Oh, that?
Well, with that I can help you out a bit.

In general, you will virtually never reach the optimal strategy by alternating maximally exploitative strategies. What will happen most of the time, is that you'll be reaching the extremes and then continue swinging indefinitely between various extremes. Maximally adjusting to what Villain is doing doesn't necessarily lead you closer to the solution; it leads you in a random direction which is sometimes closer, sometimes further.

Eg, you cannot solve a spot (not even a river spot) by just doing "max xploit" in crev for the SB and then the BB and then the SB.... CREV can calculate these swings and adjustments, but it does not lead to a solution.

You can check out these videos for the examples on it -
http://www.youtube.com/watch?v=EDGzYjRsfq4
http://www.youtube.com/watch?v=rTe-Ny3JUQ8

And if you got CREV I can ship you this particular tree and you can run max xplt OTR all day to see.
Scylla also describes in what way to use CREV to find equilibriums in those two vids IIRC.

I am surprised it worked in that trip jacks example in your book; in all the spots I've analyzed, you can almost never successfully equilibrate that way.


Right, got it. I misread that from the graph and somehow saw some of the top 30% SB's hands as being "behind" the 70% equity BB's holdings. Visual trick on me.

So 75% equity should do the trick then, I'd assume (at least theoretically, IP and for PSB, OOP I know it's a bit different)?

I figured at least this part should be simple.. I mean, it is step 1 in your outline after we covered the structure of the process!

Here they are, copypasted from EVdis -
AA,T6s-T7s,75s,T7o,75o,65o,AcKc,KcTc+,KcTd+,AcKh,KcTh+,Ac Ks,KcTs+,AdKc,AdTd-AdQd,9d5d-9d6d,7d4d,6d3d,AdKh,AdKs,AhKc,KhTc+,KhTd+,AhKh,KhT h+,AhKs,KhTs+,AsKc,KsTc+,KsTd+,AsKh,KsTh+,AsTs+,Ks Ts+,QsJs,8s4s-8s6s,7s4s,6s3s,9d9c,9h9c,9h9d,KsKc,KhKc,KhKs

AA,QTs+,JTs,QTo+,JTo,Ac9c,Kc2c+,Qc9c,Jc9c,Tc9c,9c7 c+,Ac9d,Kc9d+,Qc9d,Jc9d,Tc9d,Ac9h,Kc8h+,Qc9h,Jc9h, Tc9h,9c8h,Kc8s,KcTs+,9c8s,Ad9c,Qd9c,Jd9c,Td9c,9d8c ,Ad2d-Ad7d,Ad9d-AdJd,Qd2d,Qd9d,Jd9d,Td9d,9d7d,Ad9h,Qd9h,Jd9h,Td9h, 9d8h,9d8s,Ah9c,Kh8c+,Qh9c,Jh9c,Th9c,9h8c,Ah9d,Kh9d +,Qh9d,Jh9d,Th9d,Ah9h,Kh2h-Kh3h,Kh5h+,Qh9h,Jh9h,Th9h,9h7h+,Kh8s,KhTs+,9h8s,As 9c,Ks8c+,Qs9c,Js9c,Ts9c,As9d,Ks9d+,Qs9d,Js9d,Ts9d, As9h,Ks8h+,Qs9h,Js9h,Ts9h,As3s-As8s,AsTs-AsJs,Ks3s-Ks8s,KsTs+,Qs3s-Qs8s,Js8s,Ts8s,8s7s,7s6s,6s5s,5s4s,8s8c,8h8c,8h8s, 9d9c,9h9c,9h9d


Pot size 74bbs, remaining stack sizes 63 bbs.

The candidate strategy I got has BB leading out with all TP+ and 45% of his high card holdings. Total of 68% of the time.

He checks 32%, and calls SB's bets with any pair.
BB isn't checkcalling "enough", but the strat is not possible to exploit much and is quite robust. It nets him 28.9 bbs.

