Hello all!
     I haven't posted in a while, but I've been working on a math problem and I'm kind of stuck.  I wasn't sure whether to post this under Help! or not.  I would like this to be a help/discussion.  Anyways, I was at a casino and there is this game called four card poker.  The player receives 5 cards from a standard 52 card deck and makes the best 4-card poker hand he can out of those 5 cards.  The player also makes an initial 'ante' bet.  The dealer receives 6 cards and makes the best 4-card poker hand out of those 6 cards. The extra card that the dealer receives is what gives the casino the advantage.  Once the player receives his cards he can either fold and lose his 'ante' bet, or he can bet up to 3x his ante bet and continue against the dealer.  If the player continues and wins, he gets paid 1-to-1 on both his ante bet and additional bet.  It seems to me that the best strategy for the player would be to know which hand he receives that would give him a 50% or greater chance of winning.  If his chances of winning are 50% or greater, then he should bet 3x his ante bet and continue, otherwise he should fold.  Apparently there is a strategy that has been proposed by Stanley Ko in which he recommends...Raise 3x with pair of tens or higher...Raise 1x with a pair of twos to nines...fold all others.  I really don't understand why somebody would raise 1x.  So in order to figure out the best strategy for the player, we need to figure out the probability of the dealer winding up with various hands.  Once I started doing the math, I began to realize that this is very, very complicated.  Here's the ranking of the hands...

Four of a kind
Straight flush
Three of a kind
Flush
Straight (Ace counts both high and low)
Two pair
One pair
Nothing/High card

Here's what I have so far for the dealer.
These are the total number of ways for the dealer to receive these hands..

Four of a kind

Last edited by Fruityloop (2010-03-04 16:08:40)