Back-Propagation Neural Network Architecture for Solving the Double Dummy Bridge Problem in Contract Bridge

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

“…In bridge games, though the 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) for assignment of cards into particular hands and into public or hidden subsets, a uniform linear transformation in the range 0.10 through 0.90 where 0.10 is assigned to the smallest card value 2 with an increment of 0.067 to the next card value i.e., 3 and so on till 0.90 for the highest card value A is assigned as represented in Table 1. Though the ranking is for 'bidding' purposes only, with respect to 'play' all suits are considered equal, unless one suit has been named as 'trumps', then it beats all the other cards.…”

“…The maximum card in the suit wins the trick for the player who played it, known as playing in no-trump. The no-trump contracts seem to be potentially simpler than the suits , because it is not possible to ruff a card of a high rank with a trump card [17]. Though it simplifies the rules, it doesn't simplify the strategy as there is no guarantee that a card will take a trick, because even Aces are useless in tricks of other suits in no-trump contracts.…”

“…Though the game of bridge has not attracted much attention of the researchers of Soft Computing, there are many interesting nuances of the game of bridge from the point of view of Artificial Intelligence (AI), since many factors of the game of bridge satisfy the very definition 6 of it such as the imprecise data, imperfect information through which the fact is to ascertained etc. The two completely different phases of the game-the bidding and the play, both should be played optimally well to gain the best possible result can be matched with that of the training and testing phases of AI, since the best possible training of the neurons can alone reflect the level of accuracy of inference in the testing phase of the network.…”

“…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.…”

“…The focus of the paper is mainly on verification of ANN's abilities to learn the evaluation function to solve the Double Dummy Bridge Problems (DDBP) rather than finding the solution to the problem. There are many Feed Forward Neural Networks (FFNN) available which are trained in bridge game [3,4,5] and have been formalized in the best defense model, which also presents the strongest possible assumptions about the opponent [6,7]. This is used by human players because modeling the strongest possible opponents provides a lower bound on the pay off that can be expected when the opponents are less informed.…”