up

Ayo Will Tipton! send me a copy of this asap . You understand me?

Re #3: I don't expect to be out of print too soon :P Hope you enjoy!

Looks like there are a couple issues with your equations. The convention is that we're working with expected stack sizes at the end of the hand. If you start with 80BB, and you're not in the blinds, and you fold to an open, then you end the hand with 80BB:

EV fold = 80

Maybe you're saying Villain has 80 but you have 100? That's fine then, although it might be easier to just work with eff stacks. In any case, please fully describe the situation. I guess this is not HU? Are you in the blinds or no?

If we call, we end up with: the chance we hit times how ever much we end up with if we hit, plus the chance we miss times however much we end up with when we miss. To some approximation, this will look like

EV call = %miss * (80 - open raise size) + %hit * (stack size we expect to end up with after we hit)

I'm not exactly sure what the situation is, but yea it'll make a bit of difference if you're in the blinds. Also, it seems pretty ambitious to expect you'll both win the pot and get the guy's whole stack every single time you hit.
Set EV(call) > EV(fold) and solve for the constraint on X.

Sry for the confusion, obv that's my fault, I'm hoping I'm expressing better this time



Goal: build a simple model in order to gain experience with your EV calc method

Model 1

6max

UTG (Villain, 80bb) raises with AA
Hero (BTN, 100bb) has 44 and want to setmine

Villain cbets 100%
Hero folds everytime doesn't hit the set
When Hero hits, Villian is going to stack off 100% of the times



Maybe I didnt' understand well, I thought our expected stack size will be our stack, not the effective stack.
So in my model above, the EV fold = 80?



Model 2

6max

UTG (Villain, 80bb) raises with AA
Hero (BB, 100bb) has 44 and want to setmine

Villain cbets 100%
Hero folds everytime doesn't hit the set
When Hero hits, Villian is going to stack off 100% of the times


In the first model when we are on the BTN, the maximum that we can win is the eff stack (80bbs), but what about model 2 when we are on the BB
How much are we winning everytime we stack off?
181,5 or 180,5?



Off course, you are def right, but before working on realistic models, I have to understand perfectly how it works on the dumbest model possible

I'm working through the book and am at the chapter 2.2.1, maximally exploitative strategy exercise. I modified the exercise and would like to know if I'm doing everything correctly:
We are 25bb deep and hero is SB with T9s. Hero can either raise 2bb or fold, villain can fold or shove and hero can call shove or fold to shove.
Villain's shoving range (Sh) is 22+,A2s+,KJs+,A6o+,KQo = 18.3%=0.183
Villain folds (Fh) everything else = 81.7%=0.817
Hero's equity (EQh) against villain's shoving range is 40.58%=0.4058

EV=max(24.5BB[Fh*26BB+Sh*max(23BB,50BB*EQh)])=
=max(24.5BB[0.817*26BB+0.183*max(23BB,50BB*0.4058)])=
=max(24.5BB[0.817*26BB+0.183*max(23BB,20.29BB)])=
=max(24.5BB[0.817*26BB+0.183*23BB])=
=max(24.5BB, 25.451BB)=
=25.451BB

Therefore we can conclude that hero should raise, but fold to shove.

Ah, about the effective stacks -- the thing is, (in a cash game) it won't affect your decision at all if stacks are 80 and 100 (as they really are) or 80 and 80, since Hero's extra 20bb behind won't ever come into play. And some calculations are a bit easier if stacks are even, so I usually just do calcs as if both players had the effective stack. But let's not take that shortcut, for the sake of the exercise.

So,
EV(fold) = (stack we end up with when we fold) = 100
and
EV(call) = (chance we hit)*(stack we end up with when we hit) + (chance we miss)*(stack we end up with when we miss)

So, if you assume the blinds always fold, you hit 12.2% of the time (took that number from your earlier post), and when you miss, you snap-lose the pot, and when you hit, you stack Villain, we get:

EV(call) = 0.122*(181.5) + (1-0.122)*(100-X)

where X is how much you have to call preflop to see the flop (i.e. his open raise size).

You can set EV(call) == EV(fold) and solve for X to find the open sizing that makes calling and folding have equal EV, and then if the open size is any smaller, calling is better, and if it's any larger, folding is better.

Yea, in the first model if the blinds fold and you stack Villain, you end up with your original 100, plus the 1.5 in blinds, plus Villain's stack for 181.5 total.

In the second case, you get your original 100, plus Villain's 80, plus the SB for 180.5. (Or you could say, you end up with 1.5 in blinds, Villain's 80, plus the 99 you have after you post blinds.)

Yup, I added some commas, and card removal will make those shoving and folding freqs not quite right, but looks good.

Against an opponent folding so frequently, raising will be better than open-folding with ATC, but we'll need a strong hand (say 44+, ATo, A9s) to call a jam.

So I finally got round to finishing this book. I have a Masters degree in a pure science, and boy was this book tough, especially towards the end. I probably understood 20% of the book tbh, there was one particular chapter with lots of 'ah ha' moments and take aways that can be pretty much implemented into my game, but the majority of the book is really theoretical and intensive study is probably the only way to get anything of value out of it. Not taking anything away from this book, I do think its excellent - but only for those willing to dedicate themselves to it. Onto Volume 2!

Good luck with Vol2 if you got 20% out of Vol1.

