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

1
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
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
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 cant beat your computer at
  chess, try kickboxing.

4
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 cant 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
Highpoints of Computer Chess history

• 1950Claude Shannon writes Programming a Computer
  for Playing Chess, introduces minimax, Type A
  (search based) and Type B (knowledge based)
  programs.
• 1951Alan 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
• 1977Belle, 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
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
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
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
GUI example

10
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
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
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
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
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 101050 possible games, 1040 possible
  positions
• Typical game each player has around 50 moves,
  around 38 choices each time
• ? 38100
• 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
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
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
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
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 worlds 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
(No Transcript)