*Originally posted by kavboj84*

Well if it wasnt obvious Im looking for a GTO solution, so you thats why I didnt tell anything about the ranges. I think even if you give a massively wide 3bet range (like 66+,A8s+,KTs+,QTs+,JTs,T9s,ATo+,KTo+,QTo+,JTo) for the button he'll be still overcalling the flop due to the potsize and the fact that how hard he hits this board.

With that range, supposing the button reraises right away with what he perceives as value, he will fold a few hands (depending on what he perceives as value) from the 66 and 77 pairs, the rest of them will be bluff raises.

*Originally posted by kavboj84*

So I came up with 2 pair + and KK for a value range,and added 3 combos of 87s with a donk end plus backdoor flush draw, but this means MP2 is underbluffing, and button is overcalling the flop and if this is the best they can do it means that there is no GTO solution for the flop.

Sure there's a GTO solution. It's just beyond the "I give you 10:1 to call, therefore it's 10:1 that I bluff" principle that really applies only for the very last bet in a hand.

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I had a similar, but much easier problem hand posted some time ago. I had QT in the BB, called a raise, the flop came A8x (don't recall details). I folded - so what. With that board, I simply had to fold close to 26% (or whatever) of the range I called with preflop. Yet, the preflop call was right - as my fold. Nothing very wrong with my preflop calling range either. Note that a 26% folding frequency on a particular flop renders you seemingly exploitable to a c-bet. (Yeah, like if the c-bet isn't coming anyway...)

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The answer lies in Game Theory (GT), what it says and, in particular, what it does [B]

*not[/B]* say. GT says that given any single hand, there exists a way to play it, based on the board and the opponents moves such that the expected outcome is zero or better for all players employing the strategy. (No one can profitably deviate from it if all players present employ the strategy.)

This says that for each holding in your range, there is a GTO way of playing it.

*But this does not say explicitly that you should have a certain percentage of bluffs and value-bets for each street in a ***range**. GTO does not operate with ranges at all. GTO applied to poker results in ranges, that's very different.

Once you know how each and every hand should be played (this knowledge is what the Nash theorem ascertains the existence of), then you can

*a posteriori* just list the strategies for the individual hands and simply count the number of checks/bets/raises for the board in question. There is nothing that guarantees a certain amount of remaining bluffs, value-bets and rebluffs for each and every street. From this you [B]

*build[/B]* your unexploitable ranges, not vice versa.

I believe that it is impossible to find the solution starting in the other end, namely "guesstimating" how much value/bluff should remain for the later streets. It's only guesses, but it is the best

**we** can do.

I think you may be seemingly exploitable in some situations when playing GTO (or close to it), but you aren't. Note that in the example of the original post, both players are pretty much showdown bound, so bluffs on either part will have extremely little effect (except for in the real world, where people don't play GTO.) Likewise, in my example above, my opponent can't c-bet much more than his regular 98% either.

Sorry about my rant.