The Mathematics of Poker

[mchilger]

Nick, I found your review quite interesting. "One of the most important poker books in the last 10 years", yet you had many criticisms also.

My take on your review and from what I have heard from others is that this book has some tremendous implications on how poker will be analyzed going forward, especially in advanced circles, but has very little relevance for the average Joe, or for even the advanced Joe without a college-level math background.

I think we do hear a lot more these days about game theory...the optimal play, meta-game concepts, optimal bluffing frequency, etc. I imagine there is a lot more to be said and analyzed about these topics but I'm not sure if The Math of Poker is that book based on the reviews I have read.

I guess I'd like to have a little more opinion from you on who this book might be relevant for. Do you need a college-level degree in math to be able to appreciate this book? Would the serious poker player that you find in a Forum like ours be able to take away something from this book if they don't have a calculus background?

Matthew

[NickChristenson]

I think these are very good questions. I'll see if I can provide an answer that makes some sense.

In my opinion, Math of Poker is the first step on the path of the next generation in poker analysis. They take very simple games, such as the "Ace King Queen" game, where two players play against each other using a deck with exactly those three cards in it. Then the *prove* an optimum strategy for the game. This isn't just "come up with a strategy none of my friends can beat", this is mathematical, iron clad, mortal lock, prove the optimum strategy, such that if you played against an opponent who adopted this strategy, and played any other strategy against it, you would certainly be expected to lose in the long run. This is a tremendously strong statement, one that has been made about *no* real-world poker games. Some day, I expect that computers will be able to play real poker games this way. That will be a big breakthrough.

However, none of this tells you what your starting requirements should be in Razz, or how big should a NL holdem bet be on the river right now. They do talk about some fundamental truths in poker such as proper ratios of value bets to bluffs, but for most of the book the only way to incorporate the strategies into real poker strategies is by analogy, and not directly. So, the average Joe and the advanced Joe will have problems applying the lessons of this book to their 4-8 hold'em game.

Let's see if I can state this a little differently. I think this book will greatly affect how poker researchers approach the game. I think that the strategies they uncover will affect what people think are the proper strategies for the game, which people will adopt. So, the effects of this book will trickle down, but they won't be the direct cause of most players adopting new strategies. If you want to be on the cutting edge, though, this is where much of it will happen.

If you want to learn about optimal play, meta-game concepts, optimal bluffing frequency as they apply to generalized poker games, then Math of Poker is excellent. If you want to know how they apply to the NL hold'em game you play in without having to do a lot of translating, then it's probably not. (Blowing my own horn, our new book "Winning Strategies for No Limit Hold'em" does talk about some of these issues in a less math-heavy context. For example, we do talk about optimal vs. exploitive strategies and some about optimal bluffing frequency, so it might appeal more to those looking for a qualitative discussion on some of these issues as it applies to no-limit hold'em. In terms of depth or rigor, our discussions don't hold a candle to MoP.)

The question of how much math a person needs to understand the book is a really tough one. On the one hand, the book doesn't use any mathematical *tools* that aren't available to anyone who took 3 to 4 years of high school math (actually, it uses some, but only in side bars.) The problem is that the application of these tools is *way* more sophisticated in places than you'll see in the first few years of college math. A high school senior could probably have everything explained to them, but would they absorb it by reading it? Probably not. So, for those who haven't read college math texts on their own, it will be really tough going. If you really want to understand it, you probably need to go very slow, and it's not a small book.

There's a lot more to be said on this topic. I hope this helps a little. Remember that ultimately, this is a math text that covers poker, not a poker text that uses math.