Kelly Criterion Calculator: Optimal Bet Size
How much should you bet? The Kelly criterion answers that with a single number — the fraction of your bankroll that grows it fastest over the long run. This bet sizing calculator turns your odds, your win chance, and your bankroll into a Kelly-optimal stake, with fractional Kelly on by default and every step shown.
How the Kelly criterion calculation works
The Kelly criterion picks the stake that maximizes the expected growth rate of your bankroll — not your expected profit on any one bet, but how fast your money compounds if you bet the same edge over and over. Its answer is a fraction of your bankroll:
Here b is the decimal odds minus one (what you win per dollar risked), p is your estimated probability of winning, and q = 1 − p is the chance you lose. The numerator b·p − q is just your edge in odds terms: if it’s positive you have an advantage and Kelly stakes a slice of it; if it’s zero or negative, f* ≤ 0 and Kelly says bet nothing.
That formula falls out of maximizing expected log wealth. You want the stake that’s highest on this curve:
Log wealth is the right thing to maximize because betting compounds: a bad drawdown costs you more than the same-sized win gives back, so full Kelly is the fastest growth rate that never risks ruin — if your p is exactly right.
Why fractional (half) Kelly is the safe default
That last clause is the catch. Full Kelly assumes you know your true win probability. In real betting you don’t — your edge is an estimate, and the growth curve is steep on the downside: overestimate p and full Kelly overbets, which raises variance fast and courts a deep drawdown. Because the curve is flat near its peak, betting a fraction of full Kelly keeps most of the long-run growth while cutting the swings sharply:
A half is the standard default; a quarter is the more conservative choice when your edge estimate is especially noisy. The calculator applies the fraction you choose to the raw Kelly stake.
Worked example
Kelly sizing is the last step after you’ve found an edge. First strip the vig to find the fair line, then measure the expected value of the bet; Kelly only tells you how much once you know you’re ahead. The full method, with the animated derivation and joint sizing for correlated bets, is in the Kelly criterion guide.
Frequently asked questions
What is a Kelly criterion calculator?
A Kelly criterion calculator works out the fraction of your bankroll to stake that maximizes the long-run growth rate of that bankroll. You enter the odds, your estimated win chance, and your bankroll; it returns the Kelly-optimal bet size using the formula f* = (b·p − q)/b.
Why use fractional (half) Kelly?
Full Kelly assumes you know your true win probability exactly. In real betting your edge estimate is noisy, and overestimating it makes full Kelly stake too much — which is ruinous. Fractional Kelly (a quarter or a half of the full stake) keeps most of the growth while cutting the variance and the risk of a large drawdown, so a half is the safe default.
How much should I bet according to Kelly?
Kelly says bet f* = (b·p − q)/b of your bankroll, where b is the decimal odds minus one, p is your win probability, and q = 1 − p. If f* is zero or negative you have no edge and Kelly says bet nothing. Most bettors then scale that fraction to a half to account for uncertainty in p.