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Intelligence for Games and Puzzles1 Computer Chess Chess is the game most intensively studied.

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1 http://csiweb.ucd.ie/Staff/acater/comp30260.htmlArtificial Intelligence for Games and Puzzles1 Computer Chess Chess is the game most intensively studied thus far by the AI community. In 1965, it was called the Drosophila of Artificial Intelligence (by Russian mathematician Alexander Kronrod)

2 http://csiweb.ucd.ie/Staff/acater/comp30260.htmlArtificial Intelligence for Games and Puzzles2 Computer Chess Chess is the game most intensively studied thus far by the AI community. In 1965, it was called the Drosophila of Artificial Intelligence (by Russian mathematician Alexander Kronrod) In 1997, John McCarthy commented on this: “However computer chess has developed as genetics might have if the geneticists had concentrated their efforts starting in 1910 on breeding racing Drosophila. We would have some science, but mainly we would have very fast fruit flies.”

3 http://csiweb.ucd.ie/Staff/acater/comp30260.htmlArtificial Intelligence for Games and Puzzles3 Computer Chess Chess is the game most intensively studied thus far by the AI community. In 1965, it was called the Drosophila of Artificial Intelligence (by Russian mathematician Alexander Kronrod) In 1997, John McCarthy commented on this: “However computer chess has developed as genetics might have if the geneticists had concentrated their efforts starting in 1910 on breeding racing Drosophila. We would have some science, but mainly we would have very fast fruit flies.” Anon said: “If you can’t beat your computer at chess, try kickboxing.”

4 http://csiweb.ucd.ie/Staff/acater/comp30260.htmlArtificial Intelligence for Games and Puzzles4 Computer Chess Chess is the game most intensively studied thus far by the AI community. In 1965, it was called the Drosophila of Artificial Intelligence (by Russian mathematician Alexander Kronrod) In 1997, John McCarthy commented on this: “However computer chess has developed as genetics might have if the geneticists had concentrated their efforts starting in 1910 on breeding racing Drosophila. We would have some science, but mainly we would have very fast fruit flies.” Anon said: “If you can’t beat your computer at chess, try kickboxing.” and “At times it seems that all what we have achieved in 40 years of computer chess research is to drop the prediction time from ‘sometime in the next decade’ to ‘in the next three years’.”

5 http://csiweb.ucd.ie/Staff/acater/comp30260.htmlArtificial Intelligence for Games and Puzzles5 Highpoints of Computer Chess history 1950:Claude Shannon writes Programming a Computer for Playing Chess, introduces minimax, Type A (search based) and Type B (knowledge based) programs. 1951:Alan Turing creates & hand-simulates a B program, it loses to a weak player. 1956, 1957: A- and B- Programs implemented on computers, getting better 1958: Alpha-beta pruning introduced, it greatly reduces the work involved in tree search, enabling deeper search. 1967: MacHack-6 competes in 4 amateur chess tournaments, wins 3, draws 3, loses 12 1973: Chess 4.0 wins computer tournament comfortably, others start switching to type A 1977:Belle, with special-purpose hardware, beats a Grandmaster at speed chess. 1988: Deep Thought defeats a Grandmaster in a tournament. 1996: Deep Blue beats reigning champion Kasparov in the first game of a six-game match, but loses the match. 1997: Improved Deep Blue defeats Kasparov, though he did not play at his best.

6 http://csiweb.ucd.ie/Staff/acater/comp30260.htmlArtificial Intelligence for Games and Puzzles6 Shannon Types A, B Type A programs work by (or as if by) exploring all moves in a game tree to a uniform depth. Type B programs choose parts of a game tree to explore, doing selective move generation using chess knowledge (rules, learned weights, patterns & statistics) to distinguish promising lines of play to be explored further from poor lines of play to be explored no further (“Quiescence Search” complicates this simplistic picture, but it is not considered enough to turn an A program into a B one) Shannon believed Type B clearly superior, but (in chess anyhow) experience has not borne this out.

7 http://csiweb.ucd.ie/Staff/acater/comp30260.htmlArtificial Intelligence for Games and Puzzles7 ELO Ratings for human players 800 - Beginner 1400 - Class D or C 1600 - Class C or B 1800 - Class B or A 2000 - Class A or Expert 2200 - Expert or National Master 2300 - National Master 2520 - International Master 2600 - Grandmaster 2700+ - Super Grandmaster Each extra 100 points corresponds roughly to expecting to win two games out of three: approx 20 such steps from beginner to champion.

8 http://csiweb.ucd.ie/Staff/acater/comp30260.htmlArtificial Intelligence for Games and Puzzles8 Gross Anatomy of a chess program User Interface - most probably a GUI but this is not strict requirement Representations For board positions (perhaps also, parts of board positions) For moves (whether played or merely imagined) Chess Engine Judge legality of user-input moves Effect board position changes in response to moves Allow retraction of moves (for user convenience, also for search) Means of selecting moves for computer player  Game-Tree Search: often alpha-beta with several refinements  Evaluation Function: often dominated by material gains/losses  Opening book  Endgame database

9 http://csiweb.ucd.ie/Staff/acater/comp30260.htmlArtificial Intelligence for Games and Puzzles9 GUI example

10 http://csiweb.ucd.ie/Staff/acater/comp30260.htmlArtificial Intelligence for Games and Puzzles10 Representations required Board Positions: Board-Centric: Chess board has 64 squares, each may be empty or occupied by one of twelve kinds of chessmen. Therefore one may use an 2-d 8x8 array (or 1-d 64-vector) of 4-bit values, (or several bitboards to be described in a future lecture). Piece-Centric: A player has 16 men, each is either captured or on one of 64 squares. Therefore one may use a 1-d 16-vector of 7-bit values. Moves: A chessman belonging to one player moves from one square to another. Therefore one may use a pair (FromSquare, ToSquare) of 6-bit numbers. But …

