Hey guys, I'm trying to build my own version of ICMizer for my poker lib for a few reasons (mainly they incorrectly analyse shove spots for stack size <0.5BB but I digress)
I'm working my way through the mammoth challenge part by part and I'm currently stuck on:
How do we get the equities of four way all ins?
Essentially to update the over calling strategy for a fourth player using a Fictitious/Regret minimisation algorithm we need to calculate the EV of the over call. So we need to know the four way equities for all hands for the strategy.
This is problematic because despite having a lightening quick hand elevator (like the one open sourced by members of 2+2 using lookup tables) you cant really calculate these equities on the fly in any reasonable amount of time. I can definitely see it viable to calculate a three way equity lookup table for 3 way all in's then solve three way shoves like done in this paper:
https://www.cs.cmu.edu/~sandholm/3-p...ld.AAMAS08.pdf
Also done by the guy from Holdem Manager I think but I'm stuck trying to figure out how it could be done for four ways+, a 4(+)D matrix is infeasible (is it not?) calculating the equities on the fly is infeasible (is it not?) but ICMizer and Holdem Manager both manage to do these 9 way NE Calculations which I don't understand. I'm sure there is likely some like pruning done because the probabilities of four way all in's occurring are so so small that I could probably get away with discounting them somehow.
But it's not really ideal and going to derive incorrect results which is unappealing especially because I know both ICMizer and Holdem Resources have solved it without doing so (or have they just used some simplification/pruning trickery?).
Any thoughts?
Cheers