Tuyển tập các báo cáo nghiên cứu khoa học về toán học trên tạp chí toán học quốc tế đề tài: A solution of two-person single-suit whist. | A solution of two-person single-suit whist Johan Wastlund Department of Mathematics Linkoping University Linkoping Sweden jowas@ Submitted May 21 2001 Accepted Aug 29 2005 Published Sep 5 2005 Mathematics Subject Classification 91A46 Abstract We give a complete solution of the combinatorial game of two-person single-suit whist. This game is played with a deck consisting of a single totally ordered suit of 2n cards. Each of the two players receives n cards. Hence both players have complete information about the distribution of the cards. One of the players is said to be on lead. Play proceeds in rounds called tricks. The player on lead plays one of his cards and with knowledge of this card the other player plays one of his cards. The player with the higher card wins the trick and obtains the lead. The cards that are played are then removed. Play continues until all cards are exhausted. Each player tries to win as many tricks as possible. Our solution provides an efficient algorithm for calculating the game theoretical value of any distribution of the cards. 1 Introduction Trick taking games Playing cards were probably introduced in Europe around 1370. According to D. Parlett 8 simple trick taking games for two players were around at least as early as in the beginning of the fifteenth century. It is therefore reasonable to assume that this family of games are among the oldest games played with a deck of cards. Card games and in particular trick taking games have remained among the most popular and commonly played social games ever since. Today the family of trick taking games includes a large variety of games for different numbers of players among them the game of bridge by many considered the most intellectually challenging of all card games. Trick taking games have certain fundamental rules in common. Each player is dealt the same number of cards and the cards are played in rounds called tricks consisting of one card from each player. In each trick .
