If there was a video in RIO talking about this specific topic I would also appreciate the link :)

is your bet an all-in?

In the hand I input to Snowie where it gave me 97% value/3% bluffs it was a 3bet pot and yes it was all-in on the river, but how could it matter otherwise?

I have another examples with Snowie where it is not all-in and still suggest same proportion of bluffs, I don't see how it could matter!

"if your range is so depolarized should you really be betting in the first place?"

well I mean, as long as I have a 51% win when called I could bet and be doing nothing wrong, right? Ok ok, I know what you'll say, at least when the bet is all-in :)

lol!!! you're taking out so many of my leaks! Yes I would mean IP because OOP we could check call which could have more EV lol but I like the fact that you make me realize how theoretically lousy I am.

BTW I already read Applications, but I am revisiting again from another perspective much more deep, when I first read it in March I was kind of bored and didn't really like the theory. What stakes do you play and pokersite? Maybe you win money from me everyday :) Is it okay if when I revisit Applications part about this topic I come back if I still haven't it sorted out? What other sources do you think are the best to deepen your knowledge on GTO? Any coach on RIO besides Sauce? Any source outside RIO besides Snowie?

Hey OP, your question is absolutely valid - and far from being too vague to be answered. :)

The reason you struggle is that your "basic assumption" is not complete. Our goal when "constructing" our bluff-range is to keep the worst bluff catchers in Villain´s range break-even.

That means, we want to add enough bluffs that Villain is break-even with the bottom end of his range. Imagine, we bet pot size on the river (assume all-in, so there´s no chance for re-bluffing). Villain has to call with 50%, otherwise we could bet / bluff with any2. Our goal now is to add as many bluffs that the worst hand in his 50% range is break-even.

Our "value-range" obviously is determined by that exact calling-range of Villain (we need 50% against that range(*)), and then we add just enough bluffs that the worst hand in Villain´s range has 0EV-call.

Is that understandable?

(*) That is not exactly correct, as we´re oop and have to "protect" ourselves against bluffs, so we need < 50%, but that´s another (more complex) topic.

Hey BigFiszh,

(sorry I don't know how to quote properly)

"That means, we want to add enough bluffs that Villain is break-even with the bottom end of his range. Imagine, we bet pot size on the river (assume all-in, so there´s no chance for re-bluffing). Villain has to call with 50%, otherwise we could bet / bluff with any2. Our goal now is to add as many bluffs that the worst hand in his 50% range is break-even."

You are also assuming villain will have to call 50% on all different runnouts, which is imposible because some will be very good for him and he could call profitably more than 50% and others very bad for him and he will have to fold more than 50%. As you say, sometimes the runnout is so good we bluff our worst made hands, and other times the runnout is so bad we check-fold hands we would have otherwise value bet (J4 on QJ455).

"Our "value-range" obviously is determined by that exact calling-range of Villain (we need 50% against that range(*)), and then we add just enough bluffs that the worst hand in Villain´s range has 0EV-call."

Hmmm... I think I see your point. Your point is the nuts/air situation is a derived one from what I just quoted, right? Because he has 100% bluffcatchers and so he should call with 33% of them (in the typical spot nuts/air 1 PSB).

Now, in a less polarized situation, how would it apply? I am going to make up a spot, the only thing that matters here would be the river:

We 3bet SB vs BTN. Flop AT8r

Value: TT, 88, AT, A8s, AK (AQ is close for 3 streets on multiple runnouts, so for practical purposes it's out and assume we check call AA)
Bluffs: KQ, KJ, QJ, J9s, 97s, 76s

Turn blank 3r

Value: TT, 88, AT, A8s, AK
Bluffs: QJ, J9s, 97s (we give up gutshots)

River another brick 5r

Value shove: TT, 88, AT, A8s, AK (total of 3+3+9+2+12= 29 combos)
Bluff shove: ¿? how many combos?

Assuming villain's calldown range is: AJ, AQ, AT, A8s, 88, A3s, A5s (4bet/calls TT and AK pre)

Hey BigFiszh,

(sorry I don't know how to quote properly)

"That means, we want to add enough bluffs that Villain is break-even with the bottom end of his range. Imagine, we bet pot size on the river (assume all-in, so there´s no chance for re-bluffing). Villain has to call with 50%, otherwise we could bet / bluff with any2. Our goal now is to add as many bluffs that the worst hand in his 50% range is break-even."

