Answer first
What this calculator tells you
Calculate the Kelly fraction of a bankroll to risk from your win chance and payoff. See the largest fraction the formula supports, then decide how much less to use. Formula: Kelly fraction f* = p − (1 − p) ÷ b, where p is the chance of winning and b is the net profit per dollar risked. At the worked-example inputs, the kelly fraction to risk is 10.0%. Holding every other input steady, moving chance of winning from 51.0% to 59.0% moves the result from 2.0% to 18.0%.
Transparent method
The formula
See the largest fraction the formula supports, then decide how much less to use.
Worked example
Example inputs
How to interpret the result
The Kelly fraction is the share of a bankroll that maximizes long-run growth when the odds are known. With a 55 percent chance to win an even-money bet, it says to risk 10 percent. The formula also shows the danger: if the true win chance is lower than you think, full Kelly overbets badly, which is why many people risk half of it or less.
At the worked-example inputs the kelly fraction to risk is 10.0%. It rises with net profit per $1 risked (b) and chance of winning; bankroll does not move it.
The Kelly fraction assumes your win chance and payoff are known exactly. Real estimates are uncertain, and full Kelly can swing a bankroll hard, so many people use half of it or less. This is arithmetic, not a recommendation to bet or trade.
Before you rely on it
What to check
Be honest about the win probability. It is an estimate, and the result is only as good as that estimate.
The common error
Where people go wrong with kelly criterion calculator
Treating the fraction as a guarantee. Kelly maximizes growth on average and still allows deep losses along the way.
Sensitivity evidence
How chance of winning changes the kelly fraction to risk
Holding every other input at the worked-example value, moving chance of winning from 51.0% to 59.0% moves the kelly fraction to risk from 2.0% to 18.0%: a spread of 16.0%, or 160% of the worked-example result.
| Chance of winning | Kelly fraction to risk | Amount to risk at full Kelly | Amount to risk at half Kelly |
|---|---|---|---|
| 51.0% | 2.0% | $200 | $100 |
| 53.0% | 6.0% | $600 | $300 |
| 55.0%worked example | 10.0% | $1,000 | $500 |
| 57.0% | 14.0% | $1,400 | $700 |
| 59.0% | 18.0% | $1,800 | $900 |
Every input, tested
Which input moves the kelly fraction to risk most
Of the 3 inputs, net profit per $1 risked (b) moves the kelly fraction to risk most (9.1% across the range tested) and chance of winning moves it least (8.0%). Bankroll does not change it at all.
| Input | Tested from | To | Kelly fraction to risk at each end | Swing |
|---|---|---|---|---|
| Net profit per $1 risked (b) | 0.9 | 1.1 | 5.0% to 14.1% | 9.1% (91%) |
| Chance of winning | 53.0% | 57.0% | 6.0% to 14.0% | 8.0% (80%) |
| Bankroll | $9,000 | $11,000 | 10.0% to 10.0% | none |
Two variables at once
Kelly fraction to risk by chance of winning and net profit per $1 risked (b)
Across the grid the kelly fraction to risk runs from -10.2% to 24.8%. Moving chance of winning from 51.0% to 59.0% shifts it by 16.0% at the middle column, and moving net profit per $1 risked (b) from 0.8 to 1.2 shifts it by 18.7% at the middle row, so net profit per $1 risked (b) is the bigger lever here.
| Chance of winning \ Net profit per $1 risked (b) | 0.8 | 1 | 1.2 |
|---|---|---|---|
| 51.0% | -10.2% | 2.0% | 10.2% |
| 53.0% | -5.7% | 6.0% | 13.8% |
| 55.0% | -1.2% | 10.0% | 17.5% |
| 57.0% | 3.2% | 14.0% | 21.2% |
| 59.0% | 7.8% | 18.0% | 24.8% |
The highlighted cell is the worked example: 10.0%.
