Kelly Criterion Calculator

What the number means

Kelly answers one specific question: what fraction of a bankroll maximises the long-run growth rate of that bankroll, given a known edge? The answer is (p x D - 1) / (D - 1), which is the expected value of the bet divided by the amount you can win per unit staked. If expectation is zero or negative the formula returns zero or less, which is the correct instruction to not bet.

The growth-rate rows are the useful part of this page. They show that overbetting is punished asymmetrically: the curve rises to a peak at full Kelly and then falls away, reaching about zero at twice full Kelly and going negative past it. Underbetting costs you a little growth. Overbetting can cost you all of it while the bets themselves were still good ones.

Half Kelly is a common compromise. It captures roughly three quarters of the growth rate at roughly half the volatility, and it halves the damage from an overestimated edge. Quarter Kelly is more conservative again.

Where it misleads

Every number here is downstream of a probability you estimated. If your true edge is 2% and you believe it is 5%, Kelly will size the bet as though you had 5%, and you will be overbetting by a factor of two and a half without any signal that anything is wrong. Results will not tell you either, because variance at these stake sizes swamps the difference for hundreds of bets.

The formula also assumes one bet resolving at a time, a bankroll you can actually re-stake, a price you can get in the size the formula asks for, and no correlation between bets. Simultaneous or correlated positions require smaller fractions than the single-bet answer. Limits, minimum increments and the fact that bankrolls are also rent money all argue in the same direction.

Kelly is a sizing tool, not an edge detector. It presumes the hard problem is already solved.