11 http://csiweb.ucd.ie/Staff/acater/comp30260.htmlArtificial Intelligence for Games and Puzzles11 Requirements of representations The rules of chess have two oddities that spoil this simple representation of moves (and piece-centric board representations too) Castling: Subject to certain provisos, a king K and a rook R may move simultaneously  Each K just once per game, neither it nor R has yet moved, K is not moving out of check or through check, all spaces empty between K & R K may normally only move one square; in castling it moves two squares. Special logic could handle the implied R movement of a 2-square K move. Pawn Promotion: A pawn that reaches the 8th rank is replaced with another piece: Queen Rook Bishop or Knight Piece-Centric board representation now needs to say what type of piece (FromSquare, ToSquare) pair needs extra WhatPieceNow element

12 http://csiweb.ucd.ie/Staff/acater/comp30260.htmlArtificial Intelligence for Games and Puzzles12 Chess Engine element: The Rules The rules of movement and capture need to be represented: Different pieces may move in different ways: Pawn: forward two empty squares from its starting position; Pawn: one empty square forward from any position; Bishop: diagonally any direction any number of empty squares; Rook: forward backward or sideways any number of empty squares; Queen: diagonally like bishop or to-or-fro-or-sideways like rook; Knight: one square forward or back plus two sideways, or vice versa King: to any of eight adjacent squares, or special castling move. All pieces except pawns may capture an opposing piece by finishing their movement where it is. The opposing piece is removed. Pawns capture with a one-square forward-diagonal; There is an en-passant rule too. Read all about it!

13 http://csiweb.ucd.ie/Staff/acater/comp30260.htmlArtificial Intelligence for Games and Puzzles13 Chess Engine element: Make Move and Retract Move User-input moves, and Computer-Generated responses, must have the correct effect, and be reflected in the GUI. Interactive users should be given the opportunity to Undo a pair of moves. Therefore, Move Representation must include information on captures too, so that a captured piece can be reinstated by Undo. The Make-Move and Retract-Move functionality is needed also, intensively, while the computer player is searching the game tree Must therefore be fast Will not involve GUI

14 http://csiweb.ucd.ie/Staff/acater/comp30260.htmlArtificial Intelligence for Games and Puzzles14 Chess Engine element: Game-Tree search The full game tree for chess is so large that it is not feasible to search for the winning move. Estimates of 10 10 50 possible games, 10 40 possible positions Typical game: each player has around 50 moves, around 38 choices each time  38 100 Shannon Type A programs would use Minimax algorithm, to a fixed depth, backing up values heuristically computed by an evaluation function. The deeper the search, the better the play. There are many refinements to the basic Minimax, and some alternatives to it:

15 http://csiweb.ucd.ie/Staff/acater/comp30260.htmlArtificial Intelligence for Games and Puzzles15 Beyond Minimax Refinements: Alpha-Beta, Progressive Deepening, Principal Variation Search, Transposition Tables, Quiescence Search, Principal Variation Search (NegaScout), Scout, Aspiration Search, MTD(f), Killer Heuristic, History Heuristic, NullMove Heuristic, Selective Extensions. Alternatives: Conspiracy Number Search, Proof Number Search, B*, Monte-Carlo rollouts, UCT.

16 http://csiweb.ucd.ie/Staff/acater/comp30260.htmlArtificial Intelligence for Games and Puzzles16 Chess Engine element: Evaluation Function An evaluation function provides a number which indicates how good a position is for one player. This is vague, but should not be treated as probability of a win. Evaluation function will be heavily used in search, so should be fast. Evaluation functions for chess are typically dominated by material balance. Typical values: Pawn 1; Bishop 3; Knight 3; Rook 5; Queen 9; King infinite. Other features taken into account too: Control of the centre four squares Passed pawns Mobility, especially of the queens. The sum of possible value of all other features combined is typically regarded as no more than 1.5 pawns

17 http://csiweb.ucd.ie/Staff/acater/comp30260.htmlArtificial Intelligence for Games and Puzzles17 Chess Engine element: Opening book It quickly proved too hard to select good opening moves using limited search and an evaluation function. Centuries of human experience are codified in opening books which serious players study. Chess programs use the knowledge in these publications, perhaps augmented by team members expert or better in chess, coded by programmers into a form their program can use. A common strategy of human players confronting computers is to make moves out of the book - i.e. not found in the book - in the expectation that the computer will not be able to find the responses which make the move sub-optimal.

18 http://csiweb.ucd.ie/Staff/acater/comp30260.htmlArtificial Intelligence for Games and Puzzles18 Chess Engine element: Endgame databases An Endgame database is a tabulation of the possible positions in which only a very small number of chessmen remain on the board. For each position, it records the best move. Examples are: King and Pawn versus King (KPK) King and Rook versus King (KRK) King Rook and Pawn versus King and Rook (KRPKR) Some endgame databases did exist, as books, before computer chess. But Computer Chess has contributed enormously to the chess world’s knowledge of several endgames, through exhaustive analysis of positions too numerous for humans to tabulate. Championship contenders have been known to consult computer-generated databases overnight during an adjourned game.

19 http://csiweb.ucd.ie/Staff/acater/comp30260.htmlArtificial Intelligence for Games and Puzzles19


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