Except obviously if your opponent almost always either four bets with hands that you can't call against with your otherwise slightly positive hands, or folds with a frequency that gives you an automatic profit. If he plays that way as long as you don't three bet too often, you make more if your three bets are either your best hands or hands not worth calling with.

Game-theoretically optimal play does not take into account your opponents' tendencies. Did you even read the book? =P

His statement did not make clear that he was speaking only game theoretically. And by the way even if he was, it does not logically follow that three bet hands must be composed only of hands that are plus EV to call. It could conceivably occur that there are hands that are very slight losers if they just which called do better than slight winning (calling) hands against the range that calls your three bet. That's why Matthew can't make his statement with certainty.

I disagree. I think it was very clear that he was speaking "only" game theoretically. I'm sure most of the people who have read his book and are following this thread would agree.

I agree. But I worry about the reader who just happened to hit upon that one statement out of context.

I'm just about to start working through the book for the second time and I'm looking to implement some of the ideas into my game.

I'm looking to design ranges for defending on the button against resteals from the BB and have read over the corresponding chapter. The concept I have difficulty with is not taking into account villains resteals percentage when working out our defending range.

For example, lets say we are using the example range on p72 for an opening range of 50%. This gives us a calling range of 14.5% of all hands. If we take a villain who only resteals 7% in this spot isn't our calling range too wide against such a narrow range and liable to be dominated on a lot of boards?

Thanks in advance for any reply

You are correct in that a GTO opponent would 3bet much wider in that spot. I think you should adjust your ranges to the player pool you are a part of. If most people are 3betting tighter then you should open wider and defend tighter. Playing exploitatively is often more +EV than playing GTO.

Yes, but you have to look at the overall strategy. The money you are losing
calling wider is more than made up for the money you gain by your opponent reraising too little.

One extreme example is an opponent who only reraises with AA and always does so by going all-in. A GTO calling strategy will lose more money than an exploitive one. That is not a concern because you gain by losing less than you should against hands he should be reraising like KK. This results in your overall strategy having an EV=>0.

Notice how perfect your game theory might have to be to invoke this concept. Especially in no limit as opposed to limit. Say your opponent folds to your preflop raises a little too much which makes you a few Sklansky pennies. If you play GTO from that point on without adjusting to his actual range, you are playing a little too loose from that point on (assuming he plays his smaller than assumed range properly) and you will give most of the pennies back if you execute perfectly. But if you don't execute perfectly you will give back more than he initially gave you. That's why we felt it important to include a warning in the text.

This is a good point, and something I try to stress a lot when talking when other players.

My favorite example of this concept is calling 4-bets OOP. Let's imagine there's a spot where we think we should use a mixed strategy with 76s when facing a 4-bet in theory (so in theory we call the 4-bet sometimes and fold it sometimes). So, by definition in theory we believe both calling the 4-bet and folding to the 4-bet will be 0 EV. A world class player may be able to call the 4-bet and break even or make a slight profit, and if he's playing a world class opponent he may actually get exploited if he never flats this 4-bet. But for 99% of poker players they're likely just better off folding vs most opponents, since it's much easier for the opponent to play a 4-bet pot in position with a polarized range than it is to play 76s in a 4-bet pot out of position.

But you also need to think this through exploitatively. If your opponent's are having a hard time calling with wide ranges from the big blind, then you probably can open in the button wider than you should theoretically be able to. Likewise, other good regulars at your stake probably know this too, and should be opening the button too wide themselves. That encourages you to 3-bet even more aggressively than what is likely GTO (and most people aren't 3-betting nearly as aggro as they need to be from the blinds to begin with IMO, much less 3-betting too aggro). So at the end of the day I think the most important thing to do is make sure your logic is consistent everywhere, and if you are taking some exploitative lines be aware of them so you can reconsider them as you move up in stakes and play better opponents or as people just get better over time.

Certainly, I believe that whatever the GTO solution for NLHE is it won't be a strategy that can feasibly be played by a human. I wanted to point out however that not being able to at least breakeven in specific situations does not imply we are doing something wrong GTO-wise.
For example, if we determine that our button range cannot reasonably call down against a balanced opponent on a board like A22 or AA2 should not lead us to the conclusion our preflop play is flawed.

let me put up my review here.

It's a great book for any reg that is looking to improve his play vs nits/ other regs. First the preflop section plugged some leaks and difficulties I had there. I think playing exploitative poker >>> GTO. But by working trough some gto-stuff you can learn how to exploit better and be less unbalanced (find you own leaks). The book taught me very important concepts like 'unconventional' betsizing (overbetting and betting small), how to balance CRing ranges (and how to exploit unbalanced ones), a very different view on how to play OOP, how to play vs polarised ranges and vs densed ranges, when to keep villains range wide,...

Maybe this book hasn't much value for a crusher like lorenzovonmatterhorn but for every one else it should be a must-read.

Niice reply.

Hey Janda i'm loving the book so far! Had a question. I'm trying to solve for my EV for Cold Calling when only these factors are present:

-Someone opens 2.5x MP, we CC in CO.

-When we see a flop, we win 60% of the time (let's suppose it's always a HU pot, it never goes MW).

-When we face a squeeze (assume 20% of the time), we always fold and lose the hand.

