AI Strategies for Contract Bridge Presented on 30

AI Strategies for Contract Bridge Presented on 30 th Nov. 2009 By Akshar Prabhu Desai Salil Joshi Subhajit Datta

Introduction A card game most commonly played since 19 th century. Played in International Tournaments. Involves Educational Guessing. Required Skill-set: Memory Tactics Probability Communication

Motivation Successful implementation of AI in Deterministic games like Tic-Tac-Toe, Chess, Checkers, Billiards. Contract Bridge is a Game of imperfect information. Provides new challenges Connect. Four solved Qubic solved Othello: probably better than any human Checkers: better than any living human Chess: better than any living human Scrabble: worse than best humans Go: worse than best human 9 -year-olds Bridge: worse than the best human players

Overview Rules of the Game Overview of well-known Implementations Bidding Phase HTN Strategy Game play Phase [Bridge Baron] Conclusion

Rules of the Game Trick-taking card game involving deck of 52 cards. Played by four players. Partners sit opposite one another (i. e. North-South, East. West). Involves 2 game phases: Bidding Game Play 13 tricks to be dealt with.

Rules of the Game [Bidding] Cards are shuffled and distributed. Five strains from lowest to highest are - clubs (♣), diamonds (♦), hearts (♥), spades (♠), and no trump (NT). Statement by one partnership that they will take at least a certain number of tricks (Number of tricks = 6 [book] + Level). e. g. "3 hearts" is an assertion that the partnership will take nine tricks (6 + 3) with hearts (♥) as trump. Players may pass the turn. End of Bidding: 3 Successive passes. Last call determines the Trump (♣, ♦, ♥, ♠) or No-Trump. Highest Bidders → Declarers Opponents → Defenders

Rules of the Game [Game Play] Defender to the left of declarer starts the game. Declarer's partner's hand becomes dummy. Every player must play every trick, with the card of suit being played if available. If card of playing suit is not present, player may trump. Trump cards are elevated above their normal rank. The player with Highest card of the trick, or highest trump card wins the trick. By the end of 13 tricks, declarers should fulfill the bid to win. The score is determined accordingly. Techniques by declarer – finessing, ruffing, cross-ruffing.

Overview of well-known Implementations Bridge Baron – HTN planning [Game play] GIB Jack Wbridge 5 Microbridge 8 Q-Plus Meadowlark Tignum 2

Bidding Phase Arriving at a good final contract in the auction. Partners must communicate sufficient information about their hands to arrive at a makeable contract by the calls. A bid is any denomination on a higher level than the last bid, or a higher-ranked denomination on the same level. e. g. after a bid of 3♥, bids of 2♠ or 3♣ are not allowable, but 3♠ or 4♦ are. A call might Bid, Double, Re-double or Pass. The final contract may be doubled (by the opponents) or redoubled (by the declaring side). Self-Organizing maps are used for AI in Bidding phase (complex problem).

Hierarchical Task Network [HTN] Strategy An approach to automated planning. Dependency among actions can be given in the form of networks [Hierarchy]. Breaking down of complex tasks into smaller and smaller subtasks with restrictions which can be directly done. 3 types of tasks: Compound task: composed of a set of primitive tasks. Primitive task: action that can be executed. Goal task: task of satisfying a condition. A given task is feasible only if a set of other actions are done. Generates game trees containing only about 305, 000 nodes, as compared to 5. 55 x 1044 nodes in conventional game trees.

HTN [Example]

HTN [Example Cntd. . . ] Travel (IITB, IISc) Buy ticket (CSIA, BIAL) Travel (IITB, CSIA) Get taxi Ride taxi (IITB, CSIA) Pay driver : -) Fly (CSIA, BIAL) Travel (BIAL, IISc) Get taxi Ride taxi (BIAL, IISc) Pay driver

Game play Phase [Bridge Baron] Adaptation of HTN planning techniques to plan declarer play. Uses state information sets to represent the locations of cards about which declarer is certain. Uses belief functions to represent the probabilities associated with the locations of other cards. Subtasks are ordered in which they must be completed. Applies all methods applicable to a given state of the world to produce new states of the world. Includes implementation for finessing.

Game play Phase [Cntd. . . ] Image Source: Ref [4]

Game play Phase [Cntd. . . ] Algorithm takes a weighted average of the node’s children, based on probabilities generated by belief function. Probabilities for every card with opponents are calculated. e. g. What is the probability that the opponent in North holds at least 1 spade lower than ♠ 9? Depending on the probabilities, the game tree for the finessing is produced which expresses these probability values as edges, and scores are calculated at every node. The algorithm will choose move which will maximize the score with high probability.

Game play Phase [Cntd. . . ] Image Source: Ref [4]

Conclusion For Determinstic games, the computer programs are based on the use of “brute force” game-tree search techniques. Bridge Baron (and other compatitive programmes on bridge) bases its declarer play on the use of HTN planning technique [4]. Tree spanning and effeciency with HTN is much better than “brute force” techniques [3]. Still have far to go before programmes can compete at level better than that of expert human bridge players [2].

References 1. Jacob Bellamy-Mc. Intyre, "Case-Based Reasoning to the Game of Bridge", Dept. of Computer Science, University of Auckland, 2008 2. Lori L. De. Looze and James Downey, "Bridge Bidding with Imperfect Information", Computational Intelligence and Games, 2007. 3. Stephen J. J. Smith, Dana Nau, and Kutluhan Erol, "Control Strategies in HTN Planning: Theory Versus Practice", IAAI-98 Proceedings, 1998. 4. Stephen J. J. Smith, Dana Nau, and Tom Throop, "Computer Bridge: A Big Win for AI Planning", AI Magazine Volume 19 Number 2, 1998. 5. Wikipedia article, "Contract bridge", http: //en. wikipedia. org/wiki/Contract_bridge

Thank You! Questions?