Posted by Grimy Fellow on July 12, 1997 at 09:16:26: In Reply to: Re: What is the Kelly's theorem? posted by Bisser on July 11, 1997 at 16:08:40:You want to know the optimal proportion of bankroll to bet if you practice "proportional betting", i.e. you increase your unit size as your bankroll grows and decrease that unit size as it shrinks. Here's two reasons why:
1. If your proportion is too low or too high you aren't gaining as much from playing as you could be.
Far more important is:
2. If your proportion is too high by double the optimal your "expectation" is to win nothing, and if it's more than double the optimal your expectation is to lose.
To make an accurate determination of the optimal ratio of unit size to bankroll for a given game you must know the expected frequencies of all sizes (both negative and positive) of outcomes for that game. As David says, once you have this information the ratio is closely approximated by "advantage" (units won minus units lost, divided by units won plus units lost) divided by the variance of all of the outcomes.
Grimy