[cachews]

omg i am so sick of this stuff; running it twice has no effect at all on EV, it just lowers variance

i mean, over time you'll play like a million hands, each time running it once; if you always run it twice that's two million hands, and a million is basically the same thing as two million, you see?

say you win with probability p (ignore ties, because then it doesn't actually work)

if you run it once, you win pot*p and lose pot*(1-p)... if you run it twice you win (pot/2)*p and lose (pot/2)*(1-p), twice... so by commutatitivity, the sums are the same