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25 - Example: VNM POKER and KUHN POKER

Erich Prisner
Affiliation:
Franklin University Switzerland
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Summary

Prerequisites: Chapters 2, 8, 12, 16, 22, and 24.

Finally, a chapter on poker! Now we will learn how to play it well and make a lot of money, right? If this was your thought, I have to disappoint you. Advice on poker is possible, but the game is again too complex for a mathematical analysis. What we will do instead is study several small variants that we can analyze. This chapter will introduce the games, and do some analysis. We will complete the analysis in Chapters 31, 36, and 37.

Description

The two families of games we describe and partially analyze in this chapter are classics. What I call VNM POKER was introduced by von Neumann and Morgenstern in their monograph [VNM1944]. KUHN POKER (in the variant (3, 1, 1, 2)) was introduced by Kuhn in [K1950].

Both games have four parameters, S, r, n, and m, with m < n. There are cards of value from 1 to S in a deck, and each value occurs r times. So there are S · r cards. There are two players, Ann and Beth. Each player randomly gets a card from the deck, looks at it, but doesn't show it to her opponent. The ante is m, meaning that both player put m dollars into the pot at the start of the game. Each player's bet can raise to n if the player puts nm additional dollars in.

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Publisher: Mathematical Association of America
Print publication year: 2014

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