Qh4-d8 1 .26 Win a t C h e s s # 97 2 0 B e 5 - f 4 .010 31 61 Qg2-a8 .037 89 Win a t C h e s s # 98 2 1 Nc5xe4 .009 3 2 Nc5xe4 .140 4 5 Nc5-b3 .250 5 5 Nc5-b3 .376 6 6 Nc5xe4 .961 Win a t C h e s s # 99 2 0 Re5-e4 .037 3 0 Re5-e4 .106 31 63 Re5-h5 .269 Win a t C h e s s #100 2 0 Bd2 -e3 .003 3 0 Bd2 -e3 .008 4 0 Bd2 -e3 .020 5 0 Bd2 -e3 .043 6 0 Bd2 -e3 .084 7 0 Bd2 -e3 .176 8 0 Bd2 -e3 .338 9 0 Bd2 -e3 .61 5 10 0 Bd2 -e3 1.21 1 1 0 Bd2 -e3 2.23 12 0 Bd2 -e3 4.25 1 3 0 Bd2 -e3 7.41 14 0 Bd2 -e3 12.8 1 5 0 Bd2 -e3 22.6 16 0 Bd2 -e3 61 .3 17 0 Bd2 -e3 144. 18 0 Bd2 -e3 212. >300. Win a t C h e s s #101 2 0 Bd4-e5 .002 3 0 Bd4-e5 .028 4 0 Bd4-c3 .096 5 0 Bd4-c3 .152 6 0 Bd4-c3 .588 Win a t C h e s s #102 2 13 Q c 8 x f 8 .009 31 63 Q c 8 x f 8 . OJl 4 Win a t C h e s s #103 2 1 Rg1xg6 .039 3 1 Rg1xg6 .144 31 64 Qh6xg6 .384 Win a t C h e s s #104 2 0 Ne5xf7 .041 3 4 Qe2xh5 .135 4 4 Qe2xh5 .331 31 64 Qe2xh5 .617 Win a t C h e s s #105 2 0 Nd4-f5 .007 3 1 Qh5xh4 .057 4 1 Qh5xh4 .588 Win a t C h e s s #106 2 0 Ne4-f2 .012 3 1 R f 8 x f 1 .059 4 6 N e 4 -f2 .221 5 7 Ne4-f2 .555 Win a t C h e s s #107 2 0 Rb7xc7 .004 3 0 Rb7xc7 .014 4 0 Rb7xc7 .036 5 0 Rb7xc7 .075 6 3 Nd4-b5 .288 7 3 Nd4-b5 .497 8 3 Nd4-b5 .900 Win a t C h e s s #108 2 0 Qc5-d6 .012 3 0 Qc5-d6 .075 4 0 Qc5-d6 .303 5 0 Qc5-d6 1.04 6 4 Qc5-e5 3.03 7 4 Qc5-e5 7.55 Win a t C h e s s #109 2 0 Qd6xa3 .006 3 0 Qd6xa3 .038 4 0 Qd6xa3 .108 5 0 Qd6xa3 .280 6 1 c 4 - c 3 1.02 Win a t C h e s s #110 2 0 d6-d5 .006 3 0 d6-d5 .070 4 6 Ba7-e3 .239 5 6 Ba7-e3 .371 6 6 Ba7-e3 1.01 Win a t C h e s s #111 2 1 Qg1xh2 .017 3 0 Qg1xh2 .124 4 4 Qg1 - f 1 .395 5 5 Qg1-f1 .871 Win a t C h e s s #112 2 -3 Re1xe6 .080 3 1 Re1xe6 .119 4 1 Re1xe6 .360 5 1 Re1xe6 1.01 Win a t C h e s s #113 2 2 g 7 x f 6 .005 3 2 Qd8xf6 .015 4 2 Qd8xf6 .047 5 2 Qd8xf6 .152 6 2 Qd8xf6 .412 7 2 Qd8xf6 1.33 Win a t Che s s #114 2 0 g4xh5 .015 3 0 g4xh5 .051 4 1 Bd3xh7 .176 5 1 Bd3xh7 .400 6 1 Bd3xh7 1.87 Win a t C h e s s #115 2 0 Ne8-d6 .014 3 0 Ne8-d6 .027 4 1 Ne8-d6 .107 5 2 Ne8-d6 .193 6 2 Ne8-d6 .536 Win a t C h e s s #116 2 0 b5xa4 .005 3 0 b5xa4 .069 4 0 b5xa4 .180 5 0 b5xa4 .424 6 0 b5xa4 2.81 7 0 b5xa4 7.22 8 1 Rd8-d2 19.3 Win a t C h e s s #117 2 0 Qa7xf2 .005 3 0 Qa7xf2 .023 4 4 Nd6-e4 .104 5 4 Nd6-e4 .183 6 4 Nd6-e4 .391 7 4 Nd6-e4 1.18 Win a t C h e s s #118 2 0 R f 4 - f 5 .013 3 0 R f 4 - f 5 .147 4 0 R f 4 - f 5 .307 5 0 R f 4 - f 5 .838 6 0 R f 4 - f 5 4.17 7 4 Rf4-h4 11.1 8 4 Rf4-h4 19.1 Win a t C h e s s #119 2 2 Ne4-f2 .010 3 2 Ne4-f2 .031 4 2 Ne4-f2 .121 5 3 Qd8xd3 .440 6 3 Qd8xd3 1.35 Win a t C h e s s #120 2 1 Bf6xg7 .009 3 1 Bf6xg7 .097 4 1 Bf6xg7 .233 90 5 1 Bf6xg7 .515 6 0 Bf6xg7 2.01 7 0 Bf6xg7 6.60 8 2 g5-g6 18.5 Win a t C h e s s #121 2 0 Bh6xe3 .005 3 7 B c 6 x f 3 .032 4 7 B c 6 x f 3 .087 5 7 B c 6 x f 3 .236 6 7 B c 6 x f 3 .712 Win a t C h e s s #122 2 7 Rd1xf1 .015 3 7 Rd1xf1 .055 4 7 Rd1xf1 .208 5 7 Rd1xf1 .788 Win a t C h e s s #123 2 0 Q f 3 - f 6 .010 3 1 Re7-c7 .075 4 1 Re7-c7 .209 5 3 Bb7xd5 .680 Win a t C h e s s #124 2 0 Rd7-d8 .004 3 0 Rd7-d8 .029 4 0 Rd7-d8 .155 5 0 Rd7-d8 .541 6 2 g4-g3 1.42 7 2 g4-g3 2.89 8 2 g4-g3 6.94 Win a t C h e s s #125 2 1 Bb6xd4 .016 3 1 Bb6xd4 .046 4 3 Bb6xd4 .135 5 3 Bb6xd4 .288 6 3 Bb6xd4 .937 Win a t C h e s s #126 2 6 R f 6 x c 6 .029 3 6 R f 6 x c 6 .098 4 6 R f 6 x c 6 .320 5 6 R f 6 x c 6 1.07 Win a t C h e s s #127 2 0 f 4 x g 5 .003 3 0 f 4 x g 5 .020 4 0 f 4 x g 5 .076 5 0 f 4 x g 5 .228 6 1 Rb2xb7 .957 Win a t C h e s s #128 2 2 Bf6xg7 .011 3 2 Bf6xg7 .099 4 5 Qf7-g6 .325 5 5 Qf7-g6 .673 Win a t C h e s s #129 2 0 g7-g5 .013 3 0 g7-g5 .060 4 0 g7-g5 .175 5 0 g7-g5 .442 6 0 g7-g5 1.93 7 0 g7-g5 5.51 8 0 g7-g5 17.2 9 1 B b 7 - f 3 55.0 10 1 Bb7-f3 106. 11 1 B b 7 - f 3 223. >300. Win a t C h e s s #130 2 0 Ne3-c4 .022 3 0 Ne3-c4 .043 4 0 Ne3-c4 .109 5 0 Ne3-c4 .276 6 0 Ne3-c4 .984 7 0 Rf6-h6 4.26 8 0 Rf6-h6 7.39 9 1 Qg7-h8 26.8 Win a t C h e s s #131 2 0 Bd4-e5 .006 3 0 Bd4-e5 .070 4 1 Q f 4 - e 5 .253 5 1 Qf4-e5 .398 6 1 Qf4-e5 1.82 7 3 Re1-e8 5.68 Win a t C h e s s #132 2 0 Qh3xf1 .009 3 0 Qh3xf1 .031 4 0 Qh3xf1 .111 5 0 Qh3xf1 .353 6 0 Qh3xf1 .969 31 62 Re5-e1 3.59 Win a t C h e s s #133 2 0 e5-e6 .012 3 0 e5-e6 .130 4 0 e5-e6 .544 5 0 e5-e6 1.36 6 1 Bg3-h4 4.43 Win a t C h e s s #134 2 1 Qe5xh2 .009 3 1 Qe5xh2 .094 31 65 Rd8-d1 .303 Win a t C h e s s #135 2 0 Qd7xa7 .003 3 0 Qd7xa7 .142 4 0 Qd7xa7 .268 5 0 Qd7xa7 .492 6 2 Ne6-d4 2.17 Win a t C h e s s #136 2 1 Qg6xf5 .011 31 62 Rc1-c8 .067 Win a t C h e s s #137 2 0 Nf5-h4 .007 3 0 Nf5-h4 .168 4 0 Nf5-h4 .454 5 0 Nf5-h4 1.01 6 1 Rd1-d7 7.09 Win a t C h e s s #138 2 0 d5-d6 .009 3 0 d5-d6 .041 4 0 d5-d6 .215 5 0 d5-d6 .690 6 0 d5-d6 2.60 7 0 d5-d6 8.57 8 6 h4-h5 39.5 Win a t C h e s s #139 2 0 Kf2-g3 .100 3 0 K f 2 - g 3 .157 31 65 Ne4-f6 .310 Win a t C h e s s #140 2 0 h6xg7 .010 3 0 h6xg7 .046 4 2 Be5-c7 .358 5 2 Be5-c7 .661 6 4 Be5-c7 1.76 7 8 Rc3-c7 6.29 Win a t C h e s s #141 2 0 Kg2-f1 .010 3 0 Kg2-f1 .030 4 0 Kg2-f1 .142 5 0 Kg2-f1 .350 6 0 Kg2-f1 2.36 7 0 Kg2-f1 3.61 8 0 Kg2-f1 8.79 9 0 Kg2-f1 26.1 10 0 Kg2-f1 78.3 11 0 Kg2-f1 239. >300. Win a t C h e s s #142 2 0 d4-d5 .015 3 1 Nc4-e3 .137 4 3 Re1-e8 .444 5 3 Re1-e8 1.10 91 Win a t C h e s s #143 2 -1 Qg3-f3 .085 31 63 Rg6xh6 .175 Win a t C h e s s #144 2 0 Bg4xe2 .001 3 0 Bg4xe2 .021 4 0 Bg4xe2 .055 5 0 Bg4xe2 .150 6 0 Bg4xe2 .735 7 2 d4-d3 2.66 8 2 d4-d3 5.14 Win a t C h e s s #145 2 1 B g 5 x f 6 .016 3 1 B g 5 x f 6 .086 4 1 B g 5 x f 6 .256 5 1 B g 5 x f 6 .829 6 1 B g 5 x f 6 3.82. 7 1 B g 5 x f 6 12.4 8 7 Re1-e8 43.4 Win a t C h e s s #146 2 0 B f 5 - g 6 .002 3 0 B f 5 - g 6 .013 4 0 B f 5 - g 6 .026 5 0 B f 5 - g 6 .052 6 0 B f 5 - g 6 .117 7 0 Bf5-h3 .344 8 0 B f 5 - h 3 .430 9 0 B f 5 - h 3 .808 10 -1 Bf5-h3 4.42 11 -1 B f 5 - h 3 5.04 12 -1 B f 5 - h 3 6.42 13 -1 B f 5 - c 8 14.9 1 4 - 1 B f 5 - c 8 31.5 Win a t C h e s s #147 2 0 d5-d4 .026 3 0 d5-d4 .118 4 0 d5-d4 .385 5 0 d5-d4 .843 6 1 Nf6xg4 2.34 7 1 Nf6xg4 5.71 Win a t C h e s s #148 2 0 Qd1-e2 .025 3 0 Qd1-e2 .045 4 1 Rg1xg7 .167 5 2 Rg1xg7 .402 6 6 Rg1xg7 