Machine Learning of Bridge Bidding

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Machine Learning of Bridge Bidding
By Dan Emmons Computer Systems Laboratory 2008-200
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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

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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

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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
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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

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Current Bidding Performance
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 Pas
s Pass Pass 2S Pass 3H Pass 3S X 4C Pass 4S Pass 4
NT Pass 5C Pass 5H Pass 5S X Pass Pass Pass 5SX
Nonvul - South Making Exact Score 650
Dealer West Vulnerable All North Clubs A 8
4 Diamonds Q J 8 Hearts A T Spades A T 8 6
3 West East Clubs Q 5 2 Clubs J 6
3 Diamonds 6 4 3 2 Diamonds A T 9 Hearts 9 7
4 Hearts Q J 8 5 Spades J 7 2 Spades K Q
9 South Clubs K T 9 7 Diamonds K 7
5 Hearts K 6 3 2 Spades 5 4 South West North
East 4D Pass 4H X Pass Pass 4S X Pass Pass Pass
4SX Vul East Down 7 Score -2000
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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