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

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. Monte Carlo Sampling ? ? ? ? ? ? ? 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 ?

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

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: A K J
Diamonds: 9 7 2
Hearts:
Spades: K 9
After the club queen has been played
Clubs: K Q J
Diamonds: 9 7 2
Hearts:
Spades: K 9
After the club ace has been played

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

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: Clubs: J 2
Diamonds: Diamonds: A Q 2
Hearts: J 2 Hearts: A K
Spades: 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 Diamonds:
Hearts: 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. The computer averaged a gain of 1.83 IMPs per hand
Test Results
Computer bidding agents played online against humans with human partners who were not told they were playing with a computer on 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