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Physical Review X

Quantum Bidding in Bridge

Sadiq Muhammad, Armin Tavakoli, Maciej Kurant, Marcin Pawłowski, Marek Żukowski, Mohamed Bourennane

Published Jun 12, 2014• 39 citations
Publisher

Abstract

In a game of duplicate bridge, better information sharing between two partners about their cards means better chances of winning. Researchers devise, and experimentally demonstrate, the first quantum information-sharing protocol that lets players improve their bids, expanding the understanding and use of quantum resources.
DOI
10.1103/physrevx.4.021047

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Trick-Taking Games (TTGs) are card games in which each player plays one of his cards in turn according to a given rule. The player with the highest card then wins the trick, i.e., he gets all the cards that have been played during the round. For instance, Spades is a famous TTG proposed by online casinos, where each player must play a card that follows the leading suit when it is possible. Otherwise, he can play any of his cards. In such a game, a dishonest user can play a wrong card even if he has cards of the leading suit. Since his other cards are hidden, there is no way to detect the cheat. Hence, the other players realize the problem later, i.e., when the cheater plays a card that he is not supposed to have. In this case, the game is biased and is canceled. Our goal is to design protocols that prevent such a cheat for TTGs. We give a security model for secure Spades protocols, and we design a scheme called SecureSpades. This scheme is secure under the Decisional Diffie-Hellman assumption in the random oracle model. Our model and our scheme can be extended to several other TTGs, such as Belotte, Whist, Bridge, etc.