Excellent for beginners: http://oyc.yale.edu/economics/econ-159

No.

"Inherently beatable because it doesn't adjust" is not a correct statement, period.

Whether or not the IGT machine does or doesn't play GTO, and whether or not anybody has beaten it over a large sample size (which I've gotten multiple PMs about), is not relevant.

Honestly, I'm not sure how this is even being debated. When I saw that this thread had reached 7 pages, I figured it would be about whether or not top players think in terms of advanced game theory, not 7 pages of arguing over whether or not a GTO strategy exists in poker.

Theory of Poker by Sklansky is probably the best place to start, unless there's a better resource I don't know about.

Mathematics of Poker, by Chen and Ankenman. High school level math won't cut it, though.

Uh? You said: "they all agreed that if the machine doesn't adjust its style that it's inherently beatable. I tried to explain why that wasn't true and I'm not sure if what I was saying ever really got through." I replied that, since the machine doesn't play GTO, it is in fact beatable. (If it did play GTO then it wouldn't be). I don't really understand what your reply above means or why it justifies the response "No"?.

If you simply mean that a theoretical GTO machine which doesn't adjust is not inherently beatable then I agree.

That book doesn't have much game theory or anything about nash equilibria iirc so probably not a good text for people looking to learn about that subject.

Their argument was about if the machine is inherently beatable just because it doesn't adjust, not if the bot was GTO or not or could be beaten as it is currently.

I did qualify my statement with "headsup."

Nash's theorem only covered finite games, but later extensions have shown that Nash equilibria exist for games with infinite strategy spaces under some reasonably broad criteria. In any event, poker as played in reality clearly has a finite strategy space, since you can only bet in pennies online or in chips live.

^^ Hundrye: I agree their argument is wrong if thats what was mean't.

You know where I can get the "Mathematics of Poker" by Bill Chen? or whether its free online or online?

Amazon?

About illegal copies you might want to consult with the guy who posted two posts above you...

A few months ago I needed a copy of our book for something and didn't have one handy. I found a torrent, however. So that was useful. But surely there's some moral distinction between me doing that and you doing that.

Out of curiosity, how long would you say it took you guys to write MoP?

http://lmgtfy.com/?q=mathematics+of+poker

MoP is a rough starting point if you don't have a very strong quant background. Phil Newall's book is probably a better option in that case.

The book had originally been talked about as a project between Andy Latto and Bill. That book was envisioned to be a much more academic book, with theorems and lemmas and no hope for regular people to read it.

Later, after Bill and I were working together on things like the [0,1] game and posting about it on RGP, we floated the idea of doing the book between the three of us, but I argued that we should make the book able to be understood by less mathematically-trained but willing to expend effort people. (In other words, people like I was in 2000, before I met Bill). Then Andy had to drop out because of life issues, although he helped us after the draft was done (We got useful feedback from the three Andys: Bloch, Latto, and Prock).

We gathered up a bunch of work we had done (more Bill than I) and started figuring out what should be in and organizing. There was some idea that we would write alternate chapters, but after the first samples were generated we punted on that and instead I did almost all the writing and Bill mostly generated results, graphs, simplified overly complex formulations, etc. That process of going from "we have all these equations" to "we have the draft of a book" took like maybe 18 months of on and off work? Then there was some more time spent with an editor, layout people, etc.

Cool, glad it worked out. I learned a ton from it.

Yeah, that's what I meant. I was trying to convince them that a LHE heads up machine could be unbeatable, and their argument was basically that any machine that doesn't adjust can therefore be beaten. It's also what durrrr seemed to be suggesting earlier.

Chapter 19 is called "Game Theory and Bluffing", and goes through several sections on optimum (equilibrium) bluff frequencies. It's funny though, because you don't remember it having anything about that stuff, yet my memory was that the book was mostly that (when it's really only one chapter and then bits of it in other sections). It was such a mind-blowing chapter for me on my first read that it's basically all I remember from the book.

I guess there's definitely some other books that are better about this stuff specifically, but based on the tone of the original poster, I would bet ToP would be a good read for him anyway.

Any chance that said academic book will be completed? If I had an issue with MoP it was the lack of mathematical rigour - I know I'm representing a minority here

Sort of like... Oh never mind.

Not really. Now that I'm capable of writing such a book, I have no desire to do so, and neither does Bill, I'm sure.

durrrr where are you??? don't let you fans down you got this!!

Has the below statement been proven false?

• In heads-up NLHE, there exists a non-GTO strategy that breaks even against some GTO strategy.

its a correct statement.

a bot that plays gto except for some lines which a gto bot never plays will breakeven against a gto bot.




eg a gto bot probably never raises to 99bb from the sb 100bb deep. a bot that plays gto except that he folds everything to a 99bb raise in the bb will play breakeven against a gto bot, but it is obviously not playing gto.

Google for papers by Tom Ferguson (UCLA). You won't be disappoint.

Thanks, mate

I just read like 10 pages in two threads of people reminding people of what gto really is and them forgetting on there next post again