If I push down KTo, which has 70% equity, into his xC range instead of his betting range I am not able to get as much EV out of the spot (even after I modified his bluffing range), which goes in line with OOP players being forced to valuebet a bit looser.


Don't we know it always? I thought that the SB's calling range was always the top 50% of his hands. Assuming indifference doesn't break down and the bet was a PSB.

I'm stubborn enough that I'd probably be doing that by now. But, based on how this type of stuff has been going for me so far, I am uncertain that I'd manage to come to a decent solution without making mistakes along the way (which I couldn't spot myself), and certain it'd take me an assload of time, judging by how much it takes me to work, compose and proofread these posts using the tools I'm versed at.

Right, I understand (and the part about "BB even having a betting range" is duly noted).

That'll work and is simple enough.
"This many vbets, so with these odds add this many bluffs."

Yes, I believe that with your help I understand all this.

Well, thanks, but in fact the method does work in general . Actually, the problem you describe and its solution are mentioned on pgs 55-56, although I didn't want to get too technical about it there.

Essentially, the "mixing" part is important. Instead of switching all the way to the max expl strategy in each iteration, we only move a little bit in the direction of the maxexpl strategy in each step. That is, we update our strategy by taking a weighted average of the old strat and the new max expl one. And the weight we give to the new one decreases as the algorithm proceeds. If we do it right, convergence is guaranteed.

If you'd like another reference, see The Mathematics of Poker, pg 131.

Looks like you're right here.

Equilibrium solution of the river-only game given the all-in-or-check bet sizing model:


BB's range splitting at his first river decision point:


50% comes from making BB's strongest bluff indifferent to bluffing, and 50% is the right number to do that only if the BB's bluffing hand always loses the pot after checking. If BB is using hands w/ showdown value to bluff, SB folds more. So, essentially we need to know BB's bluffing range to find SB's calls.

Yes, that way (adjusting, but in moderation) does lead you to the solution.

That's exactly how Scylla describes it, as well.

CREV can't calculate that, it can only maximally exploit.
But it seems to be quite an awesome idea.
If I knew how to program that, I think I'd be rich.

OK, I'm already reviewing those ranges.
This looks great to me.
Do you have the EVs your solution has for BB and SB in that spot?

Wow @ xCalling with KK there!
I now have an edge in this spot on TwoSHAE when I challenge him to HU4rolls. It makes sense as you block his Kx, but still..


And how do you come up with these things so quickly, how did you solve this? Was that done with one of your custom made software pieces?

Hmmm... I see your point.
Do you think it's a big error at times to work with assuming otherwise, at least for our BB player?
I think it simplifies the things greatly; and the feel I have is that it should be about right most of the time, or close enough.
Ie the fact that he might at times turn bottom pair into a bluff, bottom pair which might at times win vs a SB who checks back his Q high missed draw, might not influence things that much when choosing strategies...

I might make some videos showing how to do it with iPython. I've started working on the code, but I'm not sure yet if it's likely to work well as a video pack.

Yes, although there are lots of them, so it's hard information to communicate..

Yes.

Yea, it's probably a pretty good guess in a lot of spots. Of course, if you start with it and then work everything else out, you can go back at the end and check if it was a good assumption, i.e. if it's consistent with the BB bluffing range you find.

Hmm.. I think the key question here is then do you think your end result, the procedure your program does, would be something that's simpler to use than what CREV does.

Ah, so no aggregate stats?

Well, I've plugged the BB ranges outlined above into CREV. I might've missed a combo that's played with a mixed strategy here or there - some boxes are half filled due to card removal, and some due to mixed strategy in your pictures - but I've gotten about 30.5 bbs EV for the BB, depending on a bluffcatcher here or there.
He's betting 62% of the time.


It is interesting what's in the indifferent bluffcatchers range - you have A high and Q high hands together with middle pairs (!).


And this is then the root of all that high stakes bluffcatching with K high. Where Jungleman's street poker comes from.