You are also assuming villain will have to call 50% on all different runnouts, which is imposible because some will be very good for him and he could call profitably more than 50% and others very bad for him and he will have to fold more than 50%. As you say, sometimes the runnout is so good we bluff our worst made hands, and other times the runnout is so bad we check-fold hands we would have otherwise value bet (J4 on QJ455).

"Our "value-range" obviously is determined by that exact calling-range of Villain (we need 50% against that range(*)), and then we add just enough bluffs that the worst hand in Villain´s range has 0EV-call."

Hmmm... I think I see your point. Your point is the nuts/air situation is a derived one from what I just quoted, right? Because he has 100% bluffcatchers and so he should call with 33% of them (in the typical spot nuts/air 1 PSB).

Now, in a less polarized situation, how would it apply? I am going to make up a spot, the only thing that matters here would be the river:

We 3bet SB vs BTN. Flop AT8r

Value: TT, 88, AT, A8s, AK (AQ is close for 3 streets on multiple runnouts, so for practical purposes it's out and assume we check call AA)
Bluffs: KQ, KJ, QJ, J9s, 97s, 76s

Turn blank 3r

Value: TT, 88, AT, A8s, AK
Bluffs: QJ, J9s, 97s (we give up gutshots)

River another brick 5r

Value shove: TT, 88, AT, A8s, AK (total of 3+3+9+2+12= 29 combos)
Bluff shove: ¿? how many combos?

Assuming villain's calldown range is: AJ, AQ, AT, A8s, 88, A3s, A5s (4bet/calls TT and AK pre)

Is his calling range 50% of his river starting range? If not then always bluff (if <50%) or never bluff (if >50%). If yes then:

What's his best folding hand? If it's some Ax then you're going to bet enough to make his Ax indifferent between calling and folding. When he has Ax, you only have 3+3+6+1+8=21 combos (or 22 if he doesn't block any A8s) of value hands so you bluff 10.5 combos. You then choose your bluffs to block as much of his calling range as possible, so something like QJo will be a profitable bluff, whereas something like 76s will be a losing one.

An often ignored point is that he won't actually call 50% of the time, he will call somewhat less than that vs your value hands and best bluff candidates and somewhat more than that vs your worst bluff candidates due to card removal. It's possible (but not necessary) that he calls 50% vs some particular hand(s) that are completely indifferent between betting and checking.

Hello Steve! Thanks for step by again!

Ok for simplicity purpose let's assume it's the typical spot where villain has a bunch of bluffcatchers that, if folds all of them we have a profitable bluff with ATC, and if he calls all of them we never bluff.

Let's assume Ax is in the range of 40% to 60% of his river range. That is, if he folds all his Ax I will always bluff, if he calls with all of them, I will never bluff.

So let's say he folds the Ax that block my semibluffing hands like AQ and some AJ maybe (doing the math in my head) and calls the ones that don't block anything, like the rest of Axs. All this is arguable and it's not my point.

My point in the post and all the thread really is:

Should the bluffing frequency be the same when my value combos include hands that will be called and lose (like AK or A8s) as when we bet only pure nuts (let's say AA in this spot)?

Intuitively I think that the answer is no, he will exploit us somehow with his bluffcatchers, bluffcatching more of them or even all of them! But I'm not sure and that's my ultimate question throughout the post! You seem to imply that we should bluff the same but I intuitively disagree!

Thanks! btw your videos are awesome, I loved the 1.A one :D

Look at the solution for 0-1 games from Mathematics of Poker, 0-1 games have the property you're looking for. Also, listen to Steve :)

He guys, I think I finally got it!!!!

I have been struggling for one whole week with this issue not having any satisfactory answer. I read the chapters of MOP and didn't understand a goddamn thing lol

But then bought Expert heads up no limit and the explanation there was a little more comprehensive than the alphabet soup in MOP.

So let me try and confirm if I am right now.

