# What is the Kelly criterion bet size?

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.

- Page: https://www.acalculator.org/game/kelly-criterion-calculator
- JSON spec: https://www.acalculator.org/game/kelly-criterion-calculator.json
- Version: b9eb6db7ff32

## Default answer

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).

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| p | Chance to win | Your own estimate of the chance the bet wins. |
| fmt | Odds format | Whether the odds are decimal (2.10) or American (+110 or −150). |
| odds | Decimal odds | The decimal odds: the total paid back for each 1 staked, stake included. |
| us | American odds | The American odds: +150 wins 150 per 100 staked, −200 stakes 200 to win 100. |
| bank | Bankroll | The money you set aside for betting. |
| mult | Kelly multiplier | The share of the full Kelly stake to bet: 100% is full Kelly, 50% is half Kelly. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| stake | Stake | Bankroll × Kelly fraction × multiplier; 0 when the bet has no edge. |
| kelly | Full Kelly fraction | f* = p − q ÷ b: the share of the bankroll full Kelly stakes (0 when f* is not above 0). |
| share | Share of bankroll to stake | The full Kelly fraction × the multiplier. |
| edge | Edge | The expected profit per 1 staked: b × p − q. |
| breakEven | Break-even chance | The chance to win at which the bet has no edge: 1 ÷ (1 + b). |
| growth | Expected growth per bet | p × ln(1 + f × b) + q × ln(1 − f) for the share staked, as a percent of the bankroll. |
| verdict | Verdict | Whether the Kelly criterion says to bet. |

## 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.

## Assumptions

- 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

1. p = 60%, fmt = decimal, odds = 2, bank = $1,000.00, mult = 100% gives kelly = 20%, stake = $200.00, edge = 20%, breakEven = 50%, growth = 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).
2. p = 55%, fmt = decimal, odds = 2.1, bank = $1,000.00, mult = 50% gives kelly = 14.090909%, share = 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).
3. p = 40%, fmt = american, us = 150, bank = $500.00, mult = 100% gives kelly = 0%, stake = $0.00, edge = 0%, breakEven = 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).
4. p = 75%, fmt = american, us = -200, bank = $1,000.00, mult = 100% gives kelly = 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).

## FAQ

### 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.

## Sources

- 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)
- Wikipedia, Kelly criterion: f* = p − q ÷ b and the 60% at even odds example. https://en.wikipedia.org/wiki/Kelly_criterion (retrieved 2026-10-05)