Here's three interesting snapshots - BB's betting range:


Here's what the EV of SB's hands looks like when the BB is perfectly balanced.
His bluffcatchers, AT QT and 9x (middle pairs) are indeed indifferent unless you like chasing 0.009 bb edges





And here's what it looks like when BB's bluffing frequency goes just slightly out of line, ie the part of his air that he's betting is weighed at 100% instead of 75% (note that he is still checkfolding a lot of air in this example. He's bluffing with his 7 high a bit more, but is xF all his T high still)




The EV of his high card bluffcatchers went up to 13-16 bbs / 100! That's a massive difference.

I now have a mathematical reason to call down with A high in 3bet pots; as if I wasn't spewing enough already.


How can I do the same (solve these spots myself)? Is that done with that Gambit thingamajig?

Does it solve the spots after I determine that BB has to bet, or does it determine that itself?

Well, first, the idea would be to solve for equilibrium strategies, which is something CREV doesn't do (despite the hacks shown in those youtube vids you reference). And second, if we teach people how to develop some of these tools for themselves, they can do whatever kinds of analysis they can imagine, unconstrained by publicly-available software.

Don't know that this set would have a super wide audience, but it seems like a fun project, which is most of why I've been playing with it.

Oh, average EVs? Sure.

At the beginning of river play, SB expects to end up with 106.46 BB and BB expects 93.54, on average over their whole ranges. Subtract off the 63 BB stacks to find how much they expect to win from the pot on the river... 43.46 and 30.54, resp.

Right after the BB bets, he expects 104.5 BB (ofc SB EV is just (200 - BB EV)). If the SB calls, BB's EV is 72.9 BB.

After BB checks, his EV is 75.3 BB. Then if SB checks back, BB's EV is 77.9, and if SB bets and BB calls, BB's average EV is 118.0.

I have him betting about 78.14 of 124 combos.

Yea, for example, take J8ss (3rd pair) and QJss (Qhigh). They're both ahead of all of BB's bluffs and behind all his valuebets. But QJ blocks more of BB's Kx -- KJ and KQ, while J8 only blocks KJ. So the Qhigh is a more profitable bluff-catch, by about 1BB (ie 100 BB/100 hands). Possibly an artifact of our starting ranges, but worth thinking about.

Can't win if you fold.


The thing about gambit is that it isn't a poker-specific program, and in practice, inputting a complicated situation like this one isn't really feasible. I'm not aware of any publicly-available software that does this stuff, even though it's pretty straightforward.

What are these programs?

I believe those screenshots are all from CardrunnersEV.

tnx man

PS. just so u know ur 2nd book is already preordered

Amazon states the 2nd book is shipped tomorrow but DandB poker says january, i'm assuming DandB is right but if anyone knows exact release date would be awesome.

Yea, I'm actually not sure how Amazon got that date, but no it's not correct. The real answer, of course, is "when it's done and as good as it can be," and it's getting there... January or not too long thereafter seems reasonable.

What? I'm was all excited! 1st time amazon let me dwn. Anyway would anyone like to dicuss the equilibrium strategies for bet sizing and calling ranges on the river? I'm currently reading this chapter and it is opening up my game and thought process.

ohh no i also was excited about november 12. Now i have to wait 2-3 months =/ seems unfair now but im sure it will be worth it in the end

I just obtained the book today. The title of the book contains the word "Exploitative" and this thread's title contains "Exploitive". I don't know what that other thread's title was, but this thread's title is incorrect.

Myself, I prefer to save a syllable when possible so I like "exploitive" better. Strangely, my browser's or OS's text edit software underlines "exploitive" with a dotted red line, which indicates a potential misspelling. But "exploitive" is a perfectly good word: consult a dictionary and you'll see that both "exploitive" and "exploitative" are provided as adjectival forms of the verb "exploit".

I'm looking forward to getting a lot from this book. I "returned" the Kindle version and ordered the paperback when I noticed that the Errata linked to on the book's web page provides only page numbers -- useless with the Kindle edition.

