Glad to hear you're enjoying the book .

Yea, my game theory code was written more or less from scratch in C++. It's pretty much just the simple fictitous play algorithm described in the book. If you're just getting started now, you might want to consider some more sophisticated algorithms like CFRM. My approach was definitely to code first and ask questions later, and I ended up re-inventing/re-discovering a lot of ideas that I later came across in the literature . Not a big deal, though -- the project was just for fun at that point, and it's a good way to learn.

As far as pointers -- my advice is to be careful with the card removal effects. They were a bit tricky to get right. Then, after your software works, there's the matter of making it fast. The equity calculations will probably be your biggest challenge there. We've actually had a pretty extensive discussion about some of those issues in the comments section of the book's website, even down to the level of particular data structures and algorithms, so you might want to check that out. I'm happy to give more info if you have specific questions.

Will, I swear I read this paragraph 4 or 5 times before I posted my review and couldn't make sense of it. But when Erdnase posted the same thing with a few more mathematical symbols, it clicked almost instantly! Hence me blaming my poor reading skills... Donkeys aren't known to be subtle after all... Anyway, a little like the poster above, I have temporarily abandoned the deep study your book deserves to develop my own software. I blame your book for this: I didn't fully realised how technologically "advanced" some posters were before reading it and now I want to have the same "toys" as you/them.

Hi, thanks for your reply. I am currently working on my algorithms. Not yet started with programming.

I have a question about page 224.
You state P/(S+P) -T of the time hero will run into villain bluff-catchers range.
I tried 2 approaches but got stuck; meaning I cannot seem to come to same conclusion.

Firstly,
Whathever hero bets, villain will always call with freq T as these hands are always beating hero's hands.
Then we consider villains bluff-catching hands; I cannot see why villain would not call with freq P / (S+P)?
Which means the freq hero will run into bluffcatchers =
(1-T)*P/(S+P)
Meaning a total villain call% of (1-T)*P/(S+P) +T = (1+TS)/(S+P)

Secondly,
T freq of villain H always beating hero's H
(considering figure 7.4, 1-T= then bluff catchers freq of villain range)
C call% with bluffcatchers
Fb fraction of hero's betting range that is air
S leftover eff stack when river play starts
P money in middle when river play starts

EV(hero F air)=EV(hero bluff air)
S=T*0 +(1-T)*(1-C)*P + (1-T)*C*(1-Fb)*(S+P) + (1+T)*C*Fb*0

S=(1-T)*(1-C)*P + (1-T)*C*(1-Fb)*(S+P)

S - (1-T)*P = C [ (1-T)*-P + (1-T)*(1-Fb)*(S+P)]

resulting into
C = [S-P+TP] / [S-SFb-PFb-TS+TSFb+TPFb]
and I am stuck.

Maybe I still not have fully understood the indifference principle.
Can you elaborate where I went wrong?

To correct a mistake, sorry:

S=T*0 +(1-T)*(1-C)*(P+S) + (1-T)*C*(1-Fb)*(2S+P) + (1+T)*C*Fb*0

S=(1-T)*(1-C)*(P+S) + (1-T)*C*(1-Fb)*(2S+P)

S - (1-T)*(P+S) = C [ -(1-T)*(P+S) + (1-T)*(1-Fb)*(2S+P)]

resulting into
C = [-P+PT+ST]/[(S-ST-2SFb+PFb+2STFb-PTFb)

It sunk in, I wrote out tree+ indifference equation for hero bluffing and figured it out.
My last 3 posts can be merged/deleted.
I derouted caused by
Flawed thinking, applying the math cleared it out.

Now that I have finished the book I would like to add some more comments.
The River chapter is a real "tour de force" on River play. It took me considerably more effort to read than the rest of the book and I would say that unless you are a game theorist, a mathematician or a very smart person it will require considerable brain power to digest (nothing to be scared of but it will require several passes to grasp, imho).

The chapter starts with the description of 8 river hand histories which will be thoroughly analyzed at the end of the chapter, after the required tools are explained. Then you will find the study of river play with symmetric and asymmetric starting distributions, from simple situations to increasingly complex decision trees, including the analysis of thin value betting, bluff catching and block betting. Finally the author returns to the 8 hand histories which are dissected using the acquired knowledge and also from the perspective of the GTO solution of the games, with additional insights on card removal considerations. As they say, this chapter alone is worth the price of the book and it will literally blow your mind!

