Game theory applied to Texas hold 'em poker...?

Question

I started trying to analyze poker strategy by modeling a 2-player, Texas hold 'em no-limit game. I started by identifying all two card starting hands and simulated lots of full games (millions) them to find probabilities of victory for any 2-cards vs. any other 2-cards.

Next I started to map out the ways the game could progress prior to the flop (raises, re-raises, re-re-raises, etc. and with several varying dollar amounts).

Now I am at a point where the complexity of posibilities is become enoormous and I am still dealing with pre-flop strategy (there are addition phases of the game as more cards are played if you don't know how to play hold 'em).

Anyhow, my question is how many people have tried something like this before and gotten lost/ given up along the way? I am starting to feel like I may never be able to fully model the game for 2 players and find an optimal strategy, let alone expand the optimal strategy to 3 to 10 players. Lost cause? Any tips? Thoughts? Thanks!

Answer 1

Sounds like you are basing your individual players by making them play all the same way. ie - raise with AA, reraise with KK, etc. Bet with top pair, or 2 pair, etc.
If you want to build a 10 player poker game you have to just program styles of which each player plays. Player A has an aggressive/tight style, Player B is loose/aggressive, Player C is loose/passive, Player D is tight/passive, etc.
I think the best structure to right this program would be to create playing styles, with hands that a loose/aggressive player will raise with (67os, A3c, etc), tight aggressive will raise from any position with AA, KK, QQ, AK, etc.
When the game starts make each playing style random to each player, so you never know when you first sit down who plays what style.

The reason this will be best will because when you play with any real 10 players you have to no clue how they play or what they will raise with, etc. Everyone plays different.

Answer 2

I think that its good that you are doing these kind of test, but a computer can't simulate table conditions or if someone bluffing out the other players at the table. That's the great thing about poker, you have the same starting hands , but there are so many ways to play them and there are never any 2 situations that are the same. math and strategy helps, but being able to put a good read on a player is something a computer can never do.

Answer 3

You're going about it in a wrong way. You don't need to know every possible move players can make. What you do need to know is, how likely it is that you are holding a winning hand right now (whenever in the game "right now" is). Then, you can devise a rule whereby you continue playing as long as the expected value of winning (the amount of money on the table times the probablility of winning) exceeds the amount of money you put on the table, but fold as soon as this rule is broken.

Answer 4

First rule of Poker... Never help a poker player! If anyone gives you, what you believe to be a good answer, don't award them the points becasue they are not a true card player! Only amatures will let secrets out.... If you want to learn how to beat slow players... play slow players and learn through experience!

Answer 5

the problem i see with your research is this: there is no mathematically optimal way to play poker, and this is in fact one of the reasons why the game is so great...it is not like chess when there is an optimal move to make every single time it is your turn, and if you make that move you can't possibly lose...there is no "right" and "wrong" way to play the game, every style is successful in its own way, there are certain plays that are obvious losing plays and certain plays that are obvious winning plays, but overall styles can be successful in their own unique way

howard lederer once said, "poker is a puzzle only you can solve for yourself", maybe you should think about that concept

Answer 6

I don't know what your goal is, but my first impression is: you don't have to model any of this, you just need to specify and/or calculate the actual probabilities of every possible action.