When facing a 3x open as opposed to a 2x open, how do we construct our calling range and 3betting range? Which hands become folds, and which hands become 3bets(compared to if facing 2x open)?

This is a great question.

A quick and dirty tip for working thru theory questions like this is go start at the extremes and work back towards the middle because the trends generally move in the same direction even if the rates differ along the way.

How would things change if a player opened to 100x rather than 2x or 3x?

The opener would be able to open fewer hands profitably and other players would be able to play fewer hands profitably against the opener.

It’s also helpful to consider the effect the preflop raise amount has on the rest of the hand. More action preflop will tighten ranges, shorten effect stack sizes and up the stakes.

It really depends on how you think villain constructs his opening range, and how he continues vs a 3-bet.
Against weak players in the micros, a smaller open is often a sign of a weaker range, especially with regard to button steals with super-wide ranges containing lots of junk. (Quite a lot of villains still open larger with premiums). If villain is one of those players that minraises with junk, you can 3-bet light more often, expecting to get folds. Why bother calling (giving villain a chance to realize the equity of his junk) and paying rake when you can often just win the pot with no variance?

If you mean in terms of theoretically optimal play, then it's often (but not always) the case that you should 3-bet more often vs a larger open. Primarily it's because you're getting worse pot odds to just call (so fewer hands are playable overall), partly because there is more dead money out there (so there's a bigger incentive to try and win it immediately), but also because calling means you'll pay more rake. 3-betting with some hands that would ordinarily just call to try and take it down with no rake (instead of calling and paying rake) apparently has a higher EV in some spots.

Exactly which hands you'd use depends on the situation. I can give some examples from Snowie.
e.g. You're in BB facing an open by CO. If it's a minraise (indicating a wide opening range), you can call AJs, ATs and AJo, and you'll do fine, as you dominate much of villain's (wide) opening range, and these hands will play pretty well with a high SPR (in a single-raised pot with only 5.5bb in the middle). If he opens for 3.5x, then he should be playing tighter. The hands I previously mentioned will (according to Snowie) get a higher EV by 3-betting, effectively as bluffs that have a good shot at picking up the extra dead money. They won't play quite so well as calls in a 7.5bb pot where villain has a stronger range to begin with.

Curiously, Snowie also offers some counter-examples. When I studied its pre-flop strat, I learned it would call AJo and KQo in the BB vs a BTN minraise and 3-bet them like in the previous examples when faced with a larger open. But it would flat KJs and KTs vs a 3x open, but 3-bet them vs a minraise. It would usually use the latter strategy with 77/66 as well, which I can't really explain. I would expect calling a minraise would make sense as a cheap set-mine, but Snowie would 3-bet middle pocket pairs vs the smaller opens, and flat vs the larger ones. Go figure. :/

thanks for the replies

I'm talking from a theoretical standpoint, not accounting for the rake.


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?


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?

How does it play small pocket pairs like 22-55? Does it 3bet more vs a 3x open with those?

The KJs and KTs strat is really interesting, any insight on this?

It's about the size of the preflop investment. 2x allows a wider opening range than 3x does and thus you can play much more often vs 2x.

I think that's broadly true, yes.
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).
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!

where did you get this idea from? This is false. Overall your 3bet% will be less facing bigger opens than smaller ones.

Yes, but you will be calling less, and 3betting more with the different (tighter) range you continue with. E.x., Continuing vs a 3.5x open requires a much tighter range than against a 2.2x open and you will be mostly 3betting that tighter range.

I know what I'm trying to say but I don't know if I explaining it clearly here?

thanks for the replies

Good points, I agree that trying to find the reasoning for a solvers overall strategies is a futile process that will consistently bring up statistical anomalies, to us at least.

There are a lot of spots though that can be explained (to a degree given a particular strategy). I guess this isn't one of them.

BB definitely 3bets more vs SB opens if its 3bb vs 2bb open in a high rake environment.

I believe this is true even in a non-rake environment

Yeah I thought so too, I just haven't done rakeless sims for that spot.

I always thought that since our flatting range v 2bb is wider we need to include more premiums to protect it.

Therefore we flat with what would be the bottom of our 3b range v 3bb open.

What 3bet/4bet sizes did you use in the tree in both the 2bb and 3bb RFI? Is this 100 Big blind deep? I've done my own work on this and I believe that a smaller raise size warrants a higher 3 bet %.

What would the logic that explains this be? Nobody should care about/believe a calculated result unless they understand the concept(s) that validate/invalidate it.

In pretty much every preflop sim I've done, the opposite has been true.

Smaller bet sizes can bet a wider range of hands. You can raise more hands against a wider range of hands, than vs a tighter range.

You can see this in post-flop sims and a lot of good regs talk about how, in postflop sims, the smallest cbet size should be attacked with raises more liberally.
I don't see any reason why this should change pre flop, and I haven't seen it change preflop. Unless one of us is using a fundamentally flawed tree.

"You can raise more hands against a wider range of hands, than vs a tighter range."

This is true, but we were not talking about wider ranges, we were talking about different opening sizes.

If the opening range is the same, then the 3b frequency is lower vs a lower opening size.