And btw, your views on pokersnowie please...

Do you mean programs for drawing equity distributions? The EDVis utility (freely available on the book's website) does this.

Well it's hard to say too much without more details. Actually, if he's folding to the second barrel 44% of the time, it seems like you do have a profitable bluff on the turn, although it depends on what bet sizing you're assuming. Other than that, it's really just a matter of whether your assumptions about Villain's strategy are accurate...

How are you calculating whether you can profitably bluff air? It might not be correct.

Oh, ok, gotcha. Yea, so you're right that sometimes you can find a profitable semi-bluff even if Villain's not folding enough that you could profitably single-barrel bluff pure air.

However, "how much equity do I need" isn't always the right question to ask. Sure, bluffing a draw is better than bluffing pure air. However, checking back a draw is also better than checking back air. So, just because you have more equity doesn't necessarily mean bluffing is better, relative to checking.

It's not always easy to see when you should use various sorts of hands to (semi-)bluff. Considerations like, how often is "Villain going to raise vs call" are very important. If Villain tends to continue with a raise rather than a call, that will generally make betting draws as bluffs a lot worse, while it won't have any effect on pure air hands, since they don't have any equity to get folded off of.

Additionally, hands won't always have the same amount of equity against Villain's initial range as versus his bet-calling range. Usually, bets get called by stronger ranges, so hands have less equity vs the calling range. So often what we want to do is not necessarily to bluff with hands with the most equity, but to bluff with those that have to give up the least amount of equity in order to turn themselves into bluffs. (For example, maybe it's better to bluff with a hand with 10% equity against both Villain's initial and bet-calling ranges, than to bluff with a hand that has 40% equity vs his initial range but only 20% equity when called.) Of course, how important these effects are in a particular spot depend strongly on the board texture and ranges involved.

So anyway, it's kind of complicated. Also, it's sort of an inherently multi-street issue which makes it a Vol 2 topic! Ch 11 talks more about this with some detailed analysis of specific examples.

Well, besides some minorish card removal issues, writing a solver for multi-street situations isn't really fundamentally more difficult than the single-street case. It's mostly just that the decision trees representing multistreet games can get big, so solving them takes more computer time/memory.

In the videos, I'll try to take the cleanest/clearest route to getting something working and give people the tools to take things further on their own -- I won't do much in the way of code optimization except in a few spots where we can get a lot of gain for little effort. That said, I expect our final result will be able to handle some multistreet postflop situations without too much trouble.

Sure, so we're looking at the solutions to the shove/fold game at 12 BB deep. Figs 3.2 and 3.3 give the equilibrium strategies for the shove/fold game at stack sizes up to 100 BB deep, and they are the figures I intended to refer to on pg 85.

You're right that it's not trivial to read a jamming frequency off of those charts. The data is presented in a way so as to make it easy to tell if a particular hand is in the shoving range at a particular stack size. (This is generally what we want to know at the tables.) To obtain an overall jamming frequency, you'd have to count how many hand combos are jammed at 12 BB deep and convert that to a frequency.

The equilibrium shoving frequency is right around 53.2%. This number was obtained by solving the shove/fold game at 12 BB computationally as described in Ch 2, but again, you should be able to get more or less the same number out of Fig 3.2. How are you arriving at 58.7%?

So, I haven't used sharky personally, but I looked at their website a while back, and they make claims like "play perfect GTO poker!" all over the place. These are simply bold-faced lies, so that doesn't inspire much confidence.

But of course that doesn't tell us how strong a player the program actually is. As far as that goes, I've heard opinions on both ends of the spectrum from people who have played it. However, the fact is, the ways in which a weak computer player is exploitable are usually much different than the ways in which a weak human is exploitable. But most of us are only trained to pick up on human-style mistakes/tendencies, so I don't have a ton of faith even in good players' ability to judge the program simply by playing it for a while.

One thing the creators of sharky could do is to enter it in the annual computer poker competition. A good showing there would give the program a lot more credibility. But if the authors are unwilling to provide that sort of test, then combined with the dishonest marketing, it seems like a scam to me.

^ oops, snowie, not sharky.

I find it hard to just rely on villain's fold vs turn/2nd barrel frequency because he will fold more or less on different flop textures and this difference can be quite noticable (eg. villain will fold more hands on 6 2 2 compared to 8s 9s Ts just to name an extreme example).

but you're right - if you knowe about villain's flatting range it becomes way more accurate to say whether to barrel or not. there are so many villains that either never c/r top pair because they want you to barrel off and on the other side those villains that c/r tp but I have rarely played regs (and I have played a lot recently) that actually c/r a polarized range, eg some top pair + some gutshots.

