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Development and Implementation of a Machine Bridge Bidding Algorithm

Development and Implementation of a Machine Bridge Bidding Algorithm. By Dan Emmons Computer Systems Laboratory 2008-2009. Bridge Bidding is Hard. Both cooperative agents and opposing agents must be dealt with Only partial information is available to each player

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Development and Implementation of a Machine Bridge Bidding Algorithm

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  1. Development and Implementation of a Machine Bridge Bidding Algorithm By Dan Emmons Computer Systems Laboratory 2008-2009

  2. Bridge Bidding is Hard • Both cooperative agents and opposing agents must be dealt with • Only partial information is available to each player • Effectiveness of all bids cannot be evaluated until the end of the entire bidding sequence • Multiplicity of meanings for each bid • Some hands can be readily handled with multiple bids while other hands can be readily handled by no bids

  3. Three Necessary Parts • A way to select bids that overcomes the limitation of partial information • A way to evaluate a bidding scenario by counting tricks that can be earned in play • A way to improve partnership bidding agreements inductively to improve overall bidding through learning

  4. ? ? ? C: QJT94 D: 732 H: AQJ S: KT ? ? C: 73 D: AK984 H: K4 S: 96 ? C: 6 D: QT85 H: 73 S: AQ9742 ? ? ? C: AQ83 D: QJ32 H: A32 S: Q5 C: T6 D: Q72 H: AQ62 S: 8732 C: J93 D: A43 H: AKQT84 S: T C: AJ8 D: K94 H: KJT5 S: K85 ? ? ? ? ? ? ? ? ? ? ? ? Monte Carlo Sampling

  5. Root Node Constraints: None Actions: Pass Constraints: 13+ HCP Actions: 1C, 1D, 1H, 1S, 1NT Constraints: 5+ Hearts Constraints: 4+ Diamonds Constraints: 15-17 HCP, Balanced Actions: 1H Actions: 1D Actions: 1NT The Bid Decision Hierarchy High Priority Low Priority

  6. Double-Dummy Solver Implementation • MTD(f) is used with a transposition table • Two pruning extra pruning techniques: • Only check one of adjacent cards in the same hand • Assume the player does not want to lose with a higher card than necessary • Hash values are computed so as to hash equivalent hand positions to the same value: Clubs: K Q J Diamonds: 9 7 2 Hearts: 6 5 4 3 2 Spades: K 9 After the club ace has been played Clubs: A K J Diamonds: 9 7 2 Hearts: 6 5 4 3 2 Spades: K 9 After the club queen has been played

  7. Sample Output of Implemented Solver • North: • Clubs: T 7 5 3 2 • Diamonds: J • Hearts: A Q J T • Spades: T 9 7 • West: East: • Clubs: 6 Clubs: A J 8 • Diamonds: A K T 7 5 Diamonds: Q 9 8 • Hearts: 9 8 4 Hearts: 5 3 • Spades: Q J 6 2 Spades: A K 8 5 4 • South: • Clubs: K Q 9 4 • Diamonds: 6 4 3 2 • Hearts: K 7 6 2 • Spades: 3 • Trick Counts for Each Declarer (North, South, East, West): • Clubs: 9 9 3 3 • Diamonds: 2 2 11 11 • Hearts: 7 7 3 3 • Spades: 0 0 11 11 • No Trump: 2 2 8 8

  8. Current Bidding Performance – No Conventions vs. Conventions Dealer: West Vulnerable: None North Clubs: A K 7 6 Diamonds: J T 8 4 Hearts: Q T 8 3 Spades: 2 West East Clubs: 9 8 5 4 Clubs: J 2 Diamonds: 9 7 6 Diamonds: A Q 2 Hearts: J 2 Hearts: A K 9 7 6 4 Spades: 8 7 6 3 Spades: K 9 South Clubs: Q T 3 Diamonds: K 5 3 Hearts: 5 Spades: A Q J T 5 4 South West North East Pass Pass Pass 2S Pass 3H Pass 3S X 4C Pass 4S Pass 4NT Pass 5C Pass 5H Pass 5S X Pass Pass Pass 5SX Nonvul - South Making Exact Score: 650 Dealer: West Vulnerable: E-W North Clubs: Q J 8 4 3 Diamonds: K T 4 Hearts: K J 9 Spades: K 7 West East Clubs: T 6 2 Clubs: 5 Diamonds: A 5 3 2 Diamonds: 9 8 7 6 Hearts: 8 6 2 Hearts: Q 5 3 Spades: Q 6 2 Spades: A J 9 4 3 South Clubs: A K 9 7 Diamonds: Q J Hearts: A T 7 4 Spades: T 8 5 West North East South Pass 1D Pass 1H Pass 2C Pass 3NT Pass 4C Pass 4H Pass Pass Pass 4H Nonvul - South Making Exact 420

  9. Test Results Computer bidding agents played online against humans with human partners who were not told they were playing with a computer on www.bridgebase.com using IMP scoring The computer averaged a gain of 1.83 IMPs per hand As compared with a typical average IMP gain per hand of 2 for experts playing novices, this constitutes success

  10. Expected Fourth Quarter Activities • Addition of a more complete set of common conventions • Development of the ability to develop conventions automatically through induction • Development of a plot of the relationship between playing strength and the number of bidding convention networks learned

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