[pzhon]

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I don't get it Troll, you post a lot here and obviously have no idea what you're talking about. wtf?

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He's a troll, someone who makes provocative, stupid posts. It's hard to tell when he is being intentionally stupid for the entertainment value. My guess is that this greatly decreases the level of feedback he gets, since no one wants to try to help him only to hear that he was just pretending to make that mistake, and is now laughing at them for believing him. I've ignored many incorrect statements of his because I didn't know whether he meant them, or just thought it was funny to try to contradict a mathematician whenever possible.

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Of course the variance approaches zero with many runs.


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Yes.

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Say you have a $100 pot, are all-in and have 50% equity. If you run it once you will have a variance of 2,500 (or SD of $50). If you run it twice you will have a variance of 417 (SD=$20). And if you run it 4 times you will have a variance of 125 (SD=$11).


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These calcluations are a bit off. The variance drops by a factor of n^2 in each pot when you run it n times. If the runs were independent, that would mean the total variance would be n/(n^2) or 1/n times the variance of running it once. Since the runs are anti-correlated, the actual variance of running it n times is slightly under 1/n times the variance of running it once. The standard deviation is reduced by about 1/sqrt(n). The exact extent of the anti-correlation depends on the hands.

Troll did make a tangentially relevant point, whether he meant to or not, that all-in variance is only part of the overall variance you experience when playing poker. (His analysis in the other thread was bad, however.) If you find someone who is happy to run each all-in situation 5 times, this will cut your all-in variance, but you will still experience large swings based on how frequently you get good hands, and how frequently your opponent gets good hands, and which hand is better when you both get good hands. However, when you are all-in, you can reduce the variance on that hnd quite a bit by running it multiple times.

As has been discussed in the Poker Theory forum recently, there are many other effects in practice when you run a hand multiple times, since it may affect the stack sizes in subsequent hands, and it may have metagame effects when you play against risk-averse players.