Cheers!

So... a long time ago, a pokerbuddy of mine solved the puzzle: Eureka! There can be two optimal bet sizes at once which optimize the EV!
(This was a breakthrough actually. Yeah, I know, it was a long time ago.
It was common wisdom back then that the optimal bet size was unique. cf. "Mathematics of Poker" for instance.)

Then, I came up with the idea, because I am the mathematician as I am:
"Why stop at two different optimal bet-sizes? How about infinitely many optimal bet-sizes? This would lead to a distribution of bet sizes."

What happened to this concept?
About the obvious "infinetely" many bet sizes, I mean.

Has there been any research about that?

Or has it been mainly focused on poker solvers, concentrating on a fixed number of bet sizes.

What I mean is:
Has there been any research about infinitely many bet-sizes? Or is this problem untractable by nowadays means?

It is obviously untractable computationally, but theoretically?

I'm pretty sure that in MoP there is (0,1) game in which every hand(number) uses different bet size.




Obv you can't put infinite number of sizings into solver and poker is not super interesting topic for academics, so most like no one doing that kind of research.

Yeah, I agree, I wouldn't do that kind of research either, if I were in academics. And 22.

Was just wondering. Maybe some poor guy had to have to write a PhD thesis about this **** which no one will ever remeber.
This **** I actually find interesting though.

Sorry.

And yes, if I understand you correctly, you are right, Haizemberg:
Not really beneficial, although actually, theoretically, really interesting. Because the implications go way further than this.
But to be frank: Only a guy like Gauss would solve the puzzle,
and since we are all not Gauss, we are happy with two optimal bet sizes.

To ba fair in real poker you don't have infinite bet sizes. In live you are limited by smallest chip and online it usually goes in 0.01bb increments, so you could solve it with powerful computer or for some simple spots.

I don't think there will have been any research, although you can probably use Google scholar to check.

I'd imagine the optimal number of bet sizes will depend on the spot, because in some spots, a solver will never use certain bet sizes. But on average, I'd imagine having the most number of possible bet sizes will maximises EV. I'd almost say it goes without saying.

I think what is more interesting is what sizes and how many of them, knowing the distribution of bet sizes used in GTO (fully solved for all these bet sizes), would make for the optimal simplification. Seen as humans wont be able to implement infinite bet sizes as part of a strategy. My guess is that a unimodal distribution could be simplified to one bet size, a bimodal to 2, etc...