Kelly Criterion Calculator

The Kelly criterion is a formula for how much of your bankroll to stake on a bet, given the price and your estimate of the chance it wins. It returns the fraction that maximises long-run growth.

Bet less than Kelly and you grow more slowly than you could. Bet more and a normal losing run compounds toward ruin rather than recovery. The penalty is asymmetric, which is why most people who use it stake a fraction of what it says — quarter Kelly keeps roughly 44% of the growth with a fraction of the volatility.

Developed by John Kelly at Bell Labs in 1956 for signal noise, and adopted by bettors and investors since.

The Kelly criterion answers a question expected value cannot: given that a bet is worth making, how much should you put on it? Bet too little and you barely grow. Bet too much and a normal losing run wipes you out before the edge can pay. Kelly finds the stake that maximises the long-run growth rate of a bankroll, and it turns out to be a fixed fraction of what you currently hold.

The formula scales with two things: how much you win when you are right, and how far your probability exceeds the break-even rate. A large edge on a long price gets a large stake; a thin edge on a short favourite gets a small one. If your probability does not clear the break-even rate at all, Kelly returns zero — not a small bet, no bet. That is the criterion working correctly, and it is the most valuable thing it does.

Now the caveat that matters more than the formula. Kelly assumes your probability is exactly right. It never is. And the penalty is asymmetric: underestimate your edge and you grow slower than optimal, but overestimate it and you overbet, and overbetting compounds toward ruin rather than toward growth. Since almost every bettor overestimates their edge, almost every bettor should bet a fraction of full Kelly.

Quarter Kelly is the sane default and is what this calculator shows first. It captures most of the growth — a quarter stake still gets you roughly 44% of the optimal growth rate — while cutting the volatility dramatically and giving you a wide margin for being wrong about your own numbers. Half Kelly is defensible if your probabilities come from a model with a real track record. Full Kelly is for people who know their edge precisely, which in practice means almost no one.

A bet at +110 you judge to be 55%, with a $5,000 bankroll. Here b = 1.10, p = 0.55, q = 0.45.

f* = (1.10 × 0.55 − 0.45) / 1.10 = (0.605 − 0.45) / 1.10 = 14.09%. Full Kelly says stake $704 — more than a seventh of everything you have, on one game. That is what full Kelly looks like in practice, and why it is rarely used.

Quarter Kelly is 3.52%, or $176. Still a confident bet, and survivable if the 55% read was really 51%. At full Kelly, that same misjudgement is betting four times too much on every bet you make, indefinitely.

Change the price to −130 and keep the 55%: the break-even rate becomes 56.52%, your edge goes negative, and Kelly returns 0%. No stake, at any fraction.

Should I bet full Kelly?

Almost certainly not. Full Kelly is optimal only if your win probability is exactly correct, and it is extremely volatile even then — drawdowns of half the bankroll are routine. Quarter Kelly keeps most of the growth with a fraction of the risk and a large margin for being wrong.

Why does Kelly say to bet nothing?

Because your win probability does not beat the break-even rate implied by the price, so the bet loses money over time. Kelly returns zero rather than a negative stake — there is no bet to place.

Do I recalculate after every bet?

Yes. Kelly is a fraction of your current bankroll, so the stake shrinks after losses and grows after wins. That self-correction is the mechanism that makes ruin mathematically impossible at full Kelly with a correct edge.

How do I use Kelly with several bets at once?

Simultaneous bets need the stakes reduced, since you cannot recalculate between them and correlated outcomes can compound. A common approach is to compute each bet’s Kelly fraction and scale them all down so the total exposure stays within your usual single-bet limit.

What if my probability estimate is unreliable?

Then use a smaller fraction, or do not bet. Kelly amplifies whatever you feed it: good estimates compound, and bad ones compound faster. The fraction you choose is really a statement about how much you trust your own numbers.

• The Kelly Criterion, Explained Without the CalculusThe mathematically optimal stake — and the reason almost nobody who understands it bets the full amount.10 min read

• Expected Value (EV) CalculatorWhat a bet is worth on average, given a price and your own probability.
• Bankroll / Unit CalculatorWhat a unit is worth, and what bankroll a unit implies.
• Bankroll SimulatorTen thousand seasons of the same edge, and where they end up.
• Risk of RuinThe chance a bankroll does not survive the variance.