When the SB is 100 BBs deep do you guys think it is better to raise 2x or 3x and why? I've been having trouble on this. Do you think raising 3x is better to people that don't 3bet hardly and 2x to people that 3bet alot? I like betting 3x to be able to stack my opponent easier. Also, around 50 BB is when I switch to strictly 2x usually.

Reading and working at the book right now. Can someone confirm that the EV for Heros play for the Equilibration exercise starting at page 46 is correct? Because for every iteration step I get a whole other EV for Hero. i first tried to solve the iteration steps with CREV but cant get the trees right so I just put the ranges and numbers in Pokerranger and my in own excel Pokersheets. With both programs I get the same Hero EV for every iteration step but the EV in the book differs very much from my own solution. I already took into account the other approach of the EV estimation in the book looking for the endstacksize and not the stacksize difference. Hmmh I dont say the book is wrong but would help if someone stated the estimated Hero EV for the iteration steps on page 48 are correct in the book. Maybe someone calculated them on his own and could state that the book is right.

Probably messed it up. Pokerranger gives me wrong Equity. Equilab gives me other Equity then CREV and Pokerranger. But using the CREV Equity with my excel sheet gives me nearly the same EV as in the book. But the Equity of CREV must be wrong here. (Always shows me 50% Eq -> cant be) But the iterations of my CREV model therefore seem to work out as in the book and comes to the same ranges but gives me other EV. So it is all a mess Will figure it out - maybe ^^

edit:For anybody who is interested ^^ okay CREV seems to work out the ranges good but does call in iteration 2 with JTo, JTs and QJs which in the book are folds. But the resulting EV is messed up anyway.

CREV doesn't come to the Equilibrium like stated in the book. Same thing happened as for the other user who posted before. It just moves back and forward with the ranges in an endless loop. CREV just shoves 71.1% of the range for Hero and not the whole range like stated in the book and Villain should call with 48.2% of his holdings when I try the unexploitable shoving tool. But I guess I missed something. Will not spam in this thread soon again. But maybe someone can state if the EVs in the book for the Equilibria exercise are correct. Well the whole procedure did make sense for me anyway.

I actually don't use CREV, so its a little hard for me to say what might be the problem, but the other reader earlier did end up getting the same results as in the book with CREV once he fixed his starting ranges. I've also re-checked the results myself, and I'm quite sure they're correct. That said, understanding this sort of thing is super useful, so I'm happy to help you get it right.

Verifying many of the maximally exploitative plays is easy to do by hand with an equity calculator. (As far as your problems with the equity calculations go, I'd definitely recommend the PokerStove utility. It's fast, free, and almost certainly correct.) I demonstrate this, and also have some suggests for other checks on your CREV calculations in this post:

http://forumserver.twoplustwo.com/sh...&postcount=120

Does that help at all?

Cheers

Hey thanks for your great reply. I use mostly Equilab as Equity Calculator cause I can store ranges there but it usually works fine and give correct distributions like stove. So I guess Pokerranger has some flaws with his Equity calculations in the EV Tab and I will soon contact the author. btw that is a great guy too. Maybe I just cant handle the tool correct because just bought it yesterday.

CREV I didnt use for a year or so and always takes time to come familiar with it again. Your book I read some weeks ago but in the first half it was obv to me that the concepts and math get a little hard so I wanted to simulate the examples with some tools to better grasp the concepts.

Thx for the link. Will maybe simulate the Equlibrate exercise another time again but will go to the next chapter for now but want to get more familiar with CREV before and use some simple simulations with all my progs to see if I find mistakes in my usage of them.

One suggestion I have in regards to your handranges in the book. It would be far more easy to work with them if they were shown in the same order like Pokerstove or Equilab so no one has to look over them again and again to make sure every hand is included. But besides that the book is great and much more valueable than the overpriced ebooks for example. I think it is on a lvl with Mathematics of NLHE - the best and most important Pokerbook so far imo. Maybe the MJ book will be another great read in the future.

Cheers

edit: Hey sry for my bad english skills but my last english lesson is > 15 years ago.

Hello yaqh. It is me again
Just wanna let you know that Iam getting the same EVs for the 12bb push or fold game on page 82 and 83 for all hands except for J4o in both tables. For the SB pushing J40 and the BB calling on p.83 CREV gives me other EVs. I read that you progged your own Analysis tool so maybe you have a minor bug there.

btw at BeXXs: best team, best beer. I support that all

Hi guesswhat, nice catch. It looks like the BB's EV after calling the shove with J4o should be 8.80 BB instead of 9.63 BB. (9.63 is actually the number for J4s, so just a misclick on my part and not a bug.) I believe the other 5 numbers for J4o in those tables are correct.

