Hi tigerjack,

Glad you're enjoying the book.

You're right -- the second subscript shouldn't be there. Thanks for pointing that out. I've been keeping a list of errata, but it's not online. I'll try to get it organized and posted soon.

I do use MATLAB sometimes, although I don't think I used it for this project. Most of the results are from my own C++ code, and I did a couple things in Mathematica. Almost all of the graphs in the book were made with xmgrace.

Cheers

Great, thanks
On page 123, in the tree, I suppose the numbers 25 and 35 should be reversed, right?

No problem.

I believe Figure 4.3 is correct as-is. As it says in the caption, the pay-offs are given from the SB's point of view. The BB's EVs are 60 minus the SB's.

The errata's now up on the book's webpage. It's pretty short so far. Hopefully it'll stay that way, although I do appreciate corrections.

Cheers

Fascinating book, Will.

I don't claim to be even close to understanding all of it (not even half of it if I'm being honest ) but having a lot of fun working my way through it for the second time.

On page 50, discussing the equilibration exercise you say

"As a point of reference, if both players were forced to check down on the river with the ranges we assigned, then Hero would win 82.5 BB on average and Villain 67.5 BB"

That would seem to imply that Hero has 55% equity
(0.55 x 150 BB final pot = 82.5 BB)

It's that figure of 55% I'm having trouble with.

When I put the two ranges into The Odds Oracle (and also when I put the ranges into PokerRanger, using a different method, so I'm not just copy-pasting) I get the 45 and 218 hand combos, agreeing with your combo counts, but I'm getting equity for Hero of 64.07%

Presumably I've screwed up somewhere, but before I dig deeper, could you kindly confirm that I've understood you correctly, and that Hero's equity should indeed be 55%?

Many Thanks.

Hey DiamondDog,

Glad you've enjoyed the book.

So, the situation here is that at the beginning of river play, there's 53 BB in the pot and 48.5 BB effective behind. You are correct that Hero has an average equity of about 64.07% at the beginning of the river. Thus, if both players just check down on the river with their whole ranges, Hero ends up on average with the 48.5 BB in his stack at the beginning of the street, plus 64.07% of the 53 BB pot, for a total of

48.5 + 0.6407*53 = 82.457 BB

It looks like you assumed in your calculation, that the final pot was 150 BB, but if there is no river betting, only the 53 BB pot is split according to the players' equities, and the 48.5 BB behind doesn't come into play.

When we then allow betting on the river, we find that Hero's EV actually increases quite a bit, despite the fact that he's out of position. This is thanks mostly to the shape of the distributions.

Cheers

Got it.

Thanks, Will. Really appreciate your help.

Have you heard the latest rumours of your evil twin brother, Wont Tipton?

I lol'd

Seriously..
He's the guy who removed the answers to a lot of the questions Will poses in the book.
Now they remain unanswered there.

Hello Will.
I am mostly HU sng player so I purchased your book.
I have to say that if other poker books are from high school of poker, this book is from University of poker.
I was looking for that EXPERT book 4 years ago after reading Moshmans HU book.
Your book really covers how to beat another experts as well.
I have a question. Can I purchase software you created you mentioned in the book to better understand your book in practice?
Thank you.
GL

Related to section 7.2.4., aiming at max exploitive strategies.
1) Let's assume our opponent always call tighter then GTO freq for wathever bet-size.
In this case indifference for our air hands breaks down each time and point towards betting with all our air. Does not matter if our river range has more then 50% air.
In this case, we just aim for the sky and go for the highest possible bet-size.

2) Let's assume our opponent always calls looser then GTO freq for wathever bet-size.
In this case indifference for our air hands breaks down each time and point towards check/folding with all our air hands.
Thing is, the moment our opponent call freq is fixed; we can start at bet-size 10% pot and keep increasing our bet-size with steps. Each increase in bet-size, increases the amount of air we can bet to gain (stack+pot) but at the same time we decrease the GTO call frequency and such comming closer to the situation where our opponent will call wider then GTO. Consequently at a certain maximum bet-size we stop betting all our air hands. Using a lower bet-size, we expect to win with all our air hands a fraction of the pot. Above that bet-size we expect to win nothing of pot with our air hands. But we still make more money with our value hands because of bigger bet-size.

Consequently, betting higher then that bet-size results in
our value hands increasing their EV by bigger bet-size &
our air hands EV decreasing their EV because they can no longer gain fraction of the pot

The moment our bet-size increases to a certain height we GET
EV gain by air hands by betting exactly the GTO size (just consider the fixed call % of opponent as the GTO call frequency) < EV gain by value hands by betting higher then GTO bet-size OR
(1-v)*(P-cP-cB) < v* (y*B)
P: pot size before river betting
c: real call freq
B: bet size @ river betting (at the GTO bet-size in the case c would be GTO c freq)
v: % of river range consisting out value hands
yB: increased bet size @ river betting (higher then GTO bet-size in the case c would be GTO call freq)

Essentially, resulting into we having to watch out if above equation is true. Meaning if there is a certain minimum amount of money left behind.
If yes, once again we aim for the sky and go for max bet-size.
If not, we are better off be betting that bet-size were opponent call frequency is actually the GTO frequency because in the area just above our EV can be actually lower.