Would I use a similar formula to the one you provided in the book (EV when btn folds)(freq. BTN folds) + (average EV when called)(freq. called) - (EV when 4bet)(facing 4bet freq)

or is this calculation below fine?

so .8 * .6 (the times we win postflop) * 4 (the money we win excluding our bet (2.5bb from the opener and 1.5 from the blinds)) = 1.92

then we need to substract
.2 * 2.5 = .5 (the times we face a squeeze and fold, losing 2.5bb)
.8 * 2.5 * .4 = 0.8 (the number of time we will see a flop, which is .8, and we will lose 2.5bb 40% of the time)

1.92 - .5 - .8 = 0.62

Correct if I'm wrong please!!

How do you know how much money you're winning (or losing) when it goes postflop?

We don't I just want to experiment with the number and see how it effects everything. Also, i wanted to see how this compares to just 3betting an open instead of CC. My goal right now is incorporate more CC in my game to force regs to play OOP, but i'm trying to weigh out my choices here between calling and having to fold some of the time to a squeeze or if CC would yield more profit through my post flop edge vs lets say a guy that's ch/f a ton post flop

If you know you'll always be heads up when you call and also know you'll get squeezed 20% of the time total and always fold, then you can calculate how much money you need to win on average to make calling +EV. I don't think you could make a formula for doing much else besides that, and there's no way to tell if calling is more +EV than 3-betting. I don't think this is going to be something you're going to be able to make a very useful equation for, because you can't solve for how much EV any hand has post-flop.

Yeah i'm afraid you're probably right. Thx for the response

I am on page 120 and it says

If we raise our opponent's 6 big blind flop bet to 18 big blinds, he must defend at least 43.8 percent of his flop betting range to prevent us from being able to profitably bluff any two cards.
(14)(1-x) - (18)(x) = 0
x = 0.438

I make immediate profit if he folds more than 43.8% then doesn't he at least have to defend 56.2% to prevent me from making immediate profit?

please help me understand it.

The variable x is how often your opponent needs to defend. And 1-x is how often he can fold without being exploited by a raise with ATC.

So he needs to defend 43.8% and you make an immediate profit if he folds more than 56.2%.

Hope that helps.

Oops, I was thinking in reverse

thanks a lot

Ok i have some questions about applying the formula: 75(1-x) - (75-200Y)(x)=0 in the "Facing a Turn Bet in Position After Calling a Flop Bet" section of the book. P.273 in my nook book.

So question 1, is this correct?: (risk)(1-x) - (current pot size - 200Y)(X)=0 ???

In the book it has both as 75 so wasn't sure which was which.

so if above is true, how do we plug everything in (for hand below) if we assume we have 35% equity and everybody folds and only raiser on the flop calls or folds?

would it be: (75)(1-x) - (56-200(.35))(x)=0 or
(102.5)(1-x) - (56-200(.35))(x)=0

is this formula even relevant in this spot? I'm obviously not great at this so any help is appreciated

$1/$2 No Limit Holdem
PokerStars
6 Players
Hand Conversion Powered by weaktight.com

Stacks:
UTG Twee taknado ($79) 40bb
UTG+1 C1awViper ($211.06) 106bb
CO vrnMike ($637.89) 319bb
BTN hydroxyacid ($203) 102bb
SB Hero ($210.46) 105bb
BB The_Meer ($211.66) 106bb

Pre-Flop: ($3, 6 players) Hero is SB 10 K
Twee taknado raises to $5, C1awViper calls $5, vrnMike calls $5, hydroxyacid calls $5, Hero calls $4, 1 fold

Flop: 10 8 9 ($27, 5 players)
Hero checks, Twee taknado bets $15, C1awViper calls $15, 1 fold, hydroxyacid raises to $55, $55 to Hero ($205.46)?

I'm having a little trouble finding the formula since the pages don't add up, but off the top of my head I'm pretty sure that formula deals with 3-bet pots when a player bets 25BB into a 50BB pot on the turn. It's designed to show how rarely a turn jam when facing a bet needs to succeed in a 3-bet pot to be profitable provided your turn jamming hand has some equity. So no, the formula isn't going to be relevant here.

The "75" in the equation is the pot size in big blinds after the opponent has bet. So here you'll need to plug in however big the pot size is before you jam (looks like about 55). That's what you win if you jam and everyone folds. Since you've risked almost nothing so far though, you'll be risking 99 or so big blinds when you go all-in, so that's what you stand to lose if you go all-in and are called and lose. But since you assume you have 35% equity when called you'll really on average get (200)(0.35) = 70BB back when you go all-in and lose, so you only end up losing about 28BB on average when you lose and are called.

In other words if you go all-in and they fold, you win approx 55BB. If you go all-in and they call, you lose about 28BB. You can set up the equation with these numbers (try it yourself first) but you'll need folds about 33% of the time with your assumptions for jamming to be +EV.

shouldn't the pot size be: 27 (current pot) + 15 + 15 + 55 = $112 so 56bb's
and so if we shove and risk our $205 (102.5 bbs's)

It would be this= (102.5)(1-x) - (56-200(.35))(x)=0

or wouldn't we add the additional $30 (15bb's) from the other two guys in the pot also, so it instead it being 200Y it's 215Y so looks like this?:
102.5(1-x) - (56-215(.35))(x)=0 ??

assuming everyone folds and we're heads up

I totally butchered this bro, i'm just not understanding how to plug the values in

alright spoke to a friend and turns out i had everything reversed.
so it's actually (current pot size)(1-x) - (risk - 200Y)(X)=0 ??
So in this case, (56)(1-x) - (103- 226.5y)(x) so in the end if they fold more than 29.8% you show a profit shoving

that cool?