The Problem

• There is a pre-flop raiser (PFR)
• We know his exact raise range
• Everyone else folded to us on the BB
• We don't know his calling range if we 3-bet all in
• The variables are the raise size and stack size.

If we can only use Equilab, are we able to calculate the GTO 3-bet range if we decide to only go all in?

If we just 3-bet all in with any hands with enough equity to call against the PFR range, it is clearly wrong because the PFR would not call with everything. There has to be a GTO solution right?

I know this is a strange question, but I'm very interested behind the math of poker, and I can't figure out how to solve this problem.

Stopped playing after BF for years online and a lot of strides have been made on game theory and I'm recently getting back into it, so I'm not too keen on running solvers. I do know I've watched some vids on this situation where flopzilla was run in a way that gives us optimal 3b ship range vs optimal call range. Obviously you simply widen from there depending how far away from that optimal range you think they are.

Sent from my SM-G965U using Tapatalk

Yes it is possible to calculate the GTO 3b jam frequencies based on raise size and stacks remaining. This has been done for heads up many times. The problem is that this hand started out multi-way and not heads up, so the actual range of the villain is not a heads up range and can vary widely even in game theory terms.

Villain can have a unified continuous value range, or villain can have discontinuous polar ranges of both value and bluffs.


Technically, game theory would also allow the villain to adjust to your response and adjust his ranges, negating your +EV and the game would still favor villain, since villain is in position and gets to act last.

However, forcing villain to play the exact range you specify will allow you to 3b with value and bluff with +EV in your favor since you are the only player who gets to have any bluffs. Unless your specified range for villain is already specifically tailored to this heads up scenario and villain is already polar, which would be unusual since there were other players in the hand that villain had to account for with the 2bet.

But, like I mentioned, what if we give Villain (which is the PFR) a specific range? We assume that we know exactly Villain's 2-bet range. Also, we have to assume that what Hero (which is the BB) can have is not affected by what the other players have folded.

So, the question is, can we figure out the GTO 3-bet all-in for Hero when we input Villain's 2-bet range?

The old pushbot spreadsheet (which can probably be found with google) did calculations like this.
If you know the stack sizes and the opening range, you can certainly work out which hands are automatically profitable as jams (because they make money whether villain calls or folds, because they have enough equity).
You could also use HRC/ICMizer (in chipEV mode) to find the solution.

The GTO reshove range is more complicated than what a push spreadsheat or a program like HRC will tell you. Pushbotting is an extremely simplistic and basic way to look at the game. I guess if you're play 10bb stacks and there's antes it might approach what equilibrium looks like, but for your typical reshove stack of ~20bbs it's wildly off from equilibrium. Stay away from those programs when dealing with that stack size.

For the exact situation of the BB it can be solved with PIO preflop solver, although even that isn't exactly accurate because it wouldn't take card removal into effect. If you want some quick and easy tips: hands that have a good blocker, struggle to realize equity OOP and have good raw equity make good reshoves from the BB. Think A5o. Also as the raise size increase your reshove frequency increases.

I don't understand this part. I thought the larger the 2-bet size, the stronger the PFR range, hence BB's 3-bet shove should be tighter. Also, I want to discuss all these in terms of cash games, not tournaments because there would be ICM implications. But, feel free to talk about tournaments if you want.

If the range stays the same, but the sizing gets bigger the ratio from the raise size to the effective stacks is smaller. This makes shoving a more attractive option.

For example, if someone opens 50x with 100% of hands, shoving all-in with A7o is the correct play. If someone opens 2x with 100% of hands, shoving all-in with A7o would be a spew.