The Mathematics of Poker

[Patrick Sileo]

For a classic and very readable text on game theory, see "Games and Decisions" by R. Duncan Luce and Howard Raiffa.

From the text:

"In the domain of mixed-strategies, every zero-sum, 2-person game has at least one equilibrium [strategy] pair, and when there are several, they are equivalent and the equivalent strategies are interchangeable."

[Djeorge]

[ QUOTE ]
For a classic and very readable text on game theory, see "Games and Decisions" by R. Duncan Luce and Howard Raiffa.

From the text:

"In the domain of mixed-strategies, every zero-sum, 2-person game has at least one equilibrium [strategy] pair, and when there are several, they are equivalent and the equivalent strategies are interchangeable."

[/ QUOTE ]

Are you saying that if a 2-player zero-sum game has 2 eqiulibria, A=(a_1,a_2) and B=(b_1,b_2), then e.g. C=(a_1, b_2) is also an equilibrium?

[chezlaw]

[ QUOTE ]
available now from sellers on amazon.co.uk if anyone's interested.

[/ QUOTE ]
High Stakes in London has copies.

chez

[BillChen]

I'd like to thank everyone for catching our errors. I have to say that we didn't expect the book to be error-free. We read over it several times along with our editors and reviewers, but at some point you have to decide to release the book. During the editing phase we made sure the sections were as understandable to our outside readers as possible, and I hope our efforts paid off there. I don't mind saying most of the clearly written prose is Jerrod's and any typos in the equations are likely to be mine:-).

Bill Chen

[BillChen]

On one extreme is the game where your opponents strategies are entirely known and they have no adaptive abilities. In this case it's relatively straightforward to calculate the best play. Jerrod dubs this the PlayStation (tm) approach to poker. We do go over several examples of this in Section II. Even though game theory is the biggest section in the book, the book is hardly all about game theory. It's just that in comparison the mathematics of playing against a known strategy is much easier. This is not to say that the sections on how to collect data against your opponent and Bayesian inference in tells aren't important--in fact, they are more useful against weak and unadaptive opponents.

But even in so called "soft" games the players are not this predictable. Even when it's claer someone plays badly because of a given play it's still unclear how badly they play. For example say you see someone make a bad call, do you know if it's the minimum hand they would call with or will they call with worse, or did they just make the call on a whim? There are certainly situations where game theory may still apply such as value betting on the end.

Even if you read your opponent perfectly for a mediocre hand--in the book we call this the clarvoyant game, if you don't have an idea of his calling frequency you may still want to play the optimal mix of bluffs and value bets at the end. This is the strategy that is the hardest for your opponent to play against.

Bill

[BillChen]

Yes. In fact B can play any mixture of b1 and b2, which means that the set of all equilibria strategies is actually convex. All the strategies in this space are "optimal" and we can talk about the space of all equilibria as the cross product A0 x B0 where A0 and B0 are both convex strategy subspaces of A and B respectively.

Bill Chen

[Djeorge]

Oh thanks for explaining, I just got the book and it looks pretty good I have to say. A lot more rigorous than any other poker book I've seen.

[uncleshady]

I bought this book at The Gambler's Book Club in Vegas based on the kudos in this thread.

I opened it up in the middle somewhere. My head assplode. I suggest a degree in mathematics as a prereq for this book. I've got a film degree so I'm screwed, but this will be perfect for some of you guys.

[DPCondit]

[ QUOTE ]
I bought this book at The Gambler's Book Club in Vegas based on the kudos in this thread.

I opened it up in the middle somewhere. My head assplode. I suggest a degree in mathematics as a prereq for this book. I've got a film degree so I'm screwed, but this will be perfect for some of you guys.

[/ QUOTE ]

You certainly don't need a mathematics degree. Start from the beginning, and work your way through it. Don't be dismayed, they work through everything and explain it so it's fairly easy to understand.

If you start from the middle, your head may very well "assplode", but it really isn't necessary.

Don

[BillChen]

Yeah since there are 382 pages not counting the roman numbered ones, I opened to 191. I see what you mean. But you aren't supposed to start reading from there. It's a little easier to start from page 1. The goal was to make the book understandable for different levels of math sophistication--I think understanding the conclusions is possible without understanding the derivation of the results, though I imagine there are lots of participants on this forum who will keep us honest on our math.

To be honest, there is some minimum math requirement, just as there is some minimum poker knowledge. If you don't know what a check-raise is, I would recommend reading something else and playing a little first. Similarly, familiarity with Algebra is a minimum. If you see "w = 3xy + 2" and don't know that it means the value of w is three times x times y plus 2 or see how that simplifies to "w - 2 = 3xy" then you may not get far with the book.

This is unfortunate as this does exclude a large portion of the population, I suspect even a large portion of the poker playing population. I feel pretty bad about this, but we can't put all prequisite material or the book will be several thousand pages long.

For the rest who meet these requirements we do feel you will understand most of the book if we have done our job well--in fact this is a good test for us as authors.

Bill