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Two-person symmetric whist
Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
2005 (English)Report (Other academic)
Abstract [en]

The game of two-person whist is played with a deck of cards. Each card belongs to a suit, and each suit is totally ordered. The cards are distributed between the two players so that each player receives the same number of cards. Hence both players have complete information about the deal. Play proceeds in tricks, with the obligation to follow suit, as in many real-world card games.

We study the symmetric case of this game, that is, we assume that in each suit, the two players have the same number of cards. Under this assumption, the second player in each trick will always be able to follow suit.

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 multisuit deal under optimal play is determined by the sum of the values of the individual suit. This allows us to play a deal perfectly, provided that we can compute the values of its single-suit components. Although we do not have an efficient algorithm for doing this in general, we give methods that will allow us to find the value of a suit quickly in most cases.

We also establish certain general facts about the game, for instance the nontrivial fact that a higher card is always at least as good as a smaller card in the same suit.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press , 2005. , 37 p.
Linköping Studies in Mathematics, ISSN 1652-4454 (online), 0348-2960 (print) ; 4
National Category
URN: urn:nbn:se:liu:diva-62948OAI: diva2:375247
Available from: 2005-02-21 Created: 2010-12-07Bibliographically approved

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Wästlund, Johan
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Applied MathematicsThe Institute of Technology

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