Re: What is the Kelly's theorem?


Posted by Bisser on July 11, 1997 at 16:08:40: In Reply to: Re: What is the Kelly's theorem? posted by David D'Aquin on July 11, 1997 at 15:31:15:


Thanks David! Let me see if I am getting it right...

Let X be my bankroll and I can place a bet of size Y which wins with probability P. Then we maximize

E(log(X+WY)),

where W is a random variable which is 1 with probability P and -1 with probability 1-P. The maximum is achieved at (2P-1)X, i.e. the fraction which you are talking about is 2P-1.

Here the variance is 1 and the exp.value is 2P-1, so the approximation ev / variance works. I will take it on faith that it will also work for the game of blackjack, where W can also be 0 (push), 1.5 (blackjack), 2, -2 etc.

I still see no reason to use all this when I play blackjack, but at least now I know what it means.

Cheers,
Bisser

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