Poker-AI.org

Dear All,

Currently I'm working on calculating optimal strategies in a 6p push/fold game with CFR. Since the goal is to apply it for tournament solving I was consider whether it is beneficial to include future hands in the tree.

Reasons for:
Top commercial solvers do that (SnG Solver)
Chip size != equity
Applying one hand optimal strategy to multiple hands might be sub-optimal

Reasons against:
The hands are dependent only through stack sizes and sitting positions
Equity is an increasing function of chips => the more chips the better

Also, solving the current hand with CFR already takes around 10kk iterations which takes a bit of time (~30min), but the inclusion of future rounds would multiply that substancially.

To conclude, I would like to ask opinions on inclusion of benefits of inclusion of future hands in calculating the optimal strategies in my case. Any related articles and/or forum threads would be appreciated greatly as well.


Cheers

no you shouldn't. logically, even doing 2 hands would take (10kk)^2 iterations = 100 trillion

if each iteration took 1ms, that would take 3000 years to complete.

you should look into ICM calcutions.
I haven't done so myself but I imagine you would transform the payouts via the icm function

another problem is handling different scenarios of player stack sizes.

so you would have to solve the game for every combination of stack sizes (or a good approximation).

Why you do in 1st place? "Top commercial" ICM calc's have way better resourses then you do. ICM gives you N! increase in O(). Since you need "only" preflop,


It's only beneficial if you include N(preflop + nextStreet), not N(0 + M) hands. The basis for this extreimly simple, as preflop consider low amount of public information, the weight of EV(as bias, for given hand) gets more influence on result, when any given move leading to EV(as leaf node, for given hand). So basicly EV(bias) -> EV(best move). Or in other words EV(bias) <= EV(best move). So, as bias is huge for preflop, you may only consider EV(bias) but not EV(best move). Though lower limit of tube must be defined, I't too hard for, so Im getting to it. But lets assume that EV(best move) >= EV(bias) >= EV(worst move of bias). So bias in other words is preseption of opponent. If bias = 100% range so EV(best move) >= EV(bias) >= EV(worst move) for EV(100%) as pure CRM deffinition. So as long EV(100%) -> e-Nash, EV(bias)-> e-Nash, for any given bias. It leads to conclusion, as bias -> 0, more presise e-Nash can be found. So, only and only EV(O(1))i for any given set of hands i{X} will give you better EV then EV(bias)i. It leads to conlusion, EV(O(1))i for i{X} => EV(bias)i => EV(100% = 169(preflop)). => it's much better to go for opponents model then CFM for any given i{X} in Z, Z = all hadns. Is clear?
look up

PS. the easy answer, - it's no worth it.