User:Celiakozlowski/Le Her

Le Her is a two-player card game extensively analyzed by mathematicians and scholars of game theory. The name comes from 17th century French for "the gentleman."

As described by Benjamin and Goldman, for example, the basic game goes like this: Each of the two players is dealt one card, which they look at but do not show to their opponent. The remainder of the deck is kept in a pile, face-down. After examining his card, the first player can keep it or swap with the second player. After this is done, the second player takes his turn and may keep his card or exchange it for the top card on the pile. The player with the high card wins one unit from the player with the low card. Mathematicians have calculated optimal strategies for the game when played with various numbers of 52-card decks, different numbers of suits, different numbers of cards in each suit, etc.

A version of the game described by Ethier is played with a standard 52-card deck with cards ranked from A, 2, 3. . . as low cards to 10, J, Q, K as high cards. Suits do not have any consequence. Exceptions to the exchange options occur with kings. When the second player has a king, it voids the first player's option to exchange cards. Similarly when the second player elects to swap for the top card on the pile and this turns out to be a king, it voids the second player's option to exchange.

references Benjamin, A. T. and Goldman, A. J. (2004). Analysis of the $N$-card version of the game Le Her. J. Optimization Theory Appl. 114, 695--704, www.math.hmc.edu/~benjamin/papers/leher.pdf