What is the Kelly criterion bet size?
Type your chance to win, the decimal or American odds, your bankroll and the share of full Kelly you want to bet. The Kelly criterion calculator gives the stake, the edge and the expected growth per bet.
- Stake
- $140.91
At a 55% chance to win, the Kelly criterion stakes $140.91 (14.09% of the bankroll).
- Full Kelly fraction
- 14.09%
- Share of bankroll to stake
- 14.09%
- Edge
- 15.5%
- Break-even chance
- 47.62%
- Expected growth per bet
- 1.091%
- Verdict
- Bet
Stake: $140.91. At a 55% chance to win, the Kelly criterion stakes $140.91 (14.09% of the bankroll).
The results are maths only. They are not betting advice or a promise of a return. Bet only what you can afford to lose. For help with gambling, call 1-800-GAMBLER. Terms of use
How to calculate
Works out the Kelly criterion stake for a bet from your win probability and the odds, as a share of your bankroll and in money, with the edge and growth rate.
Example with the default inputs (Chance to win 55%, Odds format Decimal, Decimal odds 2.1, Bankroll $1,000.00, Kelly multiplier 100%): At a 55% chance to win, the Kelly criterion stakes $140.91 (14.09% of the bankroll).
Method: b = decimal odds − 1 (or American / 100, or 100 / |American|); q = 1 − p; edge = b × p − q; f* = edge ÷ b when the edge is above 0, else 0; stake = bankroll × f* × multiplier.
- The chance to win is your own estimate; the Kelly stake is only as good as it.
- One bet at a time, with the stake lost in full on a loss and no push.
- The growth rate is the expected change in the log of the bankroll per bet, at the share staked.
Worked examples
Each example is checked against the calculator on every build.
- Chance to win 60%, Odds format Decimal, Decimal odds 2, Bankroll $1,000.00, Kelly multiplier 100% gives Full Kelly fraction 20%, Stake $200.00, Edge 20%, Break-even chance 50%, Expected growth per bet 2.013551%, Verdict Bet.Source: Wikipedia, Kelly criterion (f* = p − q ÷ b; 60% to win at even odds stakes 20%), https://en.wikipedia.org/wiki/Kelly_criterion (retrieved 2026-10-05); J. L. Kelly Jr., A New Interpretation of Information Rate, Bell System Technical Journal 35(4), 1956, https://doi.org/10.1002/j.1538-7305.1956.tb03809.x (retrieved 2026-10-05)
- Chance to win 55%, Odds format Decimal, Decimal odds 2.1, Bankroll $1,000.00, Kelly multiplier 50% gives Full Kelly fraction 14.090909%, Share of bankroll to stake 7.045455%, Stake $70.45, Edge 15.5%.Source: Wikipedia, Kelly criterion (f* = p − q ÷ b; 60% to win at even odds stakes 20%), https://en.wikipedia.org/wiki/Kelly_criterion (retrieved 2026-10-05)
- Chance to win 40%, Odds format American, American odds 150, Bankroll $500.00, Kelly multiplier 100% gives Full Kelly fraction 0%, Stake $0.00, Edge 0%, Break-even chance 40%, Verdict No bet: the odds give no edge at this chance to win.Source: Wikipedia, Kelly criterion (f* = p − q ÷ b; 60% to win at even odds stakes 20%), https://en.wikipedia.org/wiki/Kelly_criterion (retrieved 2026-10-05)
- Chance to win 75%, Odds format American, American odds -200, Bankroll $1,000.00, Kelly multiplier 100% gives Full Kelly fraction 25%, Stake $250.00, Edge 12.5%.Source: Wikipedia, Kelly criterion (f* = p − q ÷ b; 60% to win at even odds stakes 20%), https://en.wikipedia.org/wiki/Kelly_criterion (retrieved 2026-10-05)
How it works
Every typed number is used as the exact decimal you type.
Net odds b. Decimal odds d give b = d − 1. American odds A of +100 or more give b = A ÷ 100; −100 or less give b = 100 ÷ |A|. American odds between −100 and +100 give no answer.
With p the chance to win as a decimal and q = 1 − p:
- Edge = b × p − q: the expected profit per 1 staked.
- Full Kelly fraction f* = edge ÷ b (the same as p − q ÷ b) when the edge is above 0; otherwise 0, and the verdict is no bet.
- Share of bankroll = f* × multiplier (100% is full Kelly).
- Stake = bankroll × share.
- Break-even chance = 1 ÷ (1 + b).
- Expected growth per bet = p × ln(1 + s × b) + q × ln(1 − s), with s the share staked. This is the only step in floating point.
Assumptions
- One bet at a time; a loss loses the stake and a win pays b per 1 staked.
- The chance to win is strictly between 0% and 100%.
Worked examples by hand
60% at even odds (decimal 2.00), bankroll 1,000. b = 1; edge = 0.6 − 0.4 = 0.2; f* = 0.2 ÷ 1 = 20%, a stake of 200. Growth = 0.6 × ln 1.2 + 0.4 × ln 0.8 = 0.020136, 2.014% a bet. Break-even 1 ÷ 2 = 50%.
55% at decimal 2.10, half Kelly, bankroll 1,000. b = 1.1; edge = 1.1 × 0.55 − 0.45 = 0.155; f* = 0.155 ÷ 1.1 = 14.09%; half is 7.045%, a stake of 70.45.
40% at +150, bankroll 500. b = 1.5; edge = 1.5 × 0.4 − 0.6 = 0: no bet. Break-even 1 ÷ 2.5 = 40%.
75% at −200, bankroll 1,000. b = 100 ÷ 200 = 0.5; edge = 0.5 × 0.75 − 0.25 = 0.125; f* = 0.125 ÷ 0.5 = 25%, a stake of 250.
Other questions people ask
What is the Kelly criterion formula?
f* = p − q ÷ b, where p is the chance to win, q = 1 − p is the chance to lose, and b is the net odds: the profit for each 1 staked. f* is the share of your bankroll to stake.
What does the Kelly criterion say at 60% and even odds?
b = 1, so f* = 0.6 − 0.4 ÷ 1 = 0.2: stake 20% of the bankroll. That is the example Wikipedia gives.
What if the Kelly fraction is negative?
A fraction of 0 or less means the bet has no edge at your chance to win: the odds pay too little. The Kelly criterion says not to bet.
Why bet half Kelly?
Full Kelly gives the fastest long-run growth only when your chance to win is right. Half Kelly keeps about three quarters of that growth with much smaller swings, and leaves room for a wrong estimate.
How do I turn American odds into b?
For +150, b = 150 ÷ 100 = 1.5. For −200, b = 100 ÷ 200 = 0.5. For decimal odds, b = decimal odds − 1.
Who came up with the Kelly criterion?
John L. Kelly Jr. of Bell Labs, in the 1956 paper “A New Interpretation of Information Rate” in the Bell System Technical Journal.