A Solution of Two-Person Single-Suit Whist

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.