Beautiful Mates: Applying Principles of Beauty to Computer Chess Heuristics

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Universal-Publishers, 1997 - Computers - 120 pages
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A synopsis of eminent computer chess programs reveal that they are designed around a 'brute force' approach. An argument is made that by continuing the 'brute force' search approach, computer chess development is moving away from human evaluation methods. Research is done into studies of evaluation methods, and a discovery is made that humans use a form of intuition, called their 'sense of beauty', to choose the best chess move. A paper by Margulies is cited which formulates principles of beauty which apply to chess. Three versions of a chess program are developed, using no heuristics, standard chess heuristics, and beauty heuristics formulated from Margulies principles. The performance of the three versions of the program are compared using chess puzzles, and rated for how quickly they find the solution, and how few nodes they evaluate. Graphs are produced from the results of these tests, showing that beauty heuristics are, on average, 15% faster at finding the solution, and evaluate 10% fewer nodes. An improvement is implemented in all versions of the program which biases the search towards better moves, resulting in the beauty heuristics success rising to an average of 25% faster to the solution, and evaluating 33% fewer nodes, than the other heuristics. It is concluded that the beauty heuristics are closer to the way that humans evaluate chess positions.
 

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Contents

113 FAVOURED MOVES AND THE λ PARAMETER
39
1131 Improved Results from Favoured Moves
40
1141 Complexity in Mating Problems
41
1143 Method of Testing
42
1144 Standard Deviation
43
12 RESULTS
44
121 RESULTS FOR TWENTY TWO PUZZLES
45
1211 Chosen Problems
47

43 EVALUATION
16
431 Piece Ratio Exchange
17
45 PRUNING THE SEARCH
18
461 Opening Books
19
464 Transposition Tables
20
5 HUMAN CHESS PLAYING METHODS
21
52 CHUNKS
22
6 CONTRASTING HUMAN AND COMPUTER METHODS
23
7 PRINCIPLES OF BEAUTY
25
72 2 USE THE WEAKEST POSSIBLE PIECE
26
74 4 GIVE MORE AESTHETIC WEIGHT TO THE CRITICAL PIECES
27
75 5 USE ONE GIANT PIECE IN PLACE OF SEVERAL MINOR PIECES
28
77 7 AVOID BLAND STEREOTOPY
29
78 8 NEITHER STRANGENESS NOR DIFFICULTY PRODUCE BEAUTY
30
8 A DISCUSSION OF MARGULIES PAPER
31
9 APPLYING MARGULIES PRINCIPLES TO CHESS PUZZLES
32
92 REJECTED PRINCIPLES
33
93 ALL PIECES
34
10 IMPLEMENTING HEURISTICS IN CHESS
35
102 BEAUTY HEURISTICS
36
11 THE PROGRAM
37
112 OUTPUT DATA
38
1212 Mate in 2 problems
48
1213 Mate in 3 problems
49
1214 Two extra Mate in 4 and 5 problems
50
122 RESULTS FOR TWENTY TWO PROBLEMS WITH FAVOURED MOVES
52
1221 Chosen Problems with Favoured Moves
54
1222 Mate in 2 problems with Favoured Moves
55
1223 Mate in 3 problems with Favoured Moves
56
1224 Two extra Mate in 4 and 5 problems with Favoured Moves
57
13 FACTORS ARRISING FROM THE RESULTS
58
132 PERFORMANCE OF INDIVIDUAL HEURISTICS
60
133 AGGRESSION
61
14 CONCLUSION
62
15 BIBLIOGRAPHY
64
The Chess Board
68
Computer Representation
70
Heuristics
72
Sample Text Output
75
Summary Tables
79
All The Puzzles In Detail
82
Tables Of Results
107
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Page 11 - That within ten years a digital computer will be the world's chess champion, unless the rules bar it from competition. 2) That within ten years a digital computer will discover and prove an important new mathematical theorem. 3...
Page 8 - ... (4) There should be a background of knowledge concerning the activity against which the learning progress can be tested. (5) The activity should be one that is familiar to a substantial body of people so that the behavior of the program can be made understandable to them. The...
Page 8 - In checkers the goal is to deprive the opponent of the possibility of moving, and the dominant criterion is the number of pieces of each color on the board. The importance of having a known criterion will be discussed later. (3) The rules of the activity must be definite and they should be known. Games satisfy this requirement. Unfortunately, many problems of economic importance do not. While in principle the determination of the rules can be a part of the learning process, this is a complication...
Page 13 - The changes were made on the basis of specific performance weaknesses rather than on the basis of some general theoretical or conceptual model of human thinking or problem solving.

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