1.38 Win a t C h e s s #149 2 0 Be4-d5 .012 3 0 Be4-d5 .079 4 1 Be4xg2 .296 5 1 Be4xg2 .677 Win a t C h e s s #150 2 1 Qb2xe2 .004 3 2 Bd6-f8 .067 4 2 Bd6-f8 .159 5 1 Bd 6 - f 8 .629 Win a t C h e s s #151 2 0 Nc4-d6 .007 3 0 Nc4-d6 .048 4 0 Nc4-d6 .146 5 0 Nc4-d6 .244 6 0 Nc4-d6 1.47 7 0 Nc4-d6 3.07 8 0 Nc4-d6 6.28 9 1 Na4-c3 24.3 Win a t C h e s s #152 2 1 Nc3-d5 .019 3 1 Nc3-d5 .082 4 1 Nc3-d5 .170 5 1 Nc3-d5 .352 6 1 Nc3-d5 2.12 Win a t C h e s s #153 2 0 g7-g6 .041 3 0 g7-g6 .310 4 0 g7-g6 .876 5 1 Nb5xd4 1.61 6 1 Nb5xd4 2.82 7 1 Nb5xd4 5.01 Win a t C h e s s #154 31 60 Q f 2 x f 7 .005 Win a t C h e s s #155 2 0 Qc7-c8 .012 3 0 Qc7-c8 .054 4 0 Qc7-c8 .149 5 0 Qc7-c8 .688 6 0 Qc7-c8 1.69 7 0 Qc7-c8 4.43 8 0 Qc7-c8 12.5 9 0 Qc7-c8 45.7 10 0 Qc7-c8 93.3 >300. Win a t C h e s s #156 31 66 Qh3xh6 .003 Win a t C h e s s #157 2 0 Qg3xe5 .011 3 0 Qg3xe5 .046 4 0 Qg3xe5 .170 5 0 Qg3xe5 .430 6 0 Qg3xe5 1.18 7 3 h3xg4 6.68 8 3 h3xg4 12.2 9 3 h 3 ~ 1 25.3 10 3 h3xg4 65.8 11 3 Nd5-e7 172. >300. Win a t C h e s s #158 2 1 Qf5-e6 .013 31 64 Re7xg7 .030 Win a t C h e s s #159 2 5 Ng5-e6 .017 3 5 Ng5-e6 .036 4 5 Ng5-e6 .111 5 6 Ng5-e6 .355 6 6 Ng5-e6 .922 Win a t C h e s s #160 31 63 Qg4xd7 .002 Win a t C h e s s #161 2 0 Nd6-e8 .024 3 2 Rg3-g8 .144 31 64 Qh4xd8 .293 Win a t C h e s s #162 2 0 Ke1-d2 .044 3 0 Ke1-d2 .063 4 0 Ke1-d2 .230 5 4 Bc4-d5 .872 Win a t C h e s s #163 2 0 c6xd5 .008 3 0 c6xd5 .044 4 0 c6xd5 .368 5 0 c6xd5 1.57 6 0 c6xd5 3.68 7 0 c6xd5 10.4 8 0 c6xd5 45.3 9 0 c6xd5 141. >300. Win a t C h e s s #164 2 0 Nb4xd5 .009 3 2 Rc2xc4 .059 4 2 Rc2xc4 .169 5 2 Rc2xc4 .449 6 2 Rc2xc4 1 .20 Win a t C h e s s #165 2 1 Qd2-d8 .007 3 1 Qd2-d8 .022 4 1 Qd2-d8 .059 92 5 4 Re3-e2 .208 6 4 Re3-e2 .380 7 5 Re3-e2 1.16 Win a t C h e s s #166 2 1 Qa3xc5 .009 3 1 Qa3xc5 .083 4 2 d5-d4 .456 5 3 d5-d4 .850 Win a t C h e s s #167 2 0 e5-e4 .010 3 0 e5-e4 .094 4 0 e5-e4 .383 31 61 Rf2xg2 .813 Win a t C h e s s #168 2 0 c 5 - c 4 • 005 3 0 c 5 - c 4 040 4 5 Qd7-d2 • 218 5 9 Qd7-d2 • 729 a t i Chess #169 2 0 d6xc5 • 008 3 0 d6xc5 • 042 4 0 d6xc5 229 5 0 d6xc5 • 575 6 3 Bg7-h6 1 .80 7 3 Bg7-h6 4 .43 a t i Chess #170 2 0 Rg7-g5 • 012 3 0 Rg7-f7 • 052 4 3 Qa2xc4 • 302 5 4 Qa2xc4 • 803 a t i C h e s s #171 2 0 Bb3xd5 • 010 3 0 Bb3xd5 • 090 4 0 Bb3xd5 • 428 5 1 Be3-h6 1 .72 Win a t C h e s s #172 2 0 Qe5-b8 .020 31 62 Qe5-e1 .035 Win a t C h e s s #173 2 4 Qe3-h6 .040 31 65 Qe3-h6 .049 Win a t C h e s s #174 2 0 Bd5 x f 3 .003 3 0 B d 5 x f 3 .170 4 1 Nf4xg2 .251 5 1 Nf4xg2 .406 6 1 Nf4xg2 1 .72 Win a t C h e s s #175 2 0 Qd3xe4 .011 3 0 Qd3xe4 .034 4 2 Nf4-h5 .198 5 3 Nf4-h5 .552 Win a t C h e s s #176 2 0 Bd4xc3 .004 3 0 Bd4xc3 . 169 4 0 Bd4xc3 .264 5 0 Bd4xc3 .592 6 0 Bd4xc3 5.36 7 2 Rh8xh2 9.74 8 2 Rh8xh2 17.0 Win a t C h e s s #177 2 2 Qe7-a3 .036 31 65 Qe7-a3 .043 Win a t C h e s s #178 2 1 Rh2xh7 .008 3 1 Qe4xh7 .102 4 1 Qe4xh7 . 