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Báo cáo toán học: "Two-person symmetric whist"

Tuyển tập các báo cáo nghiên cứu khoa học về toán học trên tạp chí toán học quốc tế đề tài: Two-person symmetric whist. | Two-person symmetric whist Johan Wastlund Department of Mathematics Linkoping University Linkoping Sweden jowas@mai.liu.se Submitted May 21 2001 Accepted Aug 29 2005 Published Sep 5 2005 Mathematics Subject Classification 91A46 Abstract We introduce a two-person perfect information model of trick taking games. A set of cards is distributed between two players and play proceeds in tricks with the obligation to follow suit as in many real-world card games. We assume that in each suit the two players have the same number of cards. Under this assumption we show how to assign a value from a certain semigroup to each single-suit card distribution in such a way that the outcome of a multi-suit deal under optimal play is determined by the sum of the values of the individual suits. 1 Two-person whist The game of two-person whist is played with a deck of cards. Each card belongs to a suit and within each suit the cards are ordered by rank. Real-world card packs sometimes have four suits with thirteen cards in each suit. We will not restrict ourselves to the standard deck and in any case the french suited 52 card pack too is just one of many variations. There does not even have to be the same number of cards in each suit. The cards are distributed between the two players so that both players receive the same number of cards. We assume that both players have complete information about the situation. One of the players is said to have the lead. The player who has the lead plays or leads one of his cards. The other player in response to this plays one of his cards. If possible he has to follow suit that is he has to play a card in the same suit as the card that was led. The player who played the highest card in the suit that was led wins the trick and obtains the lead. The cards that have been played are removed and play continues until all cards have been played. Each player tries to win as many tricks as possible. This game is a pure form of a common type of card game trick .