Re: Fluctuation probablities?
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To use a Black Jack example. I once read that 98% of the time you should expect your BJ bankroll to be below your last highwater mark. That author (Snyder I think) was trying to point out that card counting wasn't for you if that characteristic bothers you.
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I'm not sure that's true. If he's trying to explain why card counting with a positive expectation still has high volatility, one would expect that over a given sample you would expect to be up only marginally more than 50% of the time for a single trial, not down marginally less than 100% of the time. For a sample of trials, the probability of being "up" increases, not decreases (supposing you can count effective enough to make it a positive expectation).
It doesn't make intuitive sense. Blackjack isn't a high payout / low probability game (like, say, lotto tickets).
That figure would be true if you were talking about a (hypothetical) game that paid out only 2/100 outcomes (the other 98 lose), and the 2 that do win get paid 51 times the wager... for a single trial. The expectation would be positive, but (for a single trial), you would expect to be down 98% of the time. You can see though, that as the sample increases, you expect to be "down" less often. If you were to repeat it 100 times, you would expect to be down significantly less than 98% of the time and as N approaches infinity, that percentage figure approaches zero.
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