1 96 5 1 Qe4xh7 .614 6 1 Qe4xh7 3.24 7 1 Qe4xh7 6.87 8 1 Qe4xh7 18.1 9 2 Nf4 x e 6 64.6 10 2 Nf4 x e 6 1 62. >300. Win a t C h e s s #179 2 0 Qf2-b6 .025 31 62 Qf2-g1 .043 Win a t i Chess # 180 2 0 Nf6-d7 .014 3 0 Nf6-d7 .399 4 0 Nf6-d7 .739 5 0 Nf6-d7 1 .25 6 0 Nf6-d7 3.28 7 0 Nf6-d7 11.1 8 0 Nf6-d7 25.2 9 0 Nf6-d7 66.7 10 0 Nf6-d7 203. >300. Win , at < Chess #181 2 0 Qh3xf1 .003 3 1 Nf6-g4 .053 4 5 Nf6-g4 .123 5 5 Nf6-g4 .241 6 5 Nf6-g4 .61 1 Win a t C h e s s #182 2 0 Nc4-d2 .006 3 0 Nc4-d2 .206 4 1 Ng5xh7 .483 5 1 Ng5xh7 V~E->V'7 .704 c * 7 4 Qd1-h5 8 4 Qd1-h5 13.4 9 5 Qd1-h5 46.3 Win a t C h e s s #183 2 0 Bd3 -e4 .009 3 0 Bd3' -e4 .067 4 0 Bd3 -e4 .197 5 0 Bd3 -e4 .564 6 0 Bd3 -e4 2.51 7 1 Bg5 - f 6 7.23 Win a t C h e s s #184 31 64 Qf6-e7 .015 Win a t C h e s s #185 2 0 Qh5-g4 .009 3 0 Qh5-g4 .026 4 0 Qh5-g4 .110 5 2 Qh5xh7 .696 Win a t C h e s s #186 2 1 Qh4xg4 .011 31 65 Bh6-f8 .052 Win a t C h e s s #187 2 1 Qf 5xe4 .008 3 1 Qf 5xe4 .031 4 2 Nf4-h3 .119 5 6 Nf4-h3 .332 6 6 Nf4-h3 .775 Win a t C h e s s #188 • 31 65 Qf6-g7 .006 Win a t C h e s s #189 2 0 Re4 -e2 .009 3 3 Re7 -e8 .051 4 3 Re7 -e8 .124 5 4 Re7 -e8 .319 6 5 Re7 -e8 .773 Win a t C h e s s #190 2 1 Nd1 - f 2 .015 3 1 Nd1 - f 2 .030 4 1 Nd1 - f 2 .093 5 1 Nd1 - f 2 .235 6 1 Nd1 - f 2 .710 7 1 Nd1 - f 2 2.06 8 1 Nd1 - f 2 5.18 9 1 Nd1 - f 2 15.5 93 10 6 Bd7-h3 86.7 Win a t C h e s s #191 2 0 Re8xc8 .002 3 0 Re8xc8 .021 4 7 Qe2-c4 .124 5 7 Qe2-c4 .190 31 62 Qe2-c4 .259 Win a t C h e s s #192 2 6 Nb4-d3 .028 3 6 Nb4-d3 .081 4 7 Nb4-d3 .357 5 7 Nb4-d3 1.23 Win a t C h e s s #193 2 0 f 7 - f 6 .009 3 0 f 7 - f 6 .048 4 0 f 7 - f 6 .160 5 0 f 7 - f 6 .476 6 0 f7-£6 1.65 7 0 f 7 - f 6 4.17 8 4 Qb3xe3 16.5 Win a t C h e s s #194 2 -1 Nf5-h6 .040 3 -1 Nf5-h6 .115 4 -1 Nf5-h6 .287 5 -1 Nf5-h6 .952 Win a t C h e s s #195 2 0 Rd1xd8 .005 3 0 Rd1xd8 .040 4 0 Rd1xd8 .106 5 0 Rd1xd8 .306 6 0 Rd1xd8 1.38 7 0 R d 1 x d 8 3.27 8 0 Rd1xd8 7.74 9 2 g2-g3 27.4 Win a t C h e s s #1 2 0 d5xe4 3 4 5 6 7 8 9 10 0 0 0 0 0 0 0 0 d5xe4 d5xe4 d5xe4 d5xe4 d5xe4 d5xe4 d5xe4 d5xe4 96 .007 .058 .259 .569 2.28 6.34 17.5 62.5 202. >300. Win a t C h e s s #197 2 0 Q f 2 - f 1 .012 31 68 Q f 2 - f 1 .022 Win a t C h e s s #198 2 0 Nf4-h3 .016 3 1 Nf4-e2 .109 4 1 Nf4-e2 .193 5 1 Nf4-e2 .357 6 4 Rd8-d3 1.48 Win a t C h e s s #199 2 0 Bb5xc6 .008 3 0 Bb5xc6 .250 4 0 Bb5xc6 .440 5 1 Bb5xc6 .795 Win a t C h e s s #200 2 0 d5xe6 .006 3 0 d5xe6 .064 4 0 d5xe6 .239 5 0 d5xe6 .780 6 1 B b 2 x f 6 2.09 7 1 Bb2xf6 5.35 Win a t C h e s s #201 2 0 Bd5-e4 .011 3 0 Bd5-e4 .114 4 3 Ra1-a7 .275 5 3 Ra1-a7 .486 6 4 Ra1-a7 1.24 Win a t C h e s s #202 2 1 Rc2xa2 .005 3 1 Rc2xa2 .017 4 1 Rc2xa2 .058 5 1 Rc2xa2 .125 6 1 Rc2xa2 .298 7 1 Rc2xa2 .717 Win a t C h e s s #203 2 0 Qg5-h5 .010 3 0 Qg5-h5 .032 4 1 Qg5-h6 .223 5 1 Qg5-h6 .362 31 63 Qg5-h6 .907 Win a t C h e s s #204 2 0 Nd5-e3 .007 3 1 Nd5-c7 .069 4 1 Nd5-c7 .209 5 1 Nd5-c7 .543 6 1 Re1xe5 1.73 7 1 Re1xe5 4.80 Win a t C h e s s #205 2 0 Bd4-e3 .009 3 0 Bd4-e3 .135 4 1 Qd2xg5 .402 5 1 Qd2xg5 .895 Win a t C h e s s #206 2 -1 a2-a1=Q.022 3 0 Rd6-c6 .049 A r> r> J c r. « a *? X W f i W» W WW . J 1 i 5 0 Rd6-c6 .336 6 0 Rd6-c6 .734 Win a t C h e s