So I know that the general rule of thumb is "higher cbet frequency=smaller sizing" but I've been working more with pio lately and noticed that solvers don't necessarily abide by this rule.

For example, in a CO vs BB spot on K83r board, pio has us checking at 40% frequency but heavily prefers a 33% ptsb over larger ones with the majority of its betting range, whereas that same range on a AK3r board will have us checking 50% but will heavily favor a large (75% ptsb) sizing. The range equities are almost the same (1%~).

This may not be the best example since a 10% higher checking frequency is pretty significant but I have noticed other spots where the checking frequency is nearly the same yet it still prefers a larger sizing.

I'm trying to better understand this concept.

My (limited) understanding is that it does this because it wants to polarize ranges more on certain boards early on, whereas on other boards (like K83) it prefers a smaller sizing because we're "postponing" the action to later streets since our range plays better without bloating the pot too much. Are these assumptions correct? Also does equity realization/denial have anything to do with these?

Because K83 is a board where protection is a thing so you want to bet more frequently with a smaller size and because while it is a dry board, things can still change quite a bit by the river.

AK3r is basically a lock down board, very little protection needed. On top of that you have massive massive nuts advantage which means you want to start polarizing right from the flop so you can play for stacks by the river. The beauty of this situation is that you can push quite strong hands in villains range to an indifference point very early on in the hand.

AK3r is as close as you'll get to the classic MoP example of betting geometric growth of pot, since the best hands on the flop will very seldom be outdrawn by the river. Was 75% cbet the max size you allowed? My guess is it would prefer an even bigger cbet if allowed.

can you try the following? one time giving the option to bet 33%, one time 75% and another simulation where both options are offered to the solver. if you compare the overall EVs of the whole player's range, imo it should not be such a huge difference. it is good to know how much the nut advantage is and polarization of ranges, but i don't think it is often a tremendous EV difference if you adjust the ranges to your betsize.

Yes 75% was the max I allowed. Could you please elaborate on what you mean by "The beauty of this situation is that you can push quite strong hands in villains range to an indifference point very early on in the hand." Is this because your range needs to be polarized in order to get them to that indifference point?

CO vs BB. No donk option for OOP. Sizing options are fixed at 100% on turn and river for IP player and 66% on turn and river for OOP player with a raise of 2.5x for both players on all streets.

K83r

Flop size option: 33%
Cbet Frequency: 70%


Flop size option: 75%
Cbet Frequency: 42%


Flop size option: 33%/75%
Cbet Frequency: 60% (1/3rd) 38% (3/4th) 22%

EV is 34 with all strategies

AK3r

Flop size option: 33%
Cbet Frequency: 69%

Flop size option: 75%
Cbet Frequency: 51%

Flop size option: 33%/75%
Cbet Frequency: 55% (1/3rd) 11% (3/4th) 44%

EV is 35 with all strategies

thank you for your efforts. do you also take it that way too much emphasis is put into flop betsizes? so far this has been my conclusion. in practice i ask myself "which hands do you absolutely want to cbet?" and choose an appropriate size.

I don't necessarily think that emphasis is unwarranted but I do think some people might be too focused on what the "optimal" size is on every flop vs every player instead of directing focus on why that size is deemed optimal (I'm guilty of this as well).

I say "optimal" because there really is no one optimal size for every spot (except maybe on some rivers?). On the flop in particular, what this sizing is can be very player dependant and you can really make all sorts of sizings "optimal".

I'm no gto expert but my understanding is that in many spots where we consider a certain size to be "optimal", is only optimal from the perspective of a human player. In reality though a true GTO bot would be using all sorts of sizings on all streets, though once again I'm not sure if this is true on the river due to polarization. AFAIK nobody really knows what these sizings are.

Its just conventional theory that certain sizes work better on certain textures and if you see that a solver favors one bet size over another its more practical to just use that sizing with your whole range and that will outperform the EV of attempting to play a mixed strategy, which is what's optimal, but its only optimal if you can actually implement it.

Having a basic strategy (or standard sizing) is important as a solid foundation is key to making consistently sound decisions and without them your strategy would be overly-prone to being exploited but its important to not forget that we're playing against humans and even at nosebleeds in 2019 even the best regs have tons of leaks (in comparison to true GTO).

Understanding how to construct your range in ways that puts maximum pressure on your individual opponents with minimal complexity is what I try to focus on when deciding what the "optimal" bet size is.

For example, on a 659 flop BTN vs BB the standard sizing is probably 2/3-3/4ths pot. If we know certain things about our opponent, however, say he doesn't x/r enough, or he x/r's too much, or he probes the turn too little, these are all factors that can vastly alter which size is standard in that specific scenario. If he's overfolding we can put more pressure on his range with a 1/2p sizing and force him to step out of his comfort zone, and if we're in the driver's seat and are more comfortable playing a less-trodden path than he is, in the long run he'll make more mistakes than us.

You might be thinking "well duh no ****" but I feel like flop play, in particular, is just so automated by so many regs that they don't really consider the implications that a slightly unbalanced tendency from their opponent's end has on how they should construct their range.

There is a standard sizing vs the population, but there are extremes on both ends and everything in the middle, playing around with sizings and trying to consistently put pressure on your opponents range (even if it opens yourself up for mistakes here and there) is going to be +ev in the long IMO.

i couldn't agree more with your post. i just tried to point out that if you go with a standard sizing that is mostly in the middle of what is good on a variety of boards, for example half pot, and deviate from it when you have a better plan, you won't ever make a big mistake by choosing the wrong size.

but in reality you can and should use sizes that put your opponent in bad spots, and that is often a size gto would also prefer.