Hi,

the unexploitable shoving tool from CREV is for shove or fold situations only, however the tree in the book has Hero check-folding instead of an immediate showdown. If you make a CREV tree exactly as in the book and use the maximally exploitative play tool instead it may converge to the equilibrium for this particular case (I didn't verify it). However, alternating the maximally exploitative play tool between both strategies won't work in the general case because it switches the strategy completely whereas the fictitious play algorithm will update the strategy gradually (using mixed strategies). yaqh has explained this elsewhere in the forum.

You can use pure strategies. You will end up in a cycle, but this tells you that the equilibrium solution is a combination of the strategies which make up the cycle. Then you still have to figure out the frequencies.

This book is very difficult for me to read. I might have to wait for the book about this book. I got stuck 1/3rd the way through. I keep getting the feeling that there is nothing I can practically use in this. It, at first, brief, reading seems so abstract.

Does it work in the general case? If you switch between pure strategies only can't it get stuck in local extrema?

What do you mean by a local extremum? I think this should work, even though I do not have a formal proof.

Sorry you find it challenging reading. There's certainly a trade-off between strategy discussion that is too specific/concrete and thus necessarily an over-simplification at some level (and often new and interesting only to beginners) and strategy discussion that's too abstract and thus hard to actually use at the tables. Any strategy written for advanced players must navigate that tradeoff somehow. It's a challenge but I tried to give the abstract conceptual tools necessary to understand the game and the mathematical tools to work out new situations for yourself while still diving into the practical consequences for lots of specific spots I find interesting.

As far as more practical/easy-reading portions of the book go -- if you're 1/3 way through, have you read Ch 3 on preflop-only situations? There I discuss a variety of tables for short-stack play. I don't recommend that people play strictly by tables, but it's an OK approach in some spots, and strategy advice doesn't get much more concrete and practical than a table. Of course there's also lot of discussion of exactly what tendencies you should look for in opponents in these spots and what adjustments you should make based on what you see.

If you're more interested in postflop or deeper-stacked play, you can also just skip ahead to Ch 6 (Postflop Concepts). There I have some ideas on more standard practical topics like board texture, barrelling and bluffcatching decisions, etc, that most people will find new but easy to incorporate into their games. Much of that should make sense without Chs 4 and 5, and perhaps it'll provide some extra motivation and context so that you can go back and read the other stuff with a clearer idea of why it's important.

I think your approach can be a good way to think about many situations, especially those where there's only a couple pure strategies possible. On the other hand, even in a simple situation like the preflop shove/fold game, depending somewhat on your starting guesses, the maximally exploitative strategies can oscillate from way-too-tight to way-too-loose in a way that doesn't really give you much useful info about the equilibrium.

I was thinking that finding a Nash equilibrium can be seen as an optimization problem and some methods can get stuck in local extrema. Talking about second-order knowledge here so I'm probably wrong.

Hi yaqh. Just received and started reading the book and it seems like it's going to be just as good as I thought it would be (very).

Since you're here fielding questions, I wanted to ask you about something that's been going round my head a bit lately; I guess it's slightly similar to the issue of 'loss leaders'. My question is, do you think it's possible that, as part of a GTO strat, a play can be +EV (or at least 0EV) when made sometimes, but only because it's not made all the time? For example, we're facing a reraise preflop and are considering flatting or folding, and it turns out that flatting every time with this hand (slightly) loses money. Might there be a spot like this where flatting some % of the time increases the EV of our strategy as a whole compared to always folding?

I fully expect that the answer is likely to be 'no', because I've learned that we're supposed to mix only when two or more plays have identical value if played unilaterally. I wonder though whether there is an issue specific to the game of poker that comes into play, namely that of board coverage? In other words it seems to me that the frequency with which we have a hand, and how that strengthens or weakens our overall range on various boards, strongly affects the profitability of playing the hand with all the community cards still to come.

Kinda confused about the subject tbh, would love to hear your thoughts.

Hi CoronalDischarge,

Glad to hear the book's going well so far. I expect the answers to these sorts of questions will be very clear once you finish Ch 2, but let me give you the CliffsNotes.

If our opponent's strategy is fixed, then a best response (or maximally exploitative) strategy is more or less what it sounds like -- it's a strategy where we choose the highest EV option in every spot. (Of course sometimes two actions might tie for highest EV.) Obviously there are no 'loss leader' type plays in a maximally exploitative strategy -- by definition we're doing the highest EV thing in every spot.

Equilibrium play occurs when both players are playing best response strategies at the same time. This is a special situation since neither player has any incentive to change his strategy -- doing so could only lower his expected profit, since he's already playing a best response. If we take one of the individual players' strategies from the equilibrium, we say it's an unexploitable or GTO strategy for the player.