s #207 2 0 f 2 - f 4 .027 3 0 f 2 - f 4 .043 4 0 f 2 - f 4 .229 5 0 f 2 - f 4 .445 6 1 Qg4xg7 1.68 Win a t C h e s s #208 2 0 Q f 5 - f 7 .010 3 0 Q f 5 - f 7 .070 4 0 Q f 5 - f 7 .319 5 0 Q f 5 - f 7 1.00 6 0 Q f 5 - f 7 2.56 7 3 Bh5-f7 7.73 Win a t C h e s s #209 2 1 a4xb5 .008 3 2 a4xb5 .075 4 5 Re1xe5 .510 Win a t C h e s s #210 2 0 Nd5-e3 .006 3 0 Nd5-e3 .064 4 0 Nd5-e3 .197 5 0 Nd5-e3 .488 6 1 Be2-b5 1.76 7 1 Be2-b5 5.19 8 2 Be2-b5 14.5 9 2 Be2-b5 41.0 10 3 Rd1-h1 138. >300. Win a t C h e s s #211 2 1 Qh5xh7 .006 3 1 Qh5xh7 .056 4 1 Qh5xh7 .236 31 63 Qh5xf7 .356 Win a t C h e s s #212 2 0 Ne5-g6 .022 3 0 Ne5-g6 .075 4 0 Ne5-g6 .289 31 66 Qh8xg7 1.15 Win a t C h e s s #213 2 0 Bc1-e3 .038 3 0 Bc1-e3 .075 4 0 Bc1-e3 .187 94 5 0 Bc1-e3 .434 6 -1 Bc1-e3 3.94 7 4 Rh5xh7 6.07 8 4 Rh5xh7 9.1 1 9 4 Rh5xh7 19.7 10 4 Rh5xh7 48. 1 1 1 4 Rh5xh7 116. >300. Win a t C h e s s #214 2 0 Ne5- f 3 .012 3 0 Ne5- f 3 .094 4 0 Ne5- f 3 .289 5 0 Ne5- f 3 .693 6 0 Ne5- f 3 3.65 7 0 Ne5- f 3 13.1 8 1 Ne4- g5 31.1 Win a t C h e s s #215 2 2 Re1xc1 .018 3 2 Re1xc1 .060 31 66 Qd3-h7 .133 Win a t C h e s s #216 2 0 Ne5xd7 .008 3 0 Ne5xd7 .038 4 0 Ne5xd7 .145 5 1 N e 5 x f 7 .551 Win a t C h e s s #217 2 1 N e 4 x f 6 .039 3 2 Ne4-g3 .127 4 3 Ne4-g3 .956 31 65 Qd4-d7 1.28 Win a t C h e s s #218 2 0 h5xg6 .009 3 0 h5xg6 .052 4 5 Bg5-h6 .285 5 4 Bg5-h6 .636 Win a t C h e s s #219 2 1 Bc6xe4 .006 31 65 Q f 7 - f 1 .035 Win a t C h e s s #220 2 0 N e 4 - f 6 • 009 3 0 N e 4 - f 6 • 064 4 0 N e 4 - f 6 • 533 5 5 Qe2xf1 1 .22 6 4 Qe2xf1 4 .83 a t C h e s s #221 2 0 Nc6 - d 8 • 005 3 0 N c6 - d 8 • 042 4 0 Ng3-h5 • 141 5 0 Ng3-h5 .272 6 0 Ng3-h5 1.06 7 0 Ng3-h5 3.05 8 0 Ng3-h5 5.81 9 1 N"3-h5 1S.C 10 2 Rd1-d8 39! 7 11 2 Rd1-d8 78.5 12 2 Rd1-d8 215. >300. Win a t C h e s s #222 2 1 b2xa3 .003 3 1 b2xa3 .029 4 1 b2xa3 .142 5 1 b2xa3 .357 6 1 b2xa3 1.18 7 1 b2xa3 4.02 8 1 b2xa3 9.63 9 1 b2xa3 29.7 10 1 b2xa3 95.5 11 1 b2xa3 230. > 3 0 0 . Win a t C h e s s #223 2 0 B f 4 - g 5 .005 3 0 B f 4 - g 5 .033 4 0 B f 4 - g 5 .235 5 1 Nc3xe4 .782 Win a t C h e s s #224 2 1 e 5 x f 4 .006 3 1 e 5 x f 4 .222 4 1 e 5 x f 4 .384 5 1 e 5 x f 4 .672 6 1 e 5 x f 4 1.96 7 1 e 5 x f 4 5.94 8 1 e 5 x f 4 13.9 9 2 Rd6-h6 73.7 Win a t C h e s s #225 2 0 Qe7-f7 .024 31 63 Qe7-h4 .066 Win a t C h e s s #226 2 0 Qg5-g3 .015 3 0 Qg5-g3 .137 4 0 Qg5-g3 .299 5 1 Rd1-d8 .726 6 1 Rd1 - d 8 2.07 7 2 Qg5-e7 7.83 8 3 Ne5-f7 20.4 Win a t C h e s s #227 2 0 B f 5 - g 6 . 0 0 8 3 0 B f 5 - e 6 .107 4 0 B f 5 - e 6 .211 5 2 d6-d5 • 560 a t C h e s s #228 2 0 Bd3xe4 • 003 t w Bd3:-:e4 066 4 0 Bd3xe4 • 196 5 0 Bd3xe4 • 430 6 0 Bd3xe4 2 .65 Win a t C h e s s #229 2 0 Ke4 -e5 .004 3 0 Ke4 -e5 .024 4 0 Ke4 -e5 .058 5 0 Ke4 -e5 . 122 6 0 Ke4 -e5 .296 7 0 Ke4 -e5 .728 8 0 Ke4 -e5 1 .60 9 0 Ke4 -e5 3.69 10 0 Ke4 -e5 8.00 1 1 0 Ke4 -e5 17.6 1 2 0 Ke4 -e5 40.3 13 0 Ke4 -e5 90.9 1 4 0 Ke4 -e5 215. >300. Win a t C h e s s #230 2 0 Kc6 -d7 .001 3 0 Kc6 -d7 .01 1 4 0 Kc6 -d7 .028 5 0 Kc6 -d7 .063 6 0 Kc6 -d7 . 