re: Poker & Schooling
Originally Posted by Cheetah
FP, what kind of simulations have you done? I would be interested to see the results and any conclusions you have drawn from them.
My simulations were made to try to answer the question "how bad is variance for someone with a small bankroll". Basically, I stipulated the following
a) I will beat my opponent for an amount that is proportional to the stakes I play, and
b) with higher variance I'm more likely to go on swings that will force me to move down in stakes and therefore make proportionately less money until I'm back up to where I started.
Since moving down effectively halves my income (stakes are usually like that) the idea is (was) that the safer route might generate more money since it will not be at all as likely to risk moving down.
So I decided to test how variance/EV effected money made. The simulator basically runs random all-in coin-toss situations where one guy will bet money on every toss that's 50% or better to win (pushing the edges, and the variance, to the max) and the other guy will be more careful, only taking, say, 55% edges or better before getting the money in.
I did not manage to run any simulation over any meaningful period of time where it wasn't better to take the +EV, high variance route in terms of earning money.
Of course, this is a very rough model. My code doesn't properly account for rake (although it does to some extent) which hits the high variance player harder. On the other hand, it doesn't consider pot odds
at all either, which works in favor of the high variance player, so perhaps those two simplifications somewhat cancel each other out.
Another, very real, problem with the model is that people aren't machines, and running a high variance game may be psychologically detrimental. But the pure mechanics of variance vs. EV speaks strongly (very strongly) in favor of EV.