i think ur calculete are right, i mean to make his bet BE on the riv is correct that he win 1psb, becosue is the dead money on the pot, and if u fold too much he win more... or if u call too much....or if he bluff too much he loose more.... etc.

the point of gto, for what i undestanded and my logical thinking, is to be vs player that are perfectly well balacend, and profitable vs player that bluff too much, or call too much etc...

The problem i see is vs player that never bluff,in that scenario i think GTo is bad if we dont know his range, but if u do(like should be) u can play gto vs his ranges, adding as well the time that u can steal the pot ip(i think it will matter).

ALl of this one is my interpretation, so it could be wrong, and if it is please open my eyes :)

But if im right(that im 70% sure), is a pretty cool staff and we can discuss, i will be happy about hearing every opinion.

sorry for my english :)

I haven't read the book so I have no clue what he wrote and what not. But u need to defend 50% otr vs a psb is just wrong. Where did u get that from? u risk 50 to win 150, 50/(50+100) = 0.33 (Risk/risk+reward)

As u said 33% is the correct number. He should have 33% bluffs to make u indifferent if he plays GTO, assuming he does that u calling 33% would be ev0. Calling too much will lose u money, and folding to much as well.

for get Be Opponend when bet 1psb is true that need to have 33% of bluff, but is as well true that he need 50% of FE to make it BE.

So for him he nedd to bluff 33% for us we need to defend 50% of our riv ranges, and if u loose money u problably have a wrong range there, that could be from the preflop flop or turn.

thats what i undestand.

http://www.runitonce.com/pro-training/videos/2k-6-max-plo-scoop-live-session-part-1-4/

Phil Galfond made 2 comments that could help you.

Ok, some confusing (and wrong) statements here, so let´s get everything clear:

1) You defend often enough that the weakest hands in Villain´s range (= his bluffs) are indifferent between betting and x/f.

2) Villain bluffs often enough that your bluffcatchers (!) are indifferent between calling and folding.

Now, let´s examine those rules step-by-step:

1) If Villain folds his bluffs, his EV is 0. So, we have to call often enough that Villain doesn´t make more than $0.

What are the odds, Villain is getting on his bluffs? There´s 1 in the pot and Villain bets 1, so his odds are 1:1, which means, he has to be successfull in 50%:

EV (bluff) = (0.5 * 1) + (0.5 * -1) = 0

If he wins more often, his bluffs make money:

EV (bluff) = (0.51 * 1) + (0.49 * -1) = +0.02

That means, we have to call with 50%.

2) If we simply fold our bluffcatchers to Villain´s bet, our EV is zero. So, Villain bluffs often enough, that our equity is exactly 33% - which means, after him betting pot, we´re getting just the right odds for a break-even call (2:1), but not more. That means, he´s bluffing once for every two valuebets:

EV (bluffcatch) = (0.33 * 2) + (0.67 * -1) = 0

Again, if Villain bluffs more often, we´re making money on the call:

EV (bluffcatch) = (0.35 * 2) + (0.65 * -1) = +0.05

That means, Villain has to bluff with a 2:1-ratio (identical to the odds he´s offering us).

Now, those numbers - 33% bluff%, 50% defense% marks the so called Nash Equilibrium, the point where no player can unilaterally deviate and increase his EV. Like, if Villain bets with a balanced 2:1-ratio (value/bluff), we can do what we want, we can call, fold, scream and dance around the table, nothing helps, the EV of our bluffcatchers is always zero. Same for Villain, if we call with exact 50%, he can bluff / fold / kick his dog - nothing helps, the EV of his bluffs is - zero.

At the same time - what you already recognized: when Villain bets with a perfectly balanced range, the EV of his bet (!) is always the pot. So, regardless if he bets the nuts or bluffs - on average he will win the size of the pot, which is completely okay, we can´t prevent Villain from making money with his nuts. All we can do is prevent him from making more than he deserves.

Final word: please note, that once we fold less, we again offer Villain the chance to increase his EV, namely by stop bluffing! That means, even though we´re indifferent between calling (= bluffcatching) and folding, we still have to call 50% - otherwise, Villain will either stop bluffing or bluff 100%. Obviously the same goes for Villain, if he bluffs more or less than 1/3 of his range, we´re either catching 100% or 0% - and again, maximize our EV.

OK, hope, everything got clear now?

Given the fakt, that we just call in that spot, we do have a bluffcatcher, right? An even against a range with all the non nuts value hands, we still have our bluffcatcher, right? So when we just call the river we allways bluffcatch in some way wich is simmilar to a nuts- air betting range otr, since we cant get value from or or the nuts by raising, im with big fiszh here. But i cant even see straigt tired as shit. dunno why im even here right now :P