I ran across a post the other day that I wanted to share. I was looking for an artile on odds on Wikipedia and came across Poker probability (Texas hold ’em). It’s really an excellent work on how probability fits into the game of poker. It’s not exactly a page turner but if you can sit through a bit of math you should come away with an appreciation for some of the complexities of the game that often get overlooked in other poker articles/books.
One part I found amusing was the possible hand combinations you could be up against with 9 callers (more than 622 quintillion).
If you were able to evaluate one trillion (1012) combinations every second, it would take over 670 million years to evaluate all of the hand/board combinations. While it is possible to significantly reduce the total number of combinations by pruning combinations with identical properties, the total number of situations is still well beyond the number that can be evaluated by brute force. For this reason, most software programs compute probabilities and expected values for Hold ’em poker hands against multiple opponents by simulating the play of thousands or even millions of hands to determine statistical probabilities.
If Hold’em isn’t your flavor or you’re into punishing yourself, there’s a similarly good article on Omaha Probability.