Step by step
The worked example, input by input
| Input | Value used | What it means |
|---|---|---|
| Chance of winning | 55.0% | Enter the chance of winning used in this calculation. |
| Net profit per $1 risked (b) | 1 | 1 means you win $1 for each $1 you risk. |
| Bankroll | $10,000 | Enter the bankroll used in this calculation. |
| Kelly fraction to risk | 10.0% | |
| Amount to risk at full Kelly | $1,000 | |
| Amount to risk at half Kelly | $500 | |
Inputs, definitions and assumptions
Chance of winning
Enter the chance of winning used in this calculation. The prefilled worked-example value is 55.0%.
Net profit per $1 risked (b)
1 means you win $1 for each $1 you risk. The prefilled worked-example value is 1.
Bankroll
Enter the bankroll used in this calculation. The prefilled worked-example value is $10,000.
How to use this calculator
- 1Verify the inputs. Gather chance of winning, net profit per $1 risked (b) and bankroll from your own documents; the prefilled values are examples.
- 2Save a baseline. The worked example puts the kelly fraction to risk at 10.0%. Store your own version of it as Scenario A.
- 3Test one change. Start with net profit per $1 risked (b), the input with the biggest effect here: moving net profit per $1 risked (b) from 0.9 to 1.1 takes the kelly fraction to risk from 5.0% to 14.1%, a swing of 91% of the worked-example figure.
- 4Check the boundary. Read the interpretation boundary above before acting on the result.
People also ask
Frequently asked questions
How do you calculate kelly criterion?
Kelly fraction f* = p − (1 − p) ÷ b, where p is the chance of winning and b is the net profit per dollar risked. Enter chance of winning in percent and bankroll in dollars (55 means 55%). At the worked-example inputs the kelly fraction to risk is 10.0%.
What does the kelly criterion result mean?
See the largest fraction the formula supports, then decide how much less to use. At the worked-example inputs the kelly fraction to risk is 10.0%. It rises with net profit per $1 risked (b) and chance of winning; bankroll does not move it.
How much does chance of winning change the kelly fraction to risk?
Holding every other input at the worked-example value, moving chance of winning from 51.0% to 59.0% moves the kelly fraction to risk from 2.0% to 18.0%, a spread of 16.0%.
What are the limits of this kelly criterion calculator?
The Kelly fraction assumes your win chance and payoff are known exactly. Real estimates are uncertain, and full Kelly can swing a bankroll hard, so many people use half of it or less. This is arithmetic, not a recommendation to bet or trade. The tables on this page test chance of winning only from 51.0% to 59.0%; a value outside that range is not tabulated here.
Which input moves the kelly fraction to risk most in the kelly criterion calculator?
Ranked by how far each moves the kelly fraction to risk across the range tested: net profit per $1 risked (b) (9.1%, 91%) and chance of winning (8.0%, 80%). Bankroll does not change it.
How much does net profit per $1 risked (b) matter in the kelly criterion calculator?
The worked example uses 1. With the other inputs left at the worked example, moving net profit per $1 risked (b) from 0.9 to 1.1 takes the kelly fraction to risk from 5.0% to 14.1%, a swing of 91% of the worked-example figure.
How much does bankroll matter in the kelly criterion calculator?
The worked example uses $10,000. The kelly fraction to risk does not depend on bankroll; it moves the amount to risk at full kelly from $900 to $1,100 instead when bankroll goes from $9,000 to $11,000.
Which inputs change the amount to risk at full kelly in the kelly criterion calculator?
At the worked-example inputs it is $1,000. Chance of winning takes it from $600 to $1,400, net profit per $1 risked (b) takes it from $500 to $1,409 and bankroll takes it from $900 to $1,100.
Which inputs change the amount to risk at half kelly in the kelly criterion calculator?
At the worked-example inputs it is $500. Chance of winning takes it from $300 to $700, net profit per $1 risked (b) takes it from $250 to $705 and bankroll takes it from $450 to $550.
Sources and evidence
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