On 7/26/07, Erich Friedman <efriedma@stetson.edu> wrote:
the simplest non-trivial poker game i can think of is:
1. the players ante one chip each to the pot. 2. the players are each dealt a card from a deck of three cards: 1, 2, and 3. 3. A has the opportunity to bet one chip (B must call if he wants to continue to play). 4. if A doesn't bet, B can bet one chip (A must call if he wants to continue to play). 5. if both players are still in, best hand wins the pot.
there is clearly no incentive to bluff with a 2, but there is with a 1. what are the optimal strategies for this game?
if you can manage that, what are the optimal strategies with the cards 1, 2, 3, and 4?
erich
I've seen various papers analyzing (extremely restricted) poker-like card games, and have often wondered what the best results along these lines are.
Maybe someone knows a good survey article?
The book you want is The Mathematics of Poker, by Bill Chen and Jerrod Ankenman. It analyzes a series of "toy poker games" like these, of gradually increasing complexity, some of which have optimal solutions that exhibit quite surprising results. There are also more practical sections that talk about what these results tell you about how you should play actual poker. Disclaimer: Bill and Jerrod are friends of mine, and I was originally going to be a co-author of this book, but I didn't have the time. -- Andy.Latto@pobox.com