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Would it be safe to assume that the main reason is because a lot of hands, like 67s for example, play better as a 3b now vs a 3x open since the odds on a call are worse and it realizes its equity better as a 3bet so this would out-perform the EV of flatting? Whereas vs a 2x open the ev of calling and 3betting run closer together?
I think that's broadly true, yes.
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Maybe in regards to the pocket pairs its because its 3betting for "value" whereas if opponent is using a 3x open his range is going to be tighter and middle PP's won't hold the same equity vs his calling range?
Yeah, I thought that it kind of considers 77/66 as "value raises" vs the wider opening range represented by a minraise, but then there are the counter examples. KTs isn't really a "value 3-bet" vs a 2x open, and AJo isn't a "value 3-bet" vs 3.5x (both are 3b/folds).
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How does it play small pocket pairs like 22-55? Does it 3bet more vs a 3x open with those?
55 is sometimes a 3-bet vs a minopen. It's a call vs 3x. The smaller pairs are always just calls.
A point I was gonna mention in your thread in the theory forum (about K83 and AK3) also applies here, so I may as well talk about it now.
It's really hard to make sense of solver output and Poker AIs.
Solvers (and Snowie) don't 'think' like humans. They have no concept of "value raises", "bluffs", "polarization" etc. All they do is try to maximize the EV of a strategy, based on the assumption that the opponent is also trying to maximize EV.
When Snowie was doing its reinforcement learning, it found that 77 maximized EV as a 3-bet in the BB vs a minraise, but vs a minopen it got a higher EV as a call. As humans, we like to put hands in categories and say "I'm 3-betting AQ for value" or "I'm calling 77 to setmine" or "I'm potting it with AK on AK3, to get max value from QJ/JT and dominated aces" or "I'll bet small with AK on K83, because villain folds so often if I go bigger, and I want to get a little bit of value from 8x and underpairs".
The solvers/pseudo GTO bots just think "I will do whatever makes the most money vs the optimal defence". They can't
explain how they come to their conclusions.
I saw in your theory thread that you're trying to find out
why Pio says to use one size on AK3 and a different size on K83, because it would be useful as a human to find the reasons, because we could then use the same concepts in analogous spots.
But there isn't a simple answer, in the same way there isn't a simple answer for why Snowie 3-bets 77 vs a minraise, but calls vs a 3x.
All that can be said is that it calculated/simulated or brute-forced various strategies until it found the one with the highest EV for one specific situation.
Two flops that to a human look very similar (e.g. AK3 and AQ3) can have entirely different solutions, with different sizings and betting frequencies. It's really hard to find explanations for the differences, because we can't calculate the EV of every hand in our range vs every possible counter-strategy. All that can be said is that the solver is just trying to maximize its EV. On some boards, there is a lot of EV gained by bombing it and only getting called at low frequency, and on others the EV of the entire strategy is maximized by going smaller and getting called more often.
I can't explain exactly why (on the BTN vs BB), Snowie pots it on A84tt, but goes with half pot on A74r. All I know is that was the result when Snowie experimented with different sizes and betting frequencies.
It's really complicated and very hard to draw firm conclusions, or even to detect patterns, because - to a solver - each flop is effectively an entirely different game. It's not like the solver thinks "Oh, AK3 is just like AJ2, so I'll use the same strat." It has to compute it separately.
Good luck with finding those patterns though!