1 93 7 0 Kc6 -d7 .447 8 0 Kc6 -d7 .915 9 0 Kc6 -d7 2.25 10 0 Kc6 -d7 4.78 1 1 0 Kc6 -d7 10.1 12 0 Kc6 -d7 33.4 1 3 0 Kc6 -d7 64.0 1 4 0 Kc6 -d7 1 26. >300. Win a t C h e s s #231 2 3 Rd1xd7 .006 3 3 Rd1xd7 .025 4 3 Qf5xd7 . 106 5 3 Qf5xd7 .231 6 1 Rd1xd7 1 .37 7 0 Rd1xd7 3.14 8 0 Rd1xd7 6.66 9 1 Bc1-g5 18.7 a t C h e s s #232 2 0 Rb8xe8 .002 3 0 Rb8-b4 .048 4 0 Qa6-a7 .197 5 0 Qa6-a7 .278 95 6 0 Qa6-a7 .829 7 0 Qa6-a7 2.14 8 0 Qa6-a7 4.68 9 3 Rb8xe8 13.9 10 3 Rb8xe8 29.4 Win a t C h e s s #233 2 0 Qe3xf2 .010 3 0 Qe3xf2 .040 4 0 Qe3xf2 .274 5 5 Nd4-b3 .836 Win a t Ch e s s #234 2 1 Rc1xc4 .008 3 1 Rc1xc4 .054 4 1 Rc 1 xc4 .248 5 1 Rc1xc4 .633 6 1 Rc1xc4 2.10 7 1 Rc1xc4 9.56 8 4 Rh3-b3 34.6 Win a t C h e s s #235 2 0 Qe6x f 6 .016 3 0 Qe6x f 6 .057 4 1 Qe6-e4 .228 5 1 Qe6-e4 .540 6 1 Qe6-e4 1 .32 7 1 Qe6-e4 3.60 8 1 Qe6-e4 9.1 3 9 1 Qe6-e4 22.5 1 0 1 Qe6-e4 58.5 1 1 1 Qe6-e4 147. >300. Win a t C h e s s #236 2 1 Qg3xe1 .021 3 1 Qg3xe1 .056 4 1 Qg3xe1 .191 5 1 Qg3xe1 .556 6 2 Rc3-c1 1 .36 7 2 Rc3-c1 3.20 8 2 Rc3-c1 7.81 Win a t C h e s s #237 2 1 Rc2xh2 .039 3 -1 Q f 7 - f 8 .705 4 -1 Qf7-e8 1 .49 5 - 1 Qf7-e8 3.41 6 -1 Qf7-e8 10.1 7 -1 Qf7-e8 28.0 8 0 Rc2-c1 65.5 9 1 Rc2-c1 85. 1 >300. Win a t C h e s s #238 2 0 Qg3xf4 .017 3 0 Qg3xf4 .049 4 0 Qg3xf4 .141 5 0 Qg3xf4 .451 6 0 Qg3xf4 1.12 1 ? g 2:: b 7 3.36 8 3 Bg2xb7 11.2 9 2 Bg2xb7 24.7 Win a t Ch e s s #239 2 0 f 6-f 5 .007 3 0 f 6-f 5 .058 4 0 f 6-f 5 .170 5 0 f 6-f 5 .405 6 0 f 6-f 5 1.15 7 0 f 6-f 5 2.98 8 0 f 6-f 5 7.94 9 1 Qf2-e2 25.7 10 1 Qf2-e2 44.2 1 1 1 Qf2-e2 97.3 1 2 1 Qf 2-e2 277. Win a t i Chess #240 2 0 Ng5-f3 .012 3 0 Ng5-f3 .030 4 0 Ng5-f3 . 1 20 5 0 Ng5-f3 .357 6 1 Qc2xc6 .892 Win a t i Chess #241 2 0 Ne5xc6 .013 3 0 Ne5xc6 .053 4 1 R f 5 x f 6 .269 5 1 Rf 5 x f 6 .623 6 1 R f 5 x f 6 2.10 7 1 R f 5 x f 6 8.18 8 1 R f 5 x f 6 24.4 9 1 R f 5 x f 6 77.3 31 63 Qh3xh7 164. Win a t i Chess #242 2 0 Ne4-g3 .007 3 0 Ne4-g3 .069 4 0 Ne4-g3 .215 5 1 Rd1xd7 .515 Win a t i Chess #243 2 0 Nd6-c4 .015 3 0 Nd6-c4 .073 4 0 Nd6-c4 .238 5 0 Nd6-c4 .707 6 0 Nd6-c4 2.49 7 0 Nd6-c4 8.07 8 0 Nd6-c4 20.8 9 0 Nd6-c4 68.2 10 0 Nd6-c4 226. >300. Win a t C h e s s #244 2 0 Qe3-g3 .033 3 1 Rd1xd5 .203 31 64 Qe3xc5 .606 Win a t C h e s s #245 2 0 Bd4xf6 .005 3 1 Nc3-b5 .152 4 1 Nc3-b5 .322 5 2 Qd3xg6 .920 Win a t C h e s s #246 31 62 Qg4-h5 .013 Win a t Ch e s s #247 2 - 1 Qd6-c5 .060 3 -1 Qd6-c5 .180 4 -1 Qd6-c5 .417 5 - 1 Qd6-c5 .971 6 0 Qd6-c5 2.20 7 0 Qd6-c5 4.32 8 -1 Qd6-c5 18.0 9 -1 Qd6-c5 47.3 10 1 Rb1xb5 101. 1 1 3 Rb1xb5 209. >300. Win a t Ch e s s #248 2 0 Qd6xd5 .010 3 1 Qd6xd5 .035 4 1 Qd6xd5 . 1 75 5 1 Qd6xd5 .565 6 1 Qd6xd5 1 .37 7 1 Qd6xd5 4.58 8 1 Qd6xd5 12.1 9 1 Qd6xd5 29.2 10 1 Qd6xd5 91 . 1 1 1 1 Qd6xd5 274. Win a t C h e s s #249 2 0 Qd3-e3 .012 3 0 Qd3-e3 .058 4 0 Qd3-e2 .51 1 5 0 Qd3-e2 .852 6 1 d4-d5 2.79 7 0 d4-d5 12.3 8 0 d4-d5 23.0 9 1 d4-d5 99. 