Wiki link: Kelly criterion

In probability theory, the Kelly criterion, or Kelly strategy or Kelly formula, or Kelly bet, is a formula used to determine the optimal size of a series of bets.

f* = (bp – q) / b

where

f* is the fraction of the current bankroll to wager;
b is the net odds received on the wager (that is, odds are usually quoted as “b to 1″)
p is the probability of winning;
q is the probability of losing, which is 1 − p.

You might recognize the numerator , bp – q, as expected return for one ‘unit’. The ‘Kelly return’ for one bet is f* times (bp – q).

We see that according to the Kelly criterion, for bets giving the same expected return, we should prefer the one that gives the highest probability of winning–which we already knew.

See reasons to bet less than Kelly in the article. Also we should find out how things change if bets are correlated.