Re: Major Problem with Bill Chin\'s Article on Variance
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If you think the independence of bets or sets of bets does not approximately hold, it might be interesting to hear why.
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Players will change their play as they win and lose. One common pattern is to loosen up when you win, but fail to tighten up when you lose. The gambler's ruin theorem means you will almost always be a big loser with this rule, even if you have positive expectation per hand. This violates independence and, with a player like this, I would base my long-term prediction of his wealth on his poor strategy rather than the mean and standard deviation of individual hands.
Another dependence is bluffing. If a player is caught in a bluff, he will be played differently on future hands. That's the point of bluffing.
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