This work is neck and shoulders above any other poker literature of that type.
The thoroughness and the level at which the work is (was) being done for it is surprisingly high. Figuring out that kind of stuff (conceptualizing it all then putting that to use) is really not easy.

And so it is also quite complex material.

I'm at p. 92-93 raise/shove game sub-chapter. Do I understand correctly that if SB first decision point (minraising) deviates from the GTO strategy, BB can still shove using the chart and be unexploitable? Or if BBs shoving range is different than the chart, SB can still call all-in unexploitably by following the chart?

This is from your book:
In the graph below, SB's open percentage doesn't go to 100% as soon as BB's shove percentage goes below 50%. Why is this?

Glad you guys have enjoyed it . I learned a lot from the writing too..

Um so maybe this is a question about what exactly "unexploitable" means. It means playing a strategy that's part of an equilibrium strategy pair. So yea, trivially, if one guy is playing an equilibrium strategy, and the other guy deviates, then the first guy is still playing unexploitably. More interestingly, (in heads up but not nec 3+player games) playing unexploitably does get us guaranteed lower bounds on our EV, regardless of how villain deviates. This is all really important fundamentals that I talk about a lot, so maybe browse again through Chs 1&2 if it's fuzzy.

Also, of course the chart just describes the equilibrium of the raise/shove game. The equilbria of the full game don't necessarily look similar.

Card removal. Just because BB is folding 50% of all hands doesn't mean BB is folding exactly 50% for any particular SB holding.

I am 6max player but this book together with vol.2 is by far best I ever read. And its not eaven close.

author please answer my questions:
1. which theorem in game theory tells us that there exists equilibrium solutions in HUNL?
2. if we use this principle to solve minraise/3 bet/4 bet/shove game, then the 3bet/4bet/shove should remain unchanged since they are independent of stack size. However why is their GTO frequencies depends on the effective stack size? p.118
in my opinion, we shouldn't use indifference principle to calculate the optimal strategy. because indifference principle is true if GTO tells us to play raise fold sometimes and raise 4 bet fold sometimes, so if GTO tell us never play raise fold, then indifference principle fail

i think you didn't solve minraise/3bet/4bet/shove game GTO frequencies correctly. For example, at effective stack size of 100, GTO suggests BB to have folding hand(since 3bet to 5BB is not 100%) and 3bet folding hand (since shoving frequency is not 100%), then indifference principle can be applied to BB's folding hands and 3 bet folding hands, and we obtain SB 4 bet frequency=3/7, but in the GTO graph, the frequency is about 0.3

another obvious mistake is that SB fold to shove frequency+ SB calling frequency=100%, but from figure 4.2 a) and b), the sum of two frequencies clearly not =100%

the graph have a lot of mistakes, i hope you to provide us a correct graph,

most of the time our opponents are not playing GTO, therefore, we should play maximally exploitative strategy rather than GTO (it is possible that maximally exploitative strategy=GTO) because we can have higher EV

The frequencies are not independent of stack size. Indifference considerations fix ratios between sizes of some, but not all, ranges in that game. And also, as discussed, indifferences can break down at extreme stack sizes.

Well, the point of that discussion is not so much to find the solution of the minr/3bet/4bet game (which isn't v useful in itself) but rather to understand the indifference principle. I think you'll find that it does give us a useful way to understand many aspects of many equilibrium strategies, but understanding when it doesn't apply is v important as well, and examples and discussion of that are often neglected. I spend a lot of time in that chapter talking about when indifferences break down.

Sorry if it isn't clear, but all the curves in Fig 4.2 represent sizes of ranges as fractions of all hands. So for example, we'd expect SB fold to shove + SB call shove to equal not 100%, but the fraction of all hands in SB's range when facing the shove, i.e., SB 4bet. With that in mind, I believe the graphs are correct.

thanks yaqh, everything make sense now

I own both volumes of "Expert Heads Up No Limit Holdem" and I want to study the books and possibly the video packs to improve my 6max cash game. Is there any sections and exercises that I should skip that won't help me much for 6max cash games?

If I could only buy one of the video packs, should I buy volume 1 or 2 to help improve my 6max cash game?

I'm having a difficult time trying to understand the following from page 250:

Can you explain where the second inequality comes from in a different way?

In section 7.4.3 you give the solution to a river hand where the BB can choose between block betting and a pot sized bet,

I'm pretty sure in the earlier chapters you only showed how to set up the indifference equations for one bet size or the other (essentially each was its own game with its own solution). So how do you set up indifference equations for mixed bet sizes? It isn't immediately obvious to me where to place different actions along our range

ie
(1................................................ .................................................. ........0)
(big bet call, block bet call, check call, check fold, block bet fold, big bet fold)


ie should the very bottom of our range be a big bet or small bet? The indifference equations will show the cutoff hand but not the ordering. Do you just guess and then maybe verify that the overall EV of one ordering is > than another?

Honestly the more I think about this the more confused I get. Where does check raising get put in the range?

Great book btw

I don't really think there are any entire sections that are only relevant to HU players. Pretty much every new part of the books introduces some new theoretical ideas, and HUNL is just used as an example. Even the sections which are only examples have a lot of widely-applicable observations, I think. Non-hu players feel free to chime in..

Well, again, neither really stands out as particularly HU-centric, but the packs are pretty different in their content. I'd recommend checking out the free samples (there's several hours of free content for the Solving Poker pack and lots of shorter samples from the earlier pack) to see which you think might be most useful.