Single-suit two-person card play
We consider a two-person constant sum perfect information game, which is called the End Play Game, which arises from an abstraction of simple end play positions in card games of the whist family, including bridge. This game was described in 1929 by Emanuel Lasker, the mathematician and world chess champion, who called it whistette. The game uses a deck of cards that consists of a single totally ordered suit of 2n cards. To begin play the deck is divided into two hands A and B of n cards each, help by players Left and Right, and one player is designated as having the lead. The player on lead chooses one of his cards, and the other player after seeing this card selects one of his own to play. The player with the higher cards wins a ``trick'' and obtains the lead. The cards in the trick are removed from each hand, and play then continues until all cards are exhausted. Each player strives to maximize his trick total, and the value of the game to each player is the number of tricks he takes. Despite its simple appearance, this game is quite complicated, and finding an optimal strategy seems difficult. This paper derives basic properties of the game, gives some criteria under which one hand is guaranteed to be better than another, and determines the optimal strategies and value functions for the game in several special cases.
two-person constant sum perfect information game
scientific article; zbMATH DE number 4023060
scientific article