Kelly criterion calculator

What the Kelly criterion does

Kelly answers one question: given a price and a probability, how much of the bankroll should one bet be? When the price is better than your probability requires, Kelly gives a positive share, and the larger the edge, the larger the share. When it is not, Kelly says stake nothing.

It maximises the long-run growth of the bankroll, but only if the probability you feed it is right. The probability is your estimate, and that is where the method is fragile.

The Kelly formula

With decimal odds d and a win probability p, the edge is p × d − 1, and the Kelly share of the bankroll is the edge divided by d − 1.

A worked Kelly example

Decimal odds are 2.10 and you estimate a 52% win probability. The edge is 0.52 × 2.10 − 1 = 0.092, and the full Kelly share is 0.092 ÷ 1.10 = 8.36% of the bankroll. On a bankroll of 1,000 that is 83.64; half Kelly is 41.82 and quarter Kelly is 20.91.

At odds of 1.91 and the same 52% the edge is 0.52 × 1.91 − 1 = −0.0068, so the answer is zero: the price needs a win probability above 52.36% to be worth backing.

Why most bettors use half or quarter Kelly

Full Kelly assumes your probability is exact. If your estimate is too high, full Kelly stakes too much and losing runs get deep. Betting a fraction of the Kelly stake gives up some growth in exchange for smaller swings and more room for error in the estimate.

• Full Kelly: highest growth if the probability is exactly right, the largest drawdowns.
• Half Kelly: a common compromise between growth and swings.
• Quarter Kelly: for estimates you trust less.

What Kelly leaves out

The calculator is arithmetic, and it has limits:

• The probability is your own estimate. The sportsbook's implied probability, margin included, is not a fair probability.
• It sizes one bet at a time. Several bets on the same event, or bets that move together, need a smaller stake.
• Stake limits, rounding to a sportsbook's stake steps and fees change the real stake and return.
• A sportsbook can limit an account that wins regularly.

How do I calculate the Kelly stake?

Take the decimal odds d and your win probability p. The Kelly share of the bankroll is (p × d − 1) ÷ (d − 1). At 2.10 and 52% that is 8.36% of the bankroll.

What does a negative Kelly result mean?

The price does not pay enough for the probability you entered, so there is no edge and Kelly stakes nothing. The calculator shows this as no edge.

What is half Kelly?

Half Kelly stakes half of the full Kelly amount. It reduces the swings in the bankroll and the damage from an over-optimistic probability, at the cost of slower growth.

Where does the win probability come from?

From you: your own model or judgement. A sportsbook price implies a probability with its margin included; the implied probability calculator shows how to remove the margin to get a fairer reference.

Does Kelly work for arbitrage bets?

An arbitrage covers every outcome, so the stake split comes from the prices, not from a win probability. Use the arbitrage calculator for that; Kelly applies to a single bet with a probability estimate.