Yeah thats what I did, really the only reason I posted that is because if you work out the spots with more standard cashgame dynamics there is essentially no PvBC dynamic left. Its quite rare that a villain will cap himself on the flop on such a dry board by raising the top of his range. That being said there are very often parts of our range that can play so polarizing, but combo/% wise its much less often then Will discussed in his book based on the examples.

In either case the concept definitely is explained great just I think the chosen spots were slightly off to show it. Imo the PvBC dynamic shows up much more often when flop goes check-check.

I could use some help here: p. 45
"Why is it that Hero's GTO strategy cannot involve either always checking or always leading here with all his near-nut hands?"

What's the difference of this scenario compared to the full street [0,1] game from MoP, where Hero just bets out with a fixed portion of his range, then check calls some and check folds some?

p81, BB holds the perfect mix of nuts and air.
"the SB's calling frequency would be completely unconstrained - any frequency between 0 and 100 percent would be co-optimal".
I'd think it's worth noting that if SB announces his strategy as "call 0%", BB can't exploit that, as he just doesn't have the needed extra bluffs to do that. But if SB announces his strategy as "call 100%", BB can now stop bluffing.
Shouldn't the "100%" be 1-alpha?

Will, could you share full solutions for pre-flop play in the same way you did for examples in volume 1? Textual representation of ranges where we could import it into equity visualiser would be helpful and knowing all decision points for sb and bb also.

I think it just has to do with the implications of hero's checking range if villain is betting all his nuts, and near nuts, then checking only weak hands. Villain will start to value bet very thin and hero can then increase his EV by checking a stronger hand. I'm wondering why then hero also cannot play a mixed strategy with his pure nut hands?

Logically, that could make sense, but unless I missed something obvious, MoP solved the same game using a pure strategy, i.e. predefined and fixed bet, chcall, chfold action regions.

My thoughts exactly! While BB can't decide to add any more bluffs given the range he gets there with, he certainly can decide to never bluff if SB calls more than 1-alpha.

Thanks again you guys (and unlimited too!) for the read-thrus and many, many edits and suggestions. I've high hopes that the book will prove to have very few errata thanks to you.

Also, thanks for the thorough review, Semper . How's the study group coming along?

Yea, I think this is fair. Check out Vol 1's thread for more opinions. I found one spot where I answered this previously:

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

but I think there are a number of opinions from other people in there too..

I don't think these issues show up in the paper version, and I haven't seen any of the electronic ones except the PDF which also looks fine. You're reading the epub version from the publisher's website? What device are you using?

Sharp eye. The difference is card removal effects. For example, 87o -- only the combos with 7s, 7d, and 7c are in the range. The combos with 7h are of course not in the player's range, since the 7h is on board. So, the SB's checking and betting ranges combined only contain 9 of the 12 possible 87o combos. If you think I should have adjusted for that in the figures, then you're probably right, but anyway the visualization software is faithfully representing the correct ranges.

^ this. although I made a lot of progress this weekend.

The conflict there comes from the fact that I used a simple model of the two-street play in the earlier discussion but a much more detailed one to make the for the EV distribution on pg 141. You're right -- the results differ in their play of the low gutshots. I hadn't realized that before.

I haven't used it myself, but someone mentioned Pokercruncher to me in this context recently, so it might be worth looking into.

Yup, thanks erdnase!

I'm not familiar with the Epub page numbering, but if it's about the same as in the paper version, we're working in the context of a 30 BB deep HU hand on a dry board. Playing any top pair aggressively on the flop is at least reasonable there -- certainly it's a vv different spot in that regard than 100bb 6max.

Of course you're right, though, that putting no top pairs in the BB's flop check-call range there is a simplifying assumption. There are 4 chapters on turn play, and you're in the first of them. The idea was to add additional complexity in each subsequent chapter, but we had to start somewhere!

Proper betsizing (and when GGOP is relevant in particular) is a recurring theme later in the book, and PvBC-ish situations after the flop checks through also get a lot of airtime, particularly in Chapter 12.