1 10 1 d4-d5 206. >300. Win a t C h e s s #250 2 - 1 Re3-e7 .094 3 - 1 Re3-e7 .196 4 -1 Re3-e7 .349 96 5 0 Re3-e1 1.02 6 0 Re3-e1 2.60 7 0 Re3-e1 4.07 31 62 Re3-e8 9.83 Win a t C h e s s #251 2 0 Qd4-h8 .015 3 0 Qd4-h8 .051 4 0 Qd4-h8 .167 5 0 Qd4-h8 .536 6 0 Qd4-h8 1 .44 7 0 Qd4-h8 4.67 8 2 Qd4-e5 11.5 9 8 Qd4-e5 23.9 . a t C h e s s #252 2 2 Qa2-a1 .015 3 3 N f 6 x d 5 .079 4 3 N f 6 x d 5 .302 5 3 Nf6xd5 1 .46 6 3 Nf6xd5 4.52 7 3 Nf6xd5 14.3 8 4 Re8-e2 72.2 i a t C h e s s #253 2 0 c 6 - c 7 .009 3 0 c 6 - c 7 .044 1 65 Qe3-e8 .089 i a t C h e s s #254 2 0 Rg4-g5 .013 3 1 Nf4xh3 .037 4 1 Nf4xh3 .102 5 2 Nf4xh3 .228 6 3 Nf4xh3 .836 i a t C h e s s #255 2 -4 R f 6 x g 6 .074 3 -4 R f 6 x g 6 .145 4 1 R f 6 x g 6 .273 5 1 R f 6 x g 6 .637 i a t C h e s s #256 2 0 g2-g3 .013 3 0 g2-g3 .038 4 0 Rh4-g4 .257 5 0 Rh4-g4 .478 6 0 Rh4-g4 1 .40 7 1 Nd4-f5 4.90 i a t C h e s s #257 2 0 N e 4 - f 6 .006 3 0 N e 4 - f 6 .085 4 0 N e 4 - f 6 .210 5 0 N e 4 - f 6 .529 6 3 Rd1xd4 1 .44 7 3 Rd1xd4 3.98 8 3 Rd1xd4 13.9 Win a t C h e s s #258 2 0 Rg3 gS .012 3 0 Rg3-g5 .117 4 0 h2-h3 .357 5 1 Bh5xg6 .622 Win a t C h e s s #259 2 -2 Ng5xf7 .043 3 -1 Qd1-h5 .149 4 -2 Qd1-h5 .406 5 -2 Qd1-h5 .946 Win a t C h e s s #260 2 0 Nc7-e6 .024 3 -1 Nc7-e6 .329 4 -1 Nc7-e6 .847 31 63 Qd5-e6 1.50 Win a t C h e s s #261 2 2 Qg3xg2 .017 3 2 Qg3xg2 .056 4 2 Qg3xg2 .205 5 2 Qg3xg2 .681 6 2 Qg3xg2 1.93 7 2 Qg3xg2 5.29 8 7 Nf3-d4 17.4 Win a t C h e s s #262 2 0 Bc6-e8 .009 3 0 Bc6-e8 .048 4 0 Bc6-e8 .293 5 0 Bc6-e8 .727 6 0 Bc6-e8 2.14 7 0 Bc6-e8 10.3 8 0 Bc6-e8 27.9 9 0 Bc6-e8 86.2 10 0 Bc6-e8 300. Win a t C h e s s #263 2 0 Qf7-h5 .034 3 0 Qf7-h5 .098 31 62 Qf7-g8 .360 Win a t C h e s s #264 2 2 B f 4 x h 2 .014 3 3 Rd8xd4 .098 4 3 Rd8xd4 .310 5 3 Rd8xd4 .671 Win a t C h e s s #265 2 0 Qc2xe4 .002 3 0 Qc2xe4 .017 4 0 Qc2xe4 .053 5 0 Qc2xe4 .141 6 0 Qc2xe4 .621 7 0 Qc2xe4 1 .59 8 0 Qc2xe4 4.07 g 0 Qc2xe4 12.4 10 0 Qc2xe4 34.8 1 1 0 Qc2xe4 1 18. >300. Win a t C h e s s #266 2 0 Bf2-g3 .043 3 0 Bf2-g3 .104 4 0 Bf 2 - g 3 .282 5 0 Bf2-g3 .828 31 63 Rh8xh2 2.04 Win a t C h e s s #267 2 0 a2-a3 .067 3 4 Nd5-c7 .118 4 13 Nd5-c7 .258 31 63 Nd5-c7 .274 Win a t C h e s s #268 2 -1 Re2 -e3 .027 3 4 Re2 -e8 .066 4 4 Re2 -e8 .156 5 5 Re2 -e8 .381 6 7 Re2 -e8 1.18 Win a t C h e s s #269 2 0 Bf 4 -g3 .011 3 0 Bf 4 -g3 .058 4 0 Bf 4 -93 .393 5 0 Bf 4 -g3 .983 6 0 Bf 4 -g3 2.41 7 0 Bf 4 -g3 9.14 8 0 Bf 4 -g3 22.6 9 0 Bf 4 -g3 52.4 10 0 Bf 4 -g3 196. >300. Win a t C h e s s #270 2 1 Re2xe8 .004 3 1 Re2xe8 .021 4 1 Re2xe8 .071 5 1 Re2xe8 .183 6 1 Re2xe8 .702 7 4 Qd4-g4 3.04 8 1 Re2xe8 1 1 .7 9 1 Re2xe8 19.3 10 1 Re2xe8 38.4 1 1 1 Re2xe8 81.0 12 1 Re2xe8 207. >300. Win a t C h e s s #271 97 2 0 g7-g8=Q.002 3 -4 Re6-d6 .101 4 -4 Re6-d6 .160 5 -4 Re6-d6 .282 6 0 Re 6 - d £ . £ 4 6 Win a t C h e s s #272 2 0 B e 3 - f 2 .006 3 0 B e 3 - f 2 .061 4 0 B e 3 - f 2 .205 5 0 B e 3 - f 2 .502 6 0 B e 3 - f 2 2.18 7 1 Be3xc5 7.92 Win a t C h e s s #273 2 1 Ne4-f2 .025 3 1 Ne4-f2 .115 4 1 Ne4-f2 .325 5 2 Ne4-g3 .976 Win a t C h e s s #274 2 0 Rg6--g7 .007 3 0 Rg6--g7 .047 4 0 Rg6--g5 . 