It's not 100% relevant to the thread, but this is bothering the crap out of me:
Quote:
Originally Posted by iraisetoomuch
Lets take AA vs KK AI pre flop for 100bb each. (It's a magic place with no rake, and no tipping.)
You run it once, there are two outcomes:
You are at 200bb, which happens 80% of the time.
You are at 0bb, which happens 20% of the time.
Overall EV, .8*200+.2*0= 160bb.
You run it twice, there are 4 outcomes:
You are up 200bb, which happens 64% of the time. (80% for the first, * 80% for the second.)
You are at 100bb, which happens 32% of the time. (20% you lose the first one * 80% you win the second one, + 80% you win the first one, 20% you lose the second one.)
You are at 0bb, which happens 4% of the time. (20% for the first, 20% for the second.)
Overall EV, .64*200+.32*100+.04*0= 160bb.
What I bolded is incorrect. It might still be true that the EV stays the same, but this justification is totally wrong. When you are running it twice from the same deck without replacing the cards, the pots are not independent events, as you are implicitly assuming they are to do your calculation.
To see why, take A
A
against K
K
and imagine running it 9 times.
Your method will tell you that the probability of the kings scooping all 9 pots is an astronomically small number, like .000000512 (which equals 1/1953125), but not zero.
In fact, due to card removal, the probably of the kings scooping all 9 pots is literally 0. That's also the probability of the kings scooping 8 out of 9. (There are only 2 kings in the deck and 4 queens/4 jacks/4 tens, so the kings can make 2 sets and 4 straights and then they literally have no way to win any more.)
That doesn't prove the EV is NOT the same--in fact, I think it is. But your method doesn't imply that.
As for the actual question in the thread, if my bankroll were big enough to justify playing in the game I'm in, I would never run it twice.