Does anyone know a software to make these equity distribution graphs?

Look in extras.

Hah k, well I'm glad you've been inspired one way or another . It seems that the book has at least succeeded in explaining what it means to solve poker games, showing you why it's an important and practically-useful thing, and giving you most of the theoretical tools to actually feel like you can do it.

Also you guys might want to consider working together on this project. No need to duplicate work, and as I mentioned, some parts are a bit tricky. If nothing else, at least compare results to check correctness.

Yup, there's a small, free utility to do this available on the book's webpage. Also, I've been in touch with the authors of propokertools and the holdemresources.net calculator, and both seemed to like the idea and plan to implement it in their tools, so hopefully those options will be available soon as well.

Hey Emus, glad to see you found your mistake. I have a couple comments, though, that might give you a more intuitive understanding of the result or at least help everyone else put the algebra in context.

So, we're looking at a situation where Hero is mostly polar, and Villain mostly holds bluff-catchers, but Villain has a few slowplayed or trapping hands as well. In particular, trapping hands make up a fraction T of his range, and T is fairly small -- 5% maybe. After a bit of work, we see that Villain's bluff-catching frequency must make Hero indifferent to bluffing. That is he must continue often enough when facing a bet so that for Hero's air hands, the EV of bluffing and his EV of giving up are equal.

Then, it turns out that the particular amount that Villain must continue versus a bet with hands that can beat a bluff to make those EVs equal is P/(S+P). (Here, P is the pot size, and in this example, Hero's bet is all-in, so S is the stack size and the bet size.) So, P/(S+P) of Villain's range must be continuing versus a bet. We know that T of Villain's range is nut trapping hands, and these are obviously continuing versus a bet. So, the other (P/(S+P) - T) of his range which is continuing must be made up of his bluff-catchers. Basically, Villain continues with all of his traps, and then he adds in enough bluff-catchers to his continuing range to reach the total required continuing frequency P/(S+P). Thus, we see that the fraction of Villain's range which is bluff-catchers which will call Hero's bet is (P/(S+P) - T).

Is there any particular reason that this book was not published by 2+2?

Hi Pokerlogist:

We did review it and were interested in publishing it. And to that end we sent the author our standard contract which he returned to us and by my count wanted 28 changes made.

Since our production work includes extensive editing and significant rewriting by the author if necessary, it was obvious to us that this was not someone who was going to be easy to work with. So I told Will Tipton to take his book to another publisher.

Best wishes,
Mason

Mason's account seems misleading to me, but I don't really want to get into it at this point. Suffice it to say that I believe things turned out for the best. Dan and Byron (D&B) have been a pleasure to work with, and I'm very happy with our final product.

My account is not misleading and I would appreciate it if you would retract this statement. If you would like, I can post some of our email correspondence to clear up any misunderstanding.

I also want to state that we were willing to go through our publication process with you because we felt the quality of your material was strong, and that's why we sent you our standard contract. And because we felt the material was strong, it's fine for you to discuss the content of your book on this forum.

Mason

Yes, once I figured out the P/(S+P) relation the rest sunk in pretty easy.

The thing that is confusing for me is this:
according to section 5.2 you create an eq distribution graph as follows
X h
Y EQ(h)
H0 (meaning closest to intersection) => highest EQ
H1 (after normalization) => lowest EQ
graph starts around (0,1) or upperleft & ends around (1,0) belowright

Now I look to graph at page 239,
X (1-Hb) & normalized
Y EQ(hb)
because of section 5.2 relation;
(1-Hb)0 or closest to intersection => has to have lowest EQ
(1-Hb)1 => has to have highest EQ
And therefore, the graph is to be exected to start around (0,0) belowleft & end around (1,1) upperright
BUT you started again the graph around (0,1) or upperleft & ended it around (1,0) belowright which means you first started to add the lowest EQ hands and then the highest EQ hands.

This is of course according to you page 240 Hc definition & this is not important for the math (if I got it right) but it is rather confusing once you are getting used to eq distributions.

To phrase it otherwise, by changing the definition of H in graph page 239 (by just using a different ranking method) then you did in section 5.2 you got instantly the idea that a different kind of graph was used but actually graph 239 is exactly the same as an equity graph in 5.2 the moment you realise
(1-hb) page 239 = h 5.2 OR
hb1=(1-hb)0=highest EQ = h0 5.2 =(1-h1) 5.2
(1-hb1)=hb0=lowest EQ =h1 5.2 = (1-h0) 5.2

Did I got it right?