So, an unexploitable strategy is a best response strategy, when Villain is also playing GTO. Thus, in this case, it has the no-loss-leaders property of all best response strategies we noticed above.

If Villain deviates away from GTO, then some of our hands/plays could decrease in EV and others increase. However, we're guaranteed to make more (or at least as much) on average if we keep our GTO strategy since Villain decided to stop playing a best response, and any money he loses is money we gain.

So with all of that background, let's see about your question...

It can definitely be the case that a hand is played in more than one way at the equilibrium. Of course, this must mean that all of the ways it is played have the same EV, or else the plays couldn't be part of a GTO strategy. However, in this case, as long as Villain keeps his strategy fixed, beginning to play these hands all one way or all the other won't change our EV. It's only when Villain adjusts that we begin to lose EV.

Take an example -- in an over-simplified river scenario, we're in the SB with a range of hands which are all either nuts or air (but mostly air), and the BB has all bluff-catchers. So, we bet all our nuts and some bluffs, and the BB calls sometimes and folds sometimes. At the equilibrium, the BB is calling just enough so that with our bluffs, the EV of bluffing and the EV of giving up are exactly the same. (So, you might say that bluffing is 0EV, for some definition of 0EV.) Now, if Villain keeps his strategy fixed, we can start bluffing all the time or giving up all the time and it won't change our EV, but once Villain does adjust (by beginning to call a lot or fold a lot, respectively) we lose EV.

Hope this helps.

Hi yaqh. I appreciate you clarifying those arguments for me, but to be clear, what I was suggesting was something that would constitute an exception to the rule that mixed strategies happen only at the margins and that the constituent plays have identical EV. I think I'm almost certainly wrong (I'm not going for durrrr-esque hubris ) but I'm having a hard time figuring out why. The basic idea would be that due to the poker-specific concept of board coverage, a strategy might do better by playing hand H some % of the time in a spot, than by always playing it OR always folding it. Because empirically, we have these competing concepts: on the one hand, wanting to be able to hit as wide a range of boards as possible with both hands that beat one pair and hands that can semibluff with strong equity; on the other, wanting to flop strong equity as frequently as possible, meaning overpairs and big split pairs. If we have too many of the former type of hand, we don't do the latter often enough. But if we don't have enough of the former type of hand, there are too many boards where we are capped with one pair at best while the villain has all the stronger stuff in his range. I guess I'm talking about, for example, flatting a pretty sizeable 4bet oop 150bbs deep, something like that.

Again, I think this must be wrong, and I think it must be wrong for similar reasons to why loss-leaders are wrong, and yet it's making a lot of sense to me right now.

BTW sorry if this is a derail; I'll save it for the theory forum if so

OK so having finished chapter 2...
I was clearly being foolish by suggesting that EV(call) could be higher than EV(fold) with both plays still being represented in a GTO strategy.

However, could EV(call) = EV(fold) but only when mixed in the correct proportion? I suspect not but I'm still not sure why. I'm a little hung up on this idea of board coverage you see.

All I'm really trying to ask is this:

Can the value of a preflop holding when we VP$IP with it be altered by the frequency with which we VP$IP with it, given the effect that frequency has on our range's ability to hit different boards?

In Ch 2, we saw how to directly compute the EV of taking a particular line with a hand, given Villain's fixed strategy. This calculation depended only on Villain's strategy (and the game tree -- the description of the game we're actually playing). It didn't depend on how often we play it that way or how we play any of our other hands for that matter. So, if Villain's strategy is fixed, the EV of playing a hand a certain way against it is also fixed.

If, however, Villain is adjusting his strategy to exploit us, then there can be some frequency that gets us the highest EV, as in the simple river example I described above.

+1 Same here.

Yeah, looks like I was just doing some explo thinking of the 'I think I can play this type of hand profitably, but I need to be careful not to do it too much or it'll stop being profitable' variety, and confusing it for theoretical insight

Cheers mate, loving the book.

Can this book be applyed to limit ?
Obviously Not all of it but but maybe sone portion of it ?

Hi Montrealcorp,

Please see my post here:

http://forumserver.twoplustwo.com/sh...&postcount=106

Cheers,

Will

Great book yaqh, I've already read a lot of pages, but now it's time to study them Thanks a lot for sharing with us all your knowledge

One question: does it exist an "errata corrige" of the book for the little errors?

IE page 41, line 4, it should be EQ_H instead of EQ_(H,D) or something like that, right?

One more question: do you use MATLAB for graphs and calculation, isn't it?