Posted by David D'Aquin on July 15, 1997 at 17:48:55: In Reply to: Re: This is the million dollar question! posted by Bisser on July 15, 1997 at 12:22:53:Yes, and he will win less using this different scheme. As N increases, results move towards the center. That is, the overall result moves closer and closer proportionally to the overall expectation. Betting the Kelly fraction produces the highest win possible when the expected number of wins and losses are achieved. This may not happen over the short term, but as N approaches infinity Kelly must beat all other fractions.
A few days ago I posted on the theory page my equations to predict the Kelly outcome for any game at any point in the distribution for any N. I also posted how to compute the probability of getting any particular result after N hands of Kelly betting. In a couple of days I'll post a more general equation that predicts the outcome for any proprosed fraction, not just optimal bets, for any point in the distribution. As N increases, the Kelly fraction asymptotically dominates the entire distribution of possible outcomes.
- Re: This sounds like a great reason to use Kelly... Bisser 18:08:48 7/15/97 (1)
- Re: This sounds like a great reason to use Kelly... David D'Aquin 21:06:55 7/15/97 (0)