I was wondering about which program you are referring to on p. 46 on top. I think it might be crev, not sure though.

Just noticed it repeating the equilibrium exercise.
Btw I already preordered volume 2 - really looking forward to it although it will mean a lot of work again ;-)

Hello Will! I'm a begginer player from Spain, I discoverd 2+2 forums looking for information about your book and since I started reading it I'm suscribed to this thread.
I'm very enthusiastic about the book and working hard on it, I'm about to finish it!! (just on time to start working on your videos and be ready for the next book).Thanks for the information about the ranges involved in the river examples that you upload in this thread, it was very helpful to analize them.

I'm having problems understanding the solution to Example 6, specifically in pages 313 and 314; where it is explained why having also a BB block-betting range makes more profitable the tens for the BB against a shove from the SB, when the BB previously checked to.
You explain that some SB A-high holdings that before were checked-back, now prefer to bluff because of his lower equity against the new 'BB checking range'.
And this way the BB tens are clear calls because SB is mantaining his value-betting hands but bluffing more.
Here is where I'm messed. Don't should be the SB be bluffing the same relation between bluffs and value-hands than before? He is betting the same size, so if SB do that, I see why tens are no longer indifferent, but the same thing would happen to the jacks, doesn't it? In this case the BB would be calling more than 80% of time and bluffing A-high wouldn't be ever profitable for the SB.
Maybe the equilibrium is possible because of removal efects..?

Thanks for your atention!!

OK, I think I got it. The SB bluffing range only changes slightly and despite SB shoving holdings are only better or worse than the BB tens or jacks, because of removal effects, tens have more equity than jacks versus a SB shove, son tens become clear calls and jacks clear folds.
Perhaps I don't think enough in terms of removal effects and I didn't pay much attention in the book

My high school maths skills are fairly poor/rusty in general. I get the math in the early chapters of EHUNL and MOP albeit with a good amount of effort on my part.

From what I've read so far and from your comments ITT, I recognize that you made the math as simple as necessary but no simpler.

My question:
If you were a GTO coach (I guess you are) which specific mathematical subjects would you advise your student's to be well versed in, in order to get the most out of a GTO approach; EHUNL 1&2 and related projects such as coding FP or CFR algorithms.

e.g should I be looking at linear/quad algebra/inequalities/calculus/pre-calc....? I'd really appreciate as specific as advice you can give.

Computational tools for calculating maximally exploitative strategies? Yea, CREV seems to be the most full-featured option. The holdemresources.net calculator, ICMIZER, and SNGWiz also come to mind and may be more useful for specific types of calculations.

To be honest, the math necessary to understand most applications of game theory to poker isn't all that advanced (although maybe advanced is a relative term). There's a little calculus in MoP and EHUNL, but tbh it's not that important. Mostly you just need probability/counting and algebra -- probability to write down EV equations and algebra to solve them.

That said, I feel like probability is the kind of thing that it's easy to read about and feel like it makes sense -- but when you start actually trying to solve problems yourself, you're lost. So, rather than trying to learn about lots of different math topics, I'd recommend just trying to ensure that your understanding of the basics of probability is very solid. If you like video resources, I watched the 6.041 lectures at ocw.mit.edu a while ago, and they're very well taught.

When it comes to coding FP or CFR, it's useful to be able to think about vectors and matrices, so maybe knowing about the basics of linear algebra would be helpful.

Yea, card removal effects are often subtle, but they can be important. As far as the discussion of blocking rivers, I feel like I kind of skipped from some big-picture, exploitatively-focused discussion in the chapter to dissection of very subtle details of how it worked out at equilibrium in the examples, without any big picture, equilibrium-focused discussion in between. For now, blocking works well for the blocking range for the sort of reasons described here:

http://forumserver.twoplustwo.com/sh...1&postcount=86

and removing those blocking hands from a bluff-catcher-heavy checking range works well for the checking range since less mediocre hands often means SB has to valuebet/bluff a bit less when checked to, so the checking range gets a free showdown a bit more often, which is good for it.

Also, if you're looking closely at Ex 6, please note that the bet sizes given in the hand history are a bit off. This is described in the book's errata.