Hey, Will,

Could you post us the tree/the solutions for the KQ855 example, river play?
Both when we give him the option to blockbet, as well as when he does not blockbet (but does lead), with the EVs included to see the differences and the importance of the option.
I am interested in the examples where he does have air and when he doesn't have much air, as mentioned in the text, seeing as how the frequencies change greatly.


I ask beacuse it is odd to me that he is leading "some kings and some queens" (top of page 303) and then checking "some kings and some queens", too, in one of the primers.
I cannot recreate it myself. It's as if the cutoff hands between different ranges went a little crazy.

Great thread. Buying this book very soon

Why wait, why soon...
Order it now and you'll get it "soon" anyway.

Order soon, get soon.

Just want to say that I've read this book and it is easily the best advanced poker book I've read. I'm not sure where, but I saw someone write that if poker were a university course, this would be the textbook. I couldn't agree more.

Whenever I play poker now, I am so much more confident in my river play than my play on any other street. I'm very excited for Volume 2, and will likely be rereading this one in the meantime.

nice

I know zero about programming but I am very interested in learning how do what you have done.

If you do not make a series, is there anywhere else you can point me towards for starting out? is Python the go to coding for this nowadays? What about excel game trees?

As well, +1 for making volume 1 and soon to release volume 2. Have enjoyed your book and it helped confirm my suspicions of error prone poker 'math' that is peddled at various training sites/books.

Mind-blowing book.
I've hardly scratched the surface.

Currently trying to stretch my head around Chapter 4 (the Indifference Principle).

Can someone explain where I'm going wrong with the following:

I'm assuming that the indifference principle is also at work in the shove/fold game (correct?).

So at 12 bb deep (for example):

where EQ(SB) is SB's equity when he gets all in
and EQ(BB) is BB's equity in that spot.

I want to say that at A, SB's indifference between folding and shoving gives us:

11.5 = 24EQ(SB).f2 + (1-f2).13 (equation 1)

and that at B, BB's indifference between folding and calling gives us:

11 = 24EQ(BB) (equation 2)
==>> EQ(BB) = 11/24
==>> EQ(SB) = 13/24

and then, in equation 1,
11.5 = 24 x (13/24) x f2 + 13 - 13xf2
11.5 = 13 ??

Clearly I'm missing something pretty fundamental here.
Any help you guys can give me would be much appreciated.

Re: exploitative vs exploitive, yea the thread title's doesn't match the book's, and it looks like both are correct English. Maybe shorter is better. I blame MoP :P.

As far as the errata and the kindle version, I hadn't thought of that issue before. I guess in an ideal world, known errata would always be fixed in electronic versions of the book. However, I'm not sure that Amazon makes that easy. I'll check into it...

Hope you enjoy the book!

There are a couple things to keep in mind here. First, the idea of strategies dividing all hands into nicely-separated action regions depends on the simplifying assumptions that there are no card removal effects and that hand values are well-ordered. These things are usually approximately true on the river, but sometimes not.

Second, even in the [0,1] games the structure of the solutions may not be unique. E.g., maybe we need to check some slowplays on the river from the BB for balance, but we may be able to structure our strategy so that these are drawn from our very nut holdings or from our strong-but-non-nut holdings, and still have an equilibrium either way. When solving games by hand, we make a choice and go with it, but this situation may lead to mixed strategies being played with a lot of hands in the computer.

Overall, it's not too surprising that BB is sometimes checking and sometimes leading river with both top and second pair.

Again, sorry that it's difficult to communicate these trees and strategies exactly via images, but full solutions to the river examples are linked to here:

http://forumserver.twoplustwo.com/33...l#post38858250

That only includes the case for Example 3 when BB can block the river.

As my publisher said, reviews don't get much better than this ! I'm glad to hear you've enjoyed the book, and hopefully Vol2 won't be too much longer.