You write fluent, nuanced and precise English. I am surprised no one has commented upon that fact. Your written English is far superior to that produced by most native speakers of it.

Would you say what your native language is and how you came to write English as you do?

I try my best, thanks for the compliment . French is my native language.

I have been living in London for 8 years and reading books of all kinds in English for 18 so it helps a lot. But, unlike what I can sometimes hear from optimistic new learners, I believe you don't master a second or third language after x years (x usually being a relatively low number). I think it's truly a lifetime work with new words and new ways to make sentences to be learned regardless of your current level.

Mr. Malmuth, I appreciate your kind words, but that's not the sort of thing I would have said if I didn't mean it. I was also being sincere when I said I'd rather not rehash things at this point. However, I see that it's not really fair of me to say something like that and then not back it up or take it back, so I can elaborate on my side of things if you'd like, either here or in private. If you'd like to post our correspondence, I ask that you post all of it unedited and unabridged so as to give the complete picture.

Ah, ok, I see what you mean. So, we always draw equity distributions starting with the strongest hands on the left and weakest hands on the right. Early in the book when we first see equity distributions, I label the X-axis "Hands" and it runs from 0 up to the number of hands in the range.

Later, we find it very useful if we stop thinking about particular hand combos and just think about hands in terms of their overall place in our range. So, our hand 1 is the strongest hand in our range, our hand 0 is the weakest, our hand 0.7 is the 70th percentile hand, etc. To make equity distributions with this convention, where hand 1 is plotted at X=0, hand 0.7 is plotted at X=0.3, etc, I label the X-axis "1-hand". This is discussed a bit on page 151 and again on page 240.

I agree that it's a bit confusing. The issue is really that we draw distributions with strongest hands on the left and weakest on the right when we could have done the reverse. In hindsight, I think it may have been better to do it the other way. Of course, the break from tradition also raises the possibility of confusion, and I didn't think that was worth it at the time. Another choice would have been to call our strongest hand 0 and our weakest hand 1. Of course, these are all just issues of convention -- there's nothing fundamental going on here.

I agree with your approach: language learning is a lifelong business. I, too, am learning a second language (Hindustani) and it annoys much when it is claimed of someone that he speaks X number of languages. For example, it is said of the English national football team manager, Roy Hodgson, that he speaks six languages. Roy Hodgson has worked in several foreign countries and speaks a smattering of six languages but he does not speak six languages. Of that I am sure.

Many years ago, I read a nice book on bilingualism. It related an anecdote in which a chap at a party is having a conversation in English with a stranger and he is sure the stranger is English. They then begin to converse in French and he becomes certain that his partner in conversation must be French. It is only when they begin to speak in German that he realizes his interlocutor is Russian! [The stranger despite speaking fluent English and French spoke German with his native Russian accent.]

As a consumer, I think I probably speak for most people when I say it's enough for us to know that it was due to business reasons and not the quality of the content that the book was not published by 2+2.

I doubt anyone cares enough about the specifics to have the thread cluttered by that discussion any further.

+1

2+2 missed out on publishing a great book for business reasons... the book remains great... now let's move on and keep discussing the quality info found in the book!

man this an interesting read but not easy going. Only a short way in but engrossed already. I've had to start taking notes in some spots which i guess is the point. More of a study book. To Yaqh - you mention software which can aid in some of the calculations. Would cardrunners EV be a good choice or do you have a recommendation?

Glad you're enjoying it. Feel free to shoot me any questions that come up while you're reading.

When I mentioned that there was commercially-available software that can be used to set up decision trees and solve for exploitative strategies, CREV is what I had in mind. It has a convenient interface for setting up and manipulating fairly complicated game trees. However, as far as I know, it can't calculate equilibria, and it's best response calculations have some limitations as well. It's definitely the best available choice for solving a lot of problems, though.

There's also Gambit (gambit-project.org) which is a free tool for setting up and solving games described as decision trees. However, it's not poker-specific, and setting up complicated poker situations is probably infeasible. Finally, there's the HoldemResources.net calculator which seems very promising, but at this point, it only does preflop situations.