Does my reasoning makes sense?

nvm, correct equation is actually:
v((1-c)(S+P)+c(S+P+B))+Av*((1-c)(S+P)+c(S-B))/(1-A)+(1-v-A/(1-A))*S < v((1-c)(S+P)+c(S+P+Bnew)+(1-v)S

A fraction of betting range that is air

resulting in
vcB+Av*(P-cP-cB)/(1-A) < vcBnew

Av*(P-cP-cB)/(1-A) < vcB(y-1)
term P-cP-cB always becomes 0 when entering GTO call freq + accompagnying bet-sizes resulting in 100% of the cases into 1<y

Essentially stating that any bet-size above the bet-size you get when you take the corresponding GTO bet-size when making real call% equal to GTO call%.
Resulting in once again, you just go for the maximal bet-size.

Think I got it

Hey Emus, tbh I didn't follow your whole post, but it sounds like you've got it figured out -- let me know if not.

Big picture, though, it sounds like hero is on the river with a completely polar range, villain is bluffcatching and his calling freq is fixed and doesn't depend on your bet size. So ofc our max expl play here is to jam all our nuts and minbet all our bluffs (or give up if minbluffing isn't even profitable) but you seem to want to use the same sizing with all of your betting range.

In that case, I'm pretty sure your best sizing is either going to be one of the extremes -- allin or minbet. The max expl strat will be to always bet nuts and bet air either 0 or 100 percent of the time. If its 0, bet sizing will be all in so we get max value with nuts. If its 100 then sizing will be min since EV is linear in sizing and EV obv isn't maximized when sizing is as high as possible (the sizing that makes his calling freq gto) so it must be maximized at the other extreme.

Hope that argument makes sense, but anyway the result should be intuitively pleasing. It would be pretty weird if our max EV bet sizing is the one which makes villain's calling freq be gto, since that's essentially just helping him play well, and we expect to do best by choosing a sizing that makes his choice of fixed calling freq bad.

Hey Bubucko,

Glad you've gotten a lot out of the book.

The software I developed to do the calculations isnt currently for sale. Right now, it's a command-line-based Linux program and using it requires an understanding of how it works.

I may polish it up, give it a proper gui and write some documentation someday, but it probably won't be too soon.

The holdemresources.net calculator, crev, and gambit all do some of the calculations I describe in the book.

Cheers

On page 48, 4th paragraph, aren't there only 42 combinations, not 45?
Is crev or gambit able to figure out exactly what range of hands are best to respond with for the various iterations? Where can I get those software?

No, there are 45. Perhaps at the end of the 3rd line of the range listing (sorry for the long ranges here!) you missed the hyphen in Qs6s-QsTs. This is meant to indicate the 5 combos Qs6s,Qs7s,Qs8s,Qs9s,QsTs.

CREV is at http://www.cardrunnersev.com/ and can do best response calculations, with some limitations, but can't really do equilibrium calculations.

Gambit (http://www.gambit-project.org) is a general decision-tree-analyzing software and can do equilibrium calculations, but it's not poker-specific, so setting up poker situations can be tedious or infeasible.

I'm still interested.

Thanks for this feedback. I realize I locked myself in my chain of thoughts by not considering 2 different bet-sizes. I also realized that I locked myself by only using 1 set of equations. I redid some thinking and math & I figured it out what is max EV when using 2 sizes and what is max EV when only using 1 size. For the 1 size, my above conclusions are flawed.

When using 2 sizes it is also intuitive how you can arrive to the GTO solution. After opponent tightened up vs shoves and loosened up vs minBet; you can drop in bet-size to the point where the EV loss of drop is cancelled out by widening of calling. For the minbet vice versa & such after several adjusments of me and opponent you arrive at GTO.

I however prefer (as I think this is less error-prone & intuitive more EV) switching ranges as opponents will more likely go to extreme binary adjustments. Vs shoves 100%F & vs minB 100%c.
After they realize my switching of ranges; it is either a matter of an opponent 100%F in to wathever size or 100%c to wathever size & such you can adapt again.
Or your opponent becomes irradic and you go GTO untill he as again an stable gameplan.

I'm a 6max nlhe cash player, do u recomend this book anyway?

And what about ProPokerTools? And what about the features that you would like to add to the program?

PPT does many useful things, of course, but it can't do any manipulation or solving of game trees, as far as I know.

I'd expect the book to be useful to almost any serious poker player.

I mean, I think about it this way -- people get plenty of use out of ToP even though most of its examples are drawn from games which are quite unpopular these days. The reason is that much of its discussion is of general principles which apply to many poker games.

EHUNL is also about big concepts for making good decisions in strategic situations. It presents ideas on the cutting edge of the application of game theory to poker while attempting to make them as practical as possible for use at the tables. Game theory of course applies to many poker games, and so most of the ideas in the book are widely-applicable -- it's just that I'm a HUNL player, so all of the concrete hand examples and situations in the book are drawn from HUNL.

Maybe players with more experience in other games can give an opinion too...

True. My next major poker project, however, is heavily game-theory related, so stay tuned. (No thread hijack intended).

Yaqh, I'm embarassed to say your book is still sitting on my shelf. I'm just going to have to schedule some time to read it, darn it. And I haven't forgotten your graphing suggestion...

bachfan, the ProPokerTools fairy

I just wet myself.

Sorry, couldn't help it.