No-Limit As a Math Problem

[xcleetusx]

This message is cross-posted in Beginners Questions and Probability forums.

I'm brand new to the forum, looking to explore no-limit hold-em as a mathematical optimization problem. Specifically, I'm looking for books, journal articles, and websites using equations with different input variables (quality of starting hand, bets, position, etc) to express the quality of the hand and, in turn, produce a strategy to "optimize" my play...maximize my take on the wins, minimize the losses.

I'm most interested in expressing all of this as a system of equations that can be mathematically optimized.

This is for a school project, so I'm trying to find credible source material as a start, especially journal articles (i heard from a friend there was an article in a mathematical journal on this) and books.

[RiverTheNuts]

if it was as simple as math, people could play perfect poker... in limit, this is close to possible, but the human element of how other players will act to your bets, or bet out themselves makes any poker game, especially a NL game impossible to deal with using math equations alone

[xcleetusx]

BTW, this is for a school project, so I'm trying to find reputable sources, including journals (I heard there was an article on this in a mathematical journal) and books.

[Vannek]

Here is your math:
2+2

[uuDevil]

I don't understand why people are so dismissive of this kind of thing. /images/graemlins/mad.gif

Anyway, check out the references near the bottom of this web page:

http://www.cs.ualberta.ca/~games/poker/

Come back and post a summary of your project results if it works out. Good luck. /images/graemlins/club.gif

[Kopefire]

Short answer -- because our society has a deep anti-intellectual element to it. People hate noticing that they might not be as smart as they think they are, so they're derisive of anyone and anything that points that out for them.

[RiverTheNuts]

I just dont see how you can put a mathematical equation to human nature... maybe in the future, but the brain is too complex for any person to put mathematical equations to... there are way too many variables to be considered within each individual's psyche... all of these affect bluffing, calling, how much to bet, when to bet... etc

[Elfan]

You are unlikely to find anything remotely resembling what you are describing for modern variants of poker such as Holdem, Omaha, etc. They are popular precisly there is no known "perfect" way to play them. However, there is a great deal of game theory work that has been done on older variants of poker, 5 card draw in particular. You might try ``Poker Strategy: Winning with Game Theory'' by Nesmith Ankeny.

[Kopefire]

Your argument is pointless to the discussion. The question is can the game state of an incomplete information game be modeled sufficiently such that optimal strategies can be derrived from the available information?"

The complexity of the human brain isn't part of the question.

Just like the best chess computers can't beat the best chess players consistantly, the best poker computer won't be able to beat teh best players. But they don't have to to be usefull -- even to the top players.

[RiverTheNuts]

He wants math equations so that he can play optimally at No Limit Hold Em ... thats impossible, what math equation is going to tell you, if you have aces, bet XX% of the average chipstack of all the players at the table... if this person bets this amount, it means he has this, fold...

You certainly can use odds formulas to see when you probably have the best of it, but thats what every book on probability already does... you have this many outs, this play is +EV...

Thats what everything comes down to... making every decision to be +EV, which is what this entire forum is about already... if this guy isnt doing what I think he's trying to do, then I dont see how his question is any different from what every other poker probability expert has been trying to do forever

[pzhon]

[ QUOTE ]
He wants math equations so that he can play optimally at No Limit Hold Em ... thats impossible, what math equation is going to tell you, if you have aces, bet XX% of the average chipstack of all the players at the table... if this person bets this amount, it means he has this, fold...

[/ QUOTE ]
That just shows your ignorance. Mathematics can do the things you say it can't. See Jerrod Ankenman's posts on [0,1] games in rgp.

[pzhon]

[ QUOTE ]

http://www.cs.ualberta.ca/~games/poker/


[/ QUOTE ]
That's a decent starting point. To search the mathematical literature, I strongly recommend using MathSciNet (http://www.ams.org/mathscinet). You should also check the preprint server (http://front.math.ucdavis.edu/).

[RiverTheNuts]

Its very late, but Im reading up on this 0,1 game that he posted, Ill post again when Im done and see if I have to cram my foot in my mouth /images/graemlins/smile.gif

[Henkeman]

Do a search on poker at http://www.sciencedirect.com
I know I've seen a couple of articles on poker there.

[xcleetusx]

http://www.cs.ualberta.ca/~games/poker/

Thank you, this looks like an EXCELLENT reference. I probably should have chosen limit hold-em as opposed to NL, because obviously in order to explore this problem mathematically I will have to work under the assumption that psychology is not a factor (IE, no bluffing). So this will server only as a guide.
I'm trying to consider as much as possible, though, how to mathematically quantify things like position, relative stack size, etc...all as quantifyable input variables to generate a "strategy" to maximize output. I will certainly stay attached to the board with further questions and updates. Thank you all for your help.

[felson]

This problem is hard. If you are able to solve it, then you don't need to be in school. Drop out and make millions.

[pzhon]

[ QUOTE ]
obviously in order to explore this problem mathematically I will have to work under the assumption that psychology is not a factor (IE, no bluffing).

[/ QUOTE ]
That is a misconception. Bluffing is predicted mathematically. If you don't bluff enough, your opponent can get too much information from your bets, and can fold marginal hands rather than paying you off. If you bluff too much, it costs too much, and your opponent gets to call or raise with weaker hands. In simple situations, you can work out the optimal bluffing frequency. See Theory of Poker.

Psychology is useful in poker. You can get more information out of real human opponents than is contained in the betting sequence. You can see how rapidly your opponent makes decisions or how confident your opponent is or how they behaved before. You can use this to rebalance your estimates of the probabilities of each hand. Eliminating psychology means that you focus only on the betting sequence in the current hand.