MultiStreet 0/1 poker
Posted by Schulti
Posted by
Schulti
posted in
Gen. Poker
MultiStreet 0/1 poker
Consider the following game:
Two players get dealt a number between 0 and 1, lowest number wins at showdown
Pot of 1
stacks of s behind
N streets
Players can check, or bet and raise for any size they like on every street.
Has anyone solved this game? Would it be possible to solve it numerically (In terms of computation time)?
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This question is very broad, it would make more sense to start with N=1, 2, 3.
Also continuous bet sizes are very difficult to do with numerical methods.
Agreed, the ultimate goal is to solve this problem for N=3 as that would give us a model for completely static postflop situations with equal linear ranges which would be very insightfull. But it makes more sense to start with N=1.
So I'm wondering if anyone else has thought about this problem. I don't think its possible to solve it analytically (In MoP (Page 203-215) they solve some easy simplifications and its already hard to follow).
Numerically, would be it be possible to solve this for say increments of 1 and stacks of 100? Seems like an infinite amount of possibilities already but maybe with some smart ideas you can eliminate a lot of possible strategies
Also, intuitively, how do you think the solution would look like?
For the N=1 case, the most interesting question for me is how many different betsizings are used for both players.
For N=2 and N=3 cases, one thing that i'm wondering about is whether you just play aggressively on earlier streets with the strongest portions of your range in a continuous way, or if there will be a lot of mixing where for every possible passive action you have to include some subrange of very strong numbers to keep ranges on future streets strong enough.
Good questions! Completely off the top of my head:
1) Numerical grid methods (1 to 100) that you suggested sounds useful, but I would think there's already too many variables out there that we might not be able to solve for the N=3 case. N=2 cases, though, I think it *might* be possible.
2) Another interesting simplification might be using pot-limit betting structure. I think we apply this in addition to [1, 100] restriction, such that you can bet/raise up to the pot but only for integral bet sizings.
3) For N=1 case, I wouldn't be surprised if there are lots of cooptimal solutions. If we do apply PL betting structure though, I would guess the # of solutions will be somewhat significantly decreased.
4) For N=2 and 3 cases, it's too complicated for me to comment anything on it without actually solving, or trying to solve, the problem :)
GameTheory is right. You are probably trying to work with too many variables at first. I would suggest looking at one-street, then 2 street, 3 street, and limit the number of actions players can take.
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