Imho the full solutions shouldn't be published as this data can be used for botting or to build the next "pokersnowie" for short stacks. afaik only a few stack sizes were solved but still...

but this is only preflop...

I don't see the way that could be imported into an EQ visualizer.
In the river examples, if we called a hand indifferent between 2 actions, different hand combinations of the same hand (e.g. JdTd and JcTc of JTs) would often strictly prefer one action or the other one due to removal effects.
But preflop when a lot of hands are indifferent at equilibrium, it means that each hand combination of the same hand probably should take an action with a non-zero probability (e.g JdTd and JcTc open-shove 31.4% of the time and limp 68.6% of the time, each one). I don't know any EQ visualizer that can do this.

So, I'm not quite sure what game from MoP you're talking about, but I found it useful to look at the game I'm talking about in more detail later in the book, and I stuck a full solution in Appendix 13.10 (p240).

That TestYourself question is mostly just meant to get you to go over the same line of reasoning given on the previous page, and I guess you can do that, but maybe you don't see how it applies to this game, since you think BB is always leading with his strongest hands at the equilibrium of this game?

On pg 44, I said what I mean by "near-nut" hands -- a hand strong enough that we'll always try to get all-in, and whenever Villain has a better hand, he'll always try to get all-in too. Basically, it just means that whenever we have such a hand and Villain has better, we're guaranteed to go broke.

This applies to a full 1/3 of the BB's range in this game (in the symmetric distributions case, with B=S=P). The top 1/3 of BB's range is actually indifferent between leading and check-calling at equilibrium, and indieed, he sometimes leads and sometimes checks with hands in this region. And SB puts in the same amount of money, exactly, versus both actions.

In the way the solution is normally structured, BB leads with his strongest hands and check-calls some weaker ones, but that solution isn't actually unique. Other structures (which can involve check-calling with the nuts) are co-optimal. I talk about this and this game more in one of my videos.

I believe the game trees I used (or at least the preflop part of them) are fully specified at the beginning of section 15.2 (pgs 335-7). But as far as the ranges in numerical format, yea I can do that -- give me a few days.

TBH, I don't think there's any info there that someone who's motivated couldn't get out of the graphs in the book.

EDVis can if you input ranges using the Edit box in the (undocumented) numerical format

I meant MoP #17.1, where P=1. Which seems to be exactly the same solution as in A13.10.
Yep, I don't see how it applies. Can SB somehow exploit if BB always uses the structuring from MoP or A13.10?

The co-optimality of the "check everything" from p44 and using the "bet-chcall-fold" regions came as a surprise to me. It would seem likely (though not obviously necessary) that getting the extra strategic option of betting out would help BB. Also, looking at MoP 11.3, a half street [0,1] game, IP will bet only top .222 of his range (+ bluffs) for a PSB when checked to (i.e. always), and OOP calls .444 of his range.

So I guess what I'm asking now is: if BB is sometimes playing the half-street-game, ie. check everything as per p.44, and sometimes playing the full street game (i.e. check the middle part of his range), and SB doesn't know which one it is this time (but knows the percentages), you're saying that SB still pots the top .333 (+bluffs) of his hands every time? He doesn't care at all that he's often facing the stronger checking range?

I didn't notice Qlka asked for the preflop data only. That would be interesting to see since the ranges in the book don't include every possible preflop action.

The kindle version is on amazon fyi.

pg. 267 of PDF. SB folds vs BB's half-pot check-raise more than the naive frequency of 33% and I'm not sure I understand why. If BB is deciding whether to bluff check-raise or fold and SB folds more than naive frequency, BB has incentive to never fold and always bluff check-raise, right?

I understand that on K73r BB's bluffs have less equity vs SB's continuing range than on QT9, so it seems to be that SB can fold relatively more on K73, but folding 42.3% of the time seems way too high. What am I missing?

Great book, btw. I'm really enjoying it so far.

Anyone care to help me here, can't see what I'm missing? If BB always checks everything, shouldn't SB play like MoP 11.3 (the half street game), i.e. bet only top 22% and bottom 11%? If BB sometimes plays that and sometimes has a bet out strategy, how can SB switch directly to betting top 33% and bottom 17% ?