It's all about the worst bluffcatcher in villain's range equity, right?

For example, in the hand I made up, if villain's worst bluffcatching hand is Ax, due to removal effects I am betting 22 combos that beat villain's Ax, ie for value. Suppose Pot=Bet size=Stacks=1, then I should bluff with 11 combos so that villain's Ax has an equity when calling of 33%. So it remains break even.

Now, in my example, sometimes I will valuebet AK and he will have 88 and I will lose, but it really doesn't matter to the amount of bets in my range, right? It really doesn't matter if I lose, I still bet my 33% dear bluffs!!!

I kind of feel relieved omg :D

Now (please correct me if I am wrong in the previous post)

Why the fuck does Snowie play hands no the river like the following??????

http://gyazo.com/3c61d45846f5472790cbb467d5fac040

This is almost similar to the hand from my example. I modified a little bit the sizings so that Snowie agreed completely on every decision from every player up to the river.

How is it posible that Snowie only shoves for value on the river????

You can see on the right that for the SB player, it suggest to bet A3+ for value, but no bluffs!! I don't understand, shouldn't we bet a few bluff combos here according to game theory?

Here, on the contrary, it suggests to have about 75% river cbet with 55.4% bluffs on a sizing of a little under the pot:

http://gyazo.com/3d162837dbc48004d32418fbfe253c99

This seems wrong I think, but not only that! When you go too see river action by villainm, it suggests a fold of 14.8%!

So how is it posible that in equilibrium we bet more than our fair share of bluffs, and villain calls with almost his entire range???

http://gyazo.com/8ec8fba23ccee951939398eb19207028

I did not saw the Snowie hands, but consider this: The rules for value-bluff ratios are derived from simplified models (like the 0-1 game, situations when you have nuts and bluffs against bluffcatchers etc). But there might be real game situations with different range structures and hence different solutions. Your opponent can have nuts and bluffcatchers versus your range of second nuts and bluffs for example. You cannot use ratios like in the polar vs bluffcatcher case in such situations...

Bingo!
I think I found the answer to my question here.

Suppose our bet will always be the size of the 0.75 pot and opponent can only call or fold.
When we bet the river, our opponent is getting offered 7-to-3 odds to call our bet, and this requires us to bluff 30% time.
Now you need to figure out what the value bet on the river.
“…it’s always more profitable to jam than check as long as we win over half the time when called.” Janda p.331
As we add balanced bluffs? Only for strong (how?) hands add 3 bluff to 7 value bet, and the weak value bet add without bluffs. Or our bet range should have 66% Eq versus range of the opponent (of the river or call river bet)?
For example Jh 7c 4d 2h 3c
http://www.runitonce.com/nlhe/help-me-plan-my-range-vs-range-strategy/

That's what I understood from the above explanation.
Correct please, if you see an error.
How we design KK-JJ,77,44,(A2-A5,AT):xx =33 …
QQ - the weakest value hand in the range UTG bet river, which is Eq> 50% against the calling range BB
range of BB is
9 combos of better hands (44,77,JJ)
6 combos of AJ that fold
6 combos of AJ that call
5 combos of KJs-QJs that call.
9 combos JTs,TT that fold.
QJ - weakest hand in the calling range BB. It is obvious that QJ weaker any vbet river UTG (from QQ to A5s), therefore, we need to add bluffs for all hands (3 bluffs to 7 value bets)

"Or our bet range should have 66% Eq versus range of the opponent (of the river or call river bet)? "

No. Our river bet range should have 70% equity (assuming 3/4 pot) against his worst bluffcatcher, given that our checking worst hands never win (ie, our worst hands are pure air).

If we add less than 30% bluffs to our range because it's not polarized, then he can do better by just folding his worst bluffcatchers and just call with the stronger ones.

Snowie often sucks in these river spots and it's ranges are not necessarily GTO. Of all the advice snowie gives, it's doing the worst on the river imo. You can take the concepts discussed ITT to improve your river play compared to snowie's advice.

Hi friedm, I agree 100% Snowie's ranges are OTR are random. They say that in some place. They also say the evaluation is always correct. And it always seemed pretty fine to me.

Thanks for the message :)