The Kelly criterion explained, with a worked example and its risks

The Kelly criterion is a formula for how much of your bankroll to stake when you believe you have an edge. For bookmaker odds it's f = (b × p − q) ÷ b, where b is the decimal odds minus 1, p is your probability that the bet wins, and q is 1 minus p. For a prediction market share at price c, it simplifies to f = (p − c) ÷ (1 − c). If you think a player at 50¢ has a 60% chance, Kelly says stake 20% of your bankroll. The catch is the word "think": Kelly only works if your probability is right, and when it isn't, it can lose money fast.

The formula comes from a 1956 paper by J. L. Kelly Jr. of Bell Labs, which showed how a gambler with an edge could maximise the long-run growth rate of their capital. This page explains it with tennis numbers and doesn't promise anything: no formula turns a wrong estimate into a profit.

The formula, step by step

1. Get the odds into decimal form and subtract 1. That's b, your net profit per $1 staked. Decimal 3.00 gives b = 2. The odds converter handles American and fractional odds.
2. Write down your probability that the bet wins, p, and its complement, q = 1 − p.
3. Compute f = (b × p − q) ÷ b. That's the fraction of your bankroll to stake.
4. If f is zero or negative, don't bet. Kelly is saying you have no edge at that price.

Example: odds of 3.00 and a 40% chance. b = 2, p = 0.40, q = 0.60, so f = (2 × 0.40 − 0.60) ÷ 2 = 0.10, or 10% of your bankroll. At 3.00 the bookmaker's own chance is 33%, so you'd be backing your view that the real chance is 7 points higher.

Kelly for a prediction market price

On a prediction market a share costs c and pays $1, so b = (1 − c) ÷ c, and the formula becomes f = (p − c) ÷ (1 − c). The gap between your probability and the price is your edge; Kelly divides it by what you'd stand to lose per share.

Fees reduce the edge. Polymarket's sports taker fee is shares × 5% × price × (1 minus price), which at 50¢ is 1.25¢ a share. Treat that as part of the price: a 60% view at 50¢ becomes (0.60 − 0.5125) ÷ (1 − 0.5125), about 17.9% instead of 20%. Polymarket fees explained has the fee for any price.

Where your probability comes from

Everything in Kelly hangs on p, and in tennis there's no way to know it exactly. Three reference points help:

• The market price is the crowd's estimate. If your p equals the price, Kelly says stake nothing.
• A bookmaker's fair chance, with the margin taken out by the no-vig calculator, is a second opinion.
• A model such as the win-chance calculator gives a baseline from the score and serve-hold rates, but it doesn't know about injuries or form.

If all three agree with the price, you probably don't have an edge, and the honest Kelly stake is zero.

What a simulation shows

To see what Kelly does in practice, I simulated 20,000 runs of 200 bets each, every bet a share at 50¢ with your view being 55%. The simulation ignores fees and assumes every bet is independent, so real results would be a little worse:

Three things stand out. Even with a real edge, full Kelly falls to half of a previous high in almost every run, and ends below where it started about one time in four. Betting twice the Kelly amount wipes out the growth entirely. And if your estimate is five points too high, full Kelly loses money in most runs.

Why most people stake a fraction of Kelly

• Your probability is an estimate. Overestimating your edge makes Kelly overbet, and overbetting costs far more than underbetting.
• Half Kelly gives up a little growth for much smaller swings. In the simulation, half Kelly's median run ended at 2.1 times the start against full Kelly's 2.7, with less than a third as many runs falling to half a previous high.
• Tennis bets aren't always independent. Two positions on the same match, or on players in the same draw, can lose together, which Kelly's maths doesn't account for.
• Selling changes the sum. Kelly assumes you hold to the result. If you plan to sell during the match, as in take-profit and stop-loss, your real risk per trade is smaller than the stake, and the formula overstates it.

The most useful thing Kelly teaches isn't the exact number. It's that the right stake depends on the size of your edge, and that with no edge the right stake is zero.

Sources

J. L. Kelly Jr., A New Interpretation of Information Rate, Bell System Technical Journal, July 1956. Polymarket's sports fee is from Polymarket's fee page, checked on 31 October 2026. The simulation is my own: 20,000 runs of 200 independent bets at a fixed 50¢ price, with no fees. Everything else is arithmetic.

FAQ

What is the Kelly criterion?

A formula for what fraction of your bankroll to stake when you believe you have an edge. It aims to maximise long-run growth, but only works if your probability estimate is right.

What is the Kelly formula?

f = (b times p minus q) divided by b, where b is decimal odds minus 1, p is your probability, and q is 1 minus p. For a prediction market price c, it's f = (p minus c) divided by (1 minus c).

What is half Kelly?

Staking half of what the formula says. It grows more slowly but swings far less, and it's much more forgiving if your probability is too optimistic.

Does the Kelly criterion guarantee a profit?

No. It sizes bets for an edge you believe you have. If the edge isn't real, Kelly loses money, and even with a real edge the bankroll can fall a long way before it grows.

Is there a Kelly criterion calculator?

The formula is simple enough to work by hand, as shown on this page. The no-vig calculator gives you a fair probability from bookmaker odds to compare with your own.