Texas Hold\'em under Perfect Information
 

Hi all,

Are there any books/websites/newsgroups that would have "the" model for playing Hold'em under perfect information about all other players' two cards? I’m looking for something that lets me vary number of players, starting hands, etc.

I'm having a hard time getting my head around the probability model for Hold'em. I'm also finding the specific probabilities I "must" memorize (e.g. the probability that I flop trips with a pair in the hole) a bit random. As an economist by training, I figured I might be better off starting with a perfect information model of the statistics and then understanding how imperfect information requires shortcuts and heuristics.

Thanks,
MBR

Re: Texas Hold\'em under Perfect Information
 

Don't let the numbers weigh you down, get lots of hours in of small stakes play and get a "feel" for the game.

Re: Texas Hold\'em under Perfect Information
 

I disagree. If you're chasing an inside straight or a flush without the proper pot odds you're making mistakes that are costing you money.

I too would like to know. Maybe I'll have to re-read TOP and see if it has that information.

Re: Texas Hold\'em under Perfect Information
 

Some of the poker software manufactures offer something. U. of Alberta actually devotes resources to 'poker studies'.

They claim to be working on an optimal solution to 2 player hold'em.
http://www.cs.ualberta.ca/~games/poker/

Re: Texas Hold\'em under Perfect Information
 

you may want to check out www.cardplayer.com, they have a poker odds calculator that I just discovered. It may be what you are looking for, you can set each players cards and then it will give you the percentages.

Re: Texas Hold\'em under Perfect Information
 

The Pokalyzer at http://www.pokalyzer.com seems to do what you are looking for. I only recently downloaded it and haven't had a chance to use it yet. Please let me know what you think of it.

Re: Texas Hold\'em under Perfect Information
 

Hi Mike,

You can formulate this as a stochastic dynamic programming problem (google may help here, but some algorithms background will come in handy), where you're performing a minimax optimization (i.e. minimizing the maximum amount of damage your opponents would be able to do to you, given your actions). This could be coded fairly straightforwardly, though it would be a bit slow. Hold'em is complicated enough that you probably won't find a summary that establishes rules for every situation. Furthermore, this model assumes your opponent always makes the best decision, which usually isn't the case (it would be a breakeven game if it were, and a losing game if you model a rake).

For more than 2 players, a minimax optimization may not be right, as it pretty much codes a collusion between your opponents (i.e. one might bet and the other raise in order to max charge a draw, even though the raisor knows he's behind). This makes the problem more complicated still.

Hope this helps. If you need a reference for dynamic programming, I can probably find one, but all it really does is give you a formula that you'd have to implement to understand.