1 54 5 0 Rg6--g5 .219 6 0 Rg6--g5 .390 7 1 Rg6 -g5 .655 8 2 Rg6--g5 1.21 9 2 Rg6--g5 2.03 10 2 Rg6--g5 3.76 1 1 2 Rg6 -g5 7.13 1 2 1 Rg6--b6 21.5 Win a t C h e s s #275 2 0 Nf 4 -g6 .008 3 0 Nf 4' -g6 .171 4 0 Nf 4' -g6 .427 5 0 Nf 4 -g6 .863 6 0 Nf 4 -g6 5.47 7 0 Nf 4 -g6 12.5 8 0 Nf 4' -g6 26.4 9 1 b7 -b5 80.9 10 1 b7 -b5 182. >300. Win a t C h e s s #276 2 -3 Re7xg7 .080 3 -3 Re7xg7 .155 4 5 Qd1-d5 .380 5 10 Qd1-d5 .954 Win a t C h e s s #277 2 0 Ba6xd3 .007 3 0 Ba6xd3 .071 4 0 Ba6xd3 .311 5 1 Rg8xg2 1.26 Win a t C h e s s #278 2 0 e 4 x f 5 .013 3 1 Ng5-f7 .100 4 1 MgE~f7 .274 31 60 B c 4 - f 7 .483 Win a t C h e s s #279 2 0 Ne3-g4 .012 3 0 Ne3-g4 .260 4 0 Ne3-g4 .420 5 1 N e 3 x f 5 .834 Win a t C h e s s #280 2 0 Qc2xb1 .005 3 0 Qc2xb1 .024 4 0 Qc2xb1 .082 5 0 Qc2xb1 .247 6 0 Qc2xb1 .935 7 0 Qc2xb1 2.21 8 0 Qc2xb1 6.34 9 0 Qc2xb1 18.3 10 1 B f 8 x a 3 79.5 1 1 2 B f 8 x a 3 200. >300. Win a t C h e s s #281 2 -2 Rc7-c2 .098 3 -2 Rc7-c2 .167 4 -2 Rc7-c2 .361 5 -1 Rc7xh7 1.02 Win a t C h e s s #282 2 0 Rh1-h8 .027 3 0 Rh1-h8 .042 4 0 Rh1-h8 .121 5 0 Rh1-h8 .335 31 65 Rh1-h8 .572 Win a t C h e s s #283 2 1 Re3xb3 .017 3 1 Re3xb3 .069 4 1 Re3xb3 .279 5 1 Re3xb3 .734 6 1 Re3xb3 1 .96 7 1 Re3xb3 7.94 31 69 Nh3-g5 38.8 Win a t C h e s s #284 2 -2 Qd2- e2 .043 3 -2 Qd2- e2 .087 4 -2 Nd4- f 5 . 1 64 5 -2 Nd4- f 5 .445 6 -2 Nd4- f 5 1.17 Win a t C h e s s #285 2 0 Qg2-e2 .021 3 0 Qg2-e2 .062 4 0 Qg2-e2 .262 31 69 Qg2xg7 .499 Win a t C h e s s #286 2 0 b7-b6 .014 3 2 Rd8xd5 .083 4 2 Rd8xd5 .228 5 2 Rd8xd5 .705 Win a t C h e s s #287 2 0 d4-d5 .033 3 0 d4-d5 . 1 57 4 0 d4-d5 .652 5 0 Bf 7 - h 5 2.16 6 0 Bf 7 - h 5 6.02 7 1 Qd1-h5 23. 1 Win a t C h e s s #288 2 0 Qd6-c6 .024 3 0 Qd6-c6 .061 4 - 1 Qd6-c6 .293 5 - 1 Qd6-c6 1 .33 6 2 Nh5-f6 2.51 7 3 Nh5-f6 4.36 Win a t C h e s s #289 2 0 Qe6-g4 .014 3 0 Qe6-g4 .049 4 0 Qe6-g4 .222 5 1 Qe6-e5 .738 Win a t Chess #290 2 0 Ne5-g6 .012 3 0 Ne5-g6 .070 31 63 Nf4-e2 .217 Win a t C h e s s #291 2 1 Re5xd5 .002 3 1 Re5xd5 .050 4 1 Re5xd5 .154 5 0 Re5-e7 .904 6 1 Kg1-hi 3.01 7 1 Kg1-h1 4.79 8 1 Kg1-h1 7.93 9 1 Kg1-hi 22.8 10 1 Kg1-h1 68.4 1 1 3 h2-h3 207. >300. Win a t C h e s s #292 2 0 Qb7xd7 .016 3 0 Qb7xd7 .055 4 2 d5-d6 .271 5 4 d5-d6 .646 98 Win a t Ches s #293 2 0 a4xb5 .007 3 0 a4xb5 .044 4 n a 1 x b 5 -3 1 Q 5 6 a4xb5 .661 6 0 a4xb5 2.74 7 0 a4xb5 7.30 8 0 a4xb5 15.7 9 0 a4xb5 53.7 >300. Win a t C h e s s #294 2 0 Qg4- f 4 .023 3 0 Qg4- f 4 .060 4 0 Qg4- f 4 .201 5 0 Qg4- f 4 .589 6 1 Qg4- f 4 1.81 7 1 Qg4- f 4 4.91 8 6 Bd6- •f 8 15.5 9 6 Bd6- f8 30.6 Win a t C h e s s #295 2 0 Nf4xd5 .006 31 65 Rd1xd5 .014 Win a t C h e s s #296 2 -1 Bc6-d7 .112 3 -1 Bc6-d7 .266 4 -1 Bc6-d7 .806 Win a t C h e s s #297 2 0 Bd6-f4 .007 3 0 Bd6-f4 .062 4 0 Bd6-f4 .214 5 0 Bd6-f4 .627 6 0 Bd6-f4 2.35 7 0 Bd6-f4 7.95 8 0 Bd6-f4 22.0 9 0 Bd6-f4 79.9 10 0 Bd6-f4 258. Win a t C h e s s #298 2 0 Qd8-e8 .009 3 0 Qd8-e8 .026 31 62 Qd8-h8 .149 Win a t C h e s s #299 2 0 Nc5-d7 .013 3 0 Nc5-d7 .051 4 0 Nc5-d7 .316 5 4 Nc5-a4 1.03 Win a t C h e s s #300 2 0 f6 x g 7 .009 3 0 f6 x g 7 .045 4 1 g5-g6 .213 5 1 g5-g6 .443 6 1 g5-g6 1.15 

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