[JaredL]

I picked it up yesterday. While I haven't read much (I read the intro and then skipped to the "optimal" (ugh) play section and read through a couple chapters there) here are my first impressions.

FWIW I was a math/econ double major as an undergrad. I started in Math, taking the pure track (topology, analysis etc.) and added Econ as a major when I got interested in game theory problems that were discussed in an intro class I took to fulfill general education requirements. I am currently in my fourth year of grad school in economics doing research in micro theory and experimental economics. Thus, much of my research is in game theory.

Firstly, based just on a glance through some sections and the reading I've done I think this is much more a math book about poker than a poker book with a lot of math. The book is written very much like a math book. This I really liked, though people that haven't read a lot of math texts, or haven't for a while may not find it too appealing. I'm not sure where it will end up in the store or how relevant this is, but when I was looking for it on the computer at Borders it said it didn't have it but it was categorized in the Mathematics section not the gambling section. The target audience seems to be people who have a deeper interest in why things go the way they do in gambling, what's behind the EV calculations, etc. As sputum said, people who like to think about poker as much as playing it.

The good:
It is very well written. The concepts are explained quite well. The format is easy to follow if you're accustomed to math books. There is something for pretty much everyone, no matter how expert. The section introducing game theory I didn't really need, nor the basics of probability (though I haven't read that section so I can't guarantee that I won't get more out of that than a refresher). However, just on what little I've read I've already come across things I haven't seen before, most notbaly some of the toy games, and looking in the table of contents there are a number of other things of interest. What I'm trying to say here is that this isn't a book that explains very basic EV equations that anybody with knowledge of probability would get nothing out of. I haven't read much of the toy game stuff, but it seems very interesting. It seems they've solved some more interesting versions than just the standard von Neumann poker and they suggest something a bit deeper with them than "bet your good and bad hands, check your mediocre hands." The chapter on bet sizing in NL was quite good for example, I plan on rereading it in the next couple days.

Another plus (sorry I'm thinking of them as I'm writing stuff below so this post is a bit disorganized), is that the way the book is designed, it's easy to read just stuff in which you're interested.

The bad:
I've ranted about this on numerous occasions, but I don't understand at all their nonstandard use of words. They use optimal when they should use equilibrium and use exploitive when they should use optimal or best-response. It takes some getting used to for people who have read other texts in game theory and those who haven't will have to readjust should they decide to take a course in game theory. The latter is a pretty likely outcome - those who haven't studied GT or microeconomics and enjoyed the book would do well to do so. Their (mis)use of these terms is not only not standard, but it is dare I say suboptimal. While theorists use optimal in a way that approximates the standard real-world definition of optimal (optimal given what other people are doing), they do not. They say a strategy is optimal if it's a best-response to the equilibrium strategy of the opponent, which means it's likely not optimal given what the opponent is actually doing. This doesn't really make sense, and they really would have been better off using equilibrium or non-exploitable (whichever makes the most sense each time).

To see a clear example of the problem look at rock-paper-scissors. In equilibrium a player is mixing 1/3,1/3,1/3. If I always play good old rock, then it is clearly not optimal for you to mix but to always play paper. Saying that mixing is the optimal strategy here is confusing and perhaps more importantly doesn't make sense.

Other downsides to the book you can get straight from the upsides - if you haven't read a math book in a while the way it's written might not appeal to you. At least the stuff I read shouldn't be particularly challenging to the reader, but the style may make it more of a challenge.

Also, I'm not sure how indicative it is of the book, but after reading not much of the book, I have found either an error. On the bottom of page 102 it says "Only games with either hidden information or sequential play can contain optimal mixed strategies." It's possible that they meant simultaneous instead of sequential, either way it's wrong. Matching pennies, battle of the sexes, and rock-paper-scissors all have no hidden information nor are they sequential move games. All three have a mixed-strategy equilibrium. In case they meant simultaneous, one can construct examples of sequential games with no hidden information that have equilibria where at least one player is mixing.

I don't think the above error is serious, but if these types of errors are present throughout it would indicate that the book wasn't proofread very carefully.

Overall I have really enjoyed the parts I have read thus far. I suspect that it will be among my favorite poker books. I will give a more full review later when I've read the whole thing.

Jared