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Old 02-19-2007, 08:20 PM
AaronBrown AaronBrown is offline
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Join Date: May 2005
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Default Re: Simple Kelly Problem

(a) Correct, except you meant to write 1.005 instead of 1.05. The 0.5% is correct.

(b) Almost correct. Let's do it in dollars instead of percentages, it's easier to get it right. You bet $200 with the 0.5% disadvantage, for an expected loss of $1. You bet $1,000 with the 1.5% advantage, for an expected gain of $15. If you do one of each, you win an average of $14 on $1,200 bet, $14/$1,200 = 1.1667% advantage. It doesn't matter whether you do it 2 times or 2 million, it's still 1.1667%.

Kelly tells you to bet a fraction of bankroll, not a fixed amount. So as you win money, you increase your bet sizes. With any disadvantage you bet a negative amount (that is, you take the other side of the bet). If that's impossible, you bet zero. With a positive expectation, the fraction of bankroll you bet depends on the variance of the outcome.

I assume this is blackjack you're trying to model. In this case, the variance is essentially constant, so all that matters is edge. Your bet should be proportional to edge times bankroll, and you should make the minimum possible bet when you have a disadvantage.

As a practical matter, you make the minimum bet when the count is against you, then ratchet up the bet as the count moves more in your favor, until you hit the maximum. This assumes that you are not trying to disguise your counting. As you are more successful, you move to higher limit tables.
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