^^ Thx Will

Thank you Will!
I have another issue wandering around my thoughts.
In the section 7.3.3 are solving three standard river cases where the distributions are symmetric and the bet and possible raises are: a)B=0.25P C=1.25P b)B=2/3P C=3P and c)B=P C=5P.
After reading the book, my intuation says that if an only possible size bet is allowed from BB in the symmetric cases, an optimal size will approximate to somewhat less than the pot if is not possible any raise (maybe something like 0.9P) but if is possible a raise and the stacks are deep this optimal size might go down (to 0.5P or even less). My question is: as the stacks get deeper do you think the optimal size from the BB is smaller, contrary to the standard cases? I reached to these conclusions after observing GTO bet sizing for Hero with respect to ramaining effective stacks when Villain has a bluff-catching range and also holds some slow-plays, and after looking at optimal single bet sizes for the SB in the SB bet-or-check on the River depending on different equity distributions.
Thanks

hi yaqh,

great job - it's the only poker book i've read in full so far, and it helped me a great deal. looking forward to part II.

you stated somewhere itt that the downsides of crev are that it can't compute equilibria and that the max-exploit tool is limited as well - is the latter because crev only computes pure strategies?

one silly question regarding the equilibrium exercise in your book: the starting ranges are basically a trick so that the model converges nicely into equilibrium right? since bb's range consists only of 45 combos with a ~32:13 ratio, he can never bluff enough to make sb indifferent b/w calling and folding with his bluffcatchers, and thus sb will also not call the right frequency to make bb indifferent b/w checking with air or bluffing it, correct? i guess if bb's starting range was consisting of, say, 100 combos and was more air heavy then the whole exercise wouldn't converge nicely into equilibrium by hand/using crev?

on a side note: any news yet?

Is it true that part 2 will be released on March 28th in UK? Amazon.co.uk link says so

Well first and foremost, if the river examples in Vol1 showed us anything, it was that:

• multiple betsizes are very often useful
• betsizing depends very strongly on the hand distns involved

and it turns out that distns are rarely nearly-symmetric on the river in practice.

But if you're just curious how it works out in the toy game, the way to proceed is to solve the game keeping the betsize as a variable. Then write the EV of the player whose betsize we're interested in and find the size that maximizes that EV. We did this in the book for the SB bet-or-check game and the PvBC-plus-traps, IIRC, but I don't remember results for the models you mention. The Mathematica extras on the book's website are where I would start if I wanted to do those calcs, though.

Unlikely, but it should be to the printer's by then, so not too much longer.

Glad to hear it

I'm not a CREV expert, but the use and limitations of its max-exploit tool are described in its manual:

http://www.cardrunnersev.com/manual/maxexploit.html

Actually I didn't plan it that way originally, but yea that process wouldn't necessarily converge with other starting ranges (as I mention in the text). It's nearly a PvBC situation, as described at the beginning of the river chapter, and you're right -- distributions are such that we're in one of the border cases.

Yea so it's coming along well. It'll be a full length vid pack where we develop computational tools in iPython to represent, display, and work with most of the important concepts in Vol1 -- ranges, decision trees, strategies, equity distns, etc. The ultimate goal will be to compute max expl and equilibrium strategies for arbitrary decision trees and starting distributions.

The target audience is essentially the same as for the books. In particular, I won't assume any programming knowledge, so I'll take the time to carefully explain everything as I go. However there wont be any explicit intro-to-programming segments. I'll just introduce things as they're necessary to solve our poker problems.

The focus will be on the teaching more than writing the fastest or most fully-featured code. That said, anyone who works through the pack will have fully functional equilibrium solver easily capable, for example, of any of the computations I presented in Vol1, and should be well on their way to having the skills to do their own research.

Although most of the theory that we'll use in this pack was described in the first couple chapters of Vol1, it turns out that there's a bit of a leap between theory and practice. It's one thing to think something makes sense while reading, and quite another to understand it well enough to tell a computer what to do, step by step. And of course, even if you do understand things perfectly, having software to actually do it is useful. So I think this will be a valuable set for a lot of people interested in game theoretic play.

Arent you guys scared that ppl are going to get too good watching Will's videos and reading his books?

I got Tipton's volume 1 in the mail today (along with Chen & Ankenman, while Janda still is one the way). I've already pre-ordered volume 2. This volume 1 is on top of my priority list right after I'm finished with Miller's 1%. I'm looking forward to digging into this.

I just came across section 7.2.5 (p. 221 ff.) and I understand those concepts but I find it really hard to put them into real situations. Looking at the tables on p.234 ff. I have no idea what they're about because I don't understand how they're being calculated.
Could someone please explain them to me?
I feel like it's no very useful to know all the GTO frequencies because a GTO bluffing frequency is impossible to achieve (as stated on p. 232) ingame. Do you generally think these tables are worth putting in more work or will things get more clear once you read on?

Thanks