Machine Learning of Bridge Bidding

By Dan EmmonsComputer 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

• 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

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

Monte Carlo Sampling

C: QJT94D: 732H: AQJS: KT

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C: 73D: AK984H: K4S: 96

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C: 6D: QT85H: 73S: AQ9742

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C: AQ83D: QJ32H: A32S: Q5? ?

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C: J93D: A43H: AKQT84S: T? ?

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C: T6D: Q72H: AQ62S: 8732? ?

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C: AJ8D: K94H: KJT5S: K85? ?

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The Bid Decision HierarchyRoot Node

Constraints: None

Actions: Pass

Constraints: 15-17 HCP, Balanced

Actions: 1NT

Constraints: 5+ Hearts

Actions: 1H

Constraints: 4+ Diamonds

Actions: 1D

Constraints: 13+ HCP

Actions: 1C, 1D, 1H, 1S, 1NT

High Priority

Low Priority

Double-Dummy Solver Implementation•MTD(f) is used with a transposition table

•Two pruning extra pruning techniques:

oOnly check one of adjacent cards in the same hand

oAssume 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: A K JDiamonds: 9 7 2Hearts: 6 5 4 3 2Spades: K 9

After the club queen has been played

Clubs: K Q JDiamonds: 9 7 2Hearts: 6 5 4 3 2Spades: K 9

After the club ace has been played

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

Current Bidding PerformanceDealer: WestVulnerable: All

NorthClubs: A 8 4Diamonds: Q J 8Hearts: A TSpades: A T 8 6 3

West EastClubs: Q 5 2 Clubs: J 6 3Diamonds: 6 4 3 2 Diamonds: A T 9Hearts: 9 7 4 Hearts: Q J 8 5Spades: J 7 2 Spades: K Q 9

SouthClubs: K T 9 7Diamonds: K 7 5Hearts: K 6 3 2Spades: 5 4

South West North East4D Pass 4H

X Pass Pass 4SX Pass Pass Pass

4SX Vul – EastDown 7Score: -2000

Dealer: WestVulnerable: None

NorthClubs: A K 7 6Diamonds: J T 8 4Hearts: Q T 8 3Spades: 2

West EastClubs: 9 8 5 4 Clubs: J 2Diamonds: 9 7 6 Diamonds: A Q 2Hearts: J 2 Hearts: A K 9 7 6 4Spades: 8 7 6 3 Spades: K 9

SouthClubs: Q T 3Diamonds: K 5 3Hearts: 5Spades: A Q J T 5 4

South West North EastPass Pass Pass

2S Pass 3H Pass3S X 4C Pass4S Pass 4NT Pass5C Pass 5H Pass5S X Pass PassPass

5SX Nonvul - SouthMaking ExactScore: 650

Third Quarter Improvements

•Give bidding agents a more rigid framework of rules and constraints as a basic system

•Teach agents to refine their bidding system inductively, reducing the average branching factor of the bidding look-ahead and giving the partner agent more information per bid

•Hold IMP-scored games between refined and unrefined bidders to verify improvement

•Test a computer bidding pair against human opponents