Learning to bid in bridge

Abstract

Bridge bidding is considered to be one of the most difficult problems for gameplaying programs. It involves four agents rather than two, including a cooperative agent. In addition, the partial observability of the game makes it impossible to predict the outcome of each action. In this paper we present a new decision-making algorithm that is capable of overcoming these problems. The algorithm allows models to be used for both opponent agents and partners, while utilizing a novel model-based Monte Carlo sampling method to overcome the problem of hidden information. The paper also presents a learning framework that uses the above decision-making algorithm for co-training of partners. The agents refine their selection strategies during training and continuously exchange their refined strategies. The refinement is based on inductive learning applied to examples accumulated for classes of states with conflicting actions. The algorithm was empirically evaluated on a set of bridge deals. The pair of agents that co-trained significantly improved their bidding performance to a level surpassing that of the current state-of-the-art bidding algorithm.

Boosting a Bridge Artificial Intelligence

“…Besides, the subproblem is related to a two-player process rather than to a four-player one. Automatic bidding has been studied in [1,6] where a PIDM (Partial Information Decision Making) algorithm has been designed in order to predict reasonable auctions. In [6], a self-organizing map neural network has been used to effectively bid no trump hands.…”

A work point count system coupled with back-propagation for solving double dummy bridge problem

“…It is played with a standard deck of 52 playing cards, where one of the players deals all of the cards, 13 to each player, in clockwise rotation, beginning with the player to the left of the dealer. In bridge games, basic representation includes value of each card as (Ace (A), King (K), Queen (Q), Jack (J ), 10,9,8,7,6,5,4,3,2) and suit as (Ƅ (Spades), the highest, Ɔ (Hearts), Ƈ (Diamonds), ƅ(Clubs), the lowest) for assignment of cards into particular hands and into public or hidden subsets, depending on the game rules. The ranking is for 'bidding' purposes only and in 'play' all suits are equal, unless one suit has been named as 'trumps', then it beats all the other cards.…”

“…In the standard 52-card deck used in bridge, the ace is ranked the highest followed by the king, queen, and jack and the spot-cards from ten down through two. The suit denominations 2 also have a rank order with no-trump being the highest followed by spades, hearts, diamonds and clubs.…”

“…The scoring points that are won on a deal as a result of making a contract, and the points which are lost when failing to make a contract, are both significantly increased for the side that is vulnerable. Accordingly, whether one's side is vulnerable affects its strategy for both bidding and play [2]. In certain situations, if one pair of players has made the most recent bid, in turn the other pair of players may double the stakes.…”

Reinforcement Learning in Games

“…They apply a simplified version to the Bridge-playing program GIB. Amit and Markovitch (2006) use MC sampling, but for each player, information unknown to them is masked out. The technique is applied to improved bidding in Bridge.…”