6-max 100bb eff cash game (rake unknown)
UTG opens to 3bb, BTN calls
Flop: J62r

If I allow 25%, 50% and 80% bet sizes for UTG, we're betting 75% of the time.
If I only allow 80% or only 40%, the betting frequency goes down to 60-65%.
If I only allow 20%, the betting frequency goes up to 90%.
(I have x/r set to 75,125 and IP bet size default 50%)

Why is this?


I also noticed that when using 25%, 50% and 80% together, that the solver is close to equally mixing these bet sizes.
Why?
And why does our bet frequency change if the solver is mixing the bet sizes everywhere anyways?

I would expect it to use 25% of a certain category and 80% for another, but it's not.

For example: 80% with the very top of range and our strongest bluffs.
20% with medium strength hands and weaker bluffs
But it's just close to equally mixing them over the entire range, then what's the point of having multiple bet sizes?
Shouldn't there be 1 optimal size for the entire range then? Is this the 20% pot that allows us to bet 90% of the time?
Or am I missing something?




Also, it's been a while, what's up everyone!?

I think I formulated my questions in an unclear way.

1) Why does our betting frequency change depending on allowed bet sizes?
2) Is there an optimal bet size for this situation?
3) Would the optimal bet size be the size that allows us to bet at the highest frequency?
4) Is there an optimal bet size for each specific situation, or is it sometimes optimal to have different bet sizes in one specific situation?
5) If we have a specific situation where different bet sizes are optimal, would the different sizes be evenly spread over our entire range, or should we see some parts using one size mostly and other parts using another size mostly?
6) If the different sizes are spread about evenly through our range, then what is the advantage of having multiple sizes in one specific situation?


Note: These questions are all about one specifically defined situation, like the one above.
I am NOT asking if it's good or bad to have multiple bet sizes in general. Obviously it's good to have multiple sizes in general. But I do wonder if each specific situation has it's own optimal size or if multiple sizes work better even in each singular specific situation.

1) Two reasons:
If you don't allow small sizings, marginal hands won't be able to valuebet for obvious reasons.
If you put all of your strong hands in the small sizing, villains strategy will change, and our performance with marginal hands as a bet will increase.

2) The optimal solution is the one with all options available. Having said that, there are many "almost" optimal solutions that only involve 1 sizing

3) No

4) Whatever the solver comes up with is the optimal solution for that particular model of the game

5) Depends

6) It's never spread evenly, but it could be spread "almost" evenly. In those cases, the advantage is very small.

Great questions, Yeodan!

So firstly, I'd recommend using proper preflop ranges. IP shouldn't be calling offsuit-connectors. GTO Wizard has free preflop ranges you can use.

Humans have this bias that betting more frequently is somehow better. When you only give it a 20% block-bet, all the strongest hands go in that range which provides cover to bet most of your marginal hands. However, your strongest hands would much rather use a larger size to get more value, which means checking more often with other parts of your range.

Yes. Like Aner0 said, the optimal solution will mix, but you can find good strategies using just one flop size.

No. The optimal size might actually involve checking more often.

There are situations with two or more strategically distinct strategies. A common example are spots where you have a block-bet and an overbet OOP on the river.

Typically they will cluster towards certain sizes.

It's simply a higher EV strategy. Every size will maximize value for some part of your range. Though in practice it's very hard to implement this correctly.

Thanks, this helped

Based on the above replies you can already imagine that small sizes will be optimal when it’s important to bet marginal hands, and big sizes will be optimal when it’s not. Eg BTN vs BB we cbet big on AKx because Kx is perfectly fine with checking (doesn’t need protection). Whereas if we tried to play big bet or check on A82, we lose a ton of EV because we wouldn’t have the option to bet our 8x (and deny equity against hands like QJ/JT).

There are also some boards where your marginal hands are okay with betting or checking, and those tend to be the boards where you see lots of mixing.

Wait, I'm supposed to check Kx on a AKx flop on the BTN vs BB? What?

It's the more theory approved play, yes

I might be able to shed some light on this phenomenon

The solver usually prefers an overbet/check strategy on disconnected AKX flops in single raised pots. There are a few reasons for that:

1) Your 2nd pair is not vulnerable to any more overcards, so it's less incentivized to bet. Since your betting range carries fewer medium hands it's allowed to size up more drastically.
2) The aggressor has a huge nut & range advantage.
3) The defender lacks the ability to effectively counter-attack your aggression.

Checking some aggregate reports, these are among the most overbet flops:


Zooming in on the betting frequencies, it seems to check more than half the time and overbet around ~130% pot.



We can see on a board like AK6, the aggressor has many more hands in the 80%+ equity region, indicating a significant nut advantage, and we observe a solid range advantage throughout:


When we shift to a more polarized strategy, 2nd pair hands will prefer to check. If Kx overbets it just ends up folding out worse and mostly getting called by better.



With all that said, there are likely many reasonable strategies on such a great flop. If you only gave the solver a 1/3 bet, it would probably bet most of its Kx. But the solver finds more value with an overbet/check game plan. Hope this helps!


GTO Wizard