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INTELLIGENT SYSTEM FOR PLAYING TAROK

INTELLIGENT SYSTEM FOR PLAYING TAROK. Mitja Luštrek & Matjaž Gams Jožef Stefan Institute Ljubljana, Slovenia. PERFECT AND IMPERFECT INFORMATION GAMES. Perfect information (players have full knowledge of the state of the game) Chess, backgammon Checkers, Othello Connect-four ...

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INTELLIGENT SYSTEM FOR PLAYING TAROK

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  1. INTELLIGENT SYSTEMFOR PLAYING TAROK Mitja Luštrek & Matjaž Gams Jožef Stefan Institute Ljubljana, Slovenia

  2. PERFECT AND IMPERFECT INFORMATION GAMES • Perfect information(players have full knowledge of the state of the game) • Chess, backgammon • Checkers, Othello • Connect-four • ... • Imperfect information(players have only partial knowledge of the state of the game) • Bridge • Poker • Tarok • ...

  3. THE GAME – TAROK • Very popular in Central Europe • Many variants (tarock, taroky, königsrufen...) • Three players: two against one • 54 cards: suits and trumps – taroks • The objective is winning tricks

  4. THE PROGRAM – SILICON TAROKIST • Tarok-playing programs exist, but little is known of how they work. • Tarok.net (www.tarok.net) • Tarock World (www.gatecentral.com/triangle) • ... • We developed SiliconTarokist. • Freely available(tarok.bocosoft.com) • Plays reasonably wellas judged by humanplayers.

  5. GAME TREE SEARCH • Alpha-beta algorithm is used to search a single game tree. • Nodes – game states • Edges – moves

  6. SAMPLING • Monte Carlo sampling is used to generate samples of other players’ hands.

  7. ALPHA-BETA ENHANCEMENTS • Transposition table • Fuzzy transposition table • Similar to partition search (bridge program GIB, M. L. Ginsberg, 1996) • Move ordering • Adjusting the width of search window • Pruning the game tree

  8. TRANSPOSITION TABLE • Usually: transposition table stores single game states and their values. • Partition search: for each encountered game state, a set of states with equal value is calculated and stored together with the value. • Silicon Tarokist: the set of equivalent game states is determined heuristically.

  9. OTHER ALPHA-BETA ENHANCEMENTS • Move ordering • Moves that cause cut-offs should be tried first. • History heuristic: moves that have caused cut-offs in previously searched game states are given priority. • Adjusting the width of search window • Narrower search window causes more cut-offs, thus speeding up the search. • Minimal window search: non-first children of a node are searched with minimal window, since we are trying to show they are inferior to the first one. • Pruning the game tree • Some moves can be discarded because they are either clearly bad or redundant – the same effect can be achieved by another move.

  10. MONTE CARLO SAMPLINGENHANCEMENT • Monte Carlo sampling has demonstrable deficiencies. • Nevertheless, it works. • Deficiency we observed: • An assumption about the state of the game is made. • Sequence of bad, but inevitable move – good move is evaluated equally as good move – bad, but inevitable move. • Sometimes bad, but inevitable move is made first. • Then it turns out it is not inevitable. • Solution: • In addition to full search, search to the depth of one trick is performed. • This emphasizes immediate profit. • A combination of both searches is used for the final decision.

  11. RESULTS • Game tree search algorithm in Silicon Tarokist searches 184-times less nodes than alpha-beta using uses 86-times less time. • The program does not play flawlessly, but it is a challenging opponent. • For truly high-level play, game tree search that we use in inadequate. • It is too shallow for long-term strategies to be developed. • It will either have to be improved significantly • or another –probably knowledge-based–way to develop long-term strategies will have to be devised.

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