How to use the kelly criterion calculator
- Enter your chance of winning as a percent. This is your own estimate.
- Enter what a win pays for each dollar risked. Even money pays $1.
- Set the fraction of Kelly to use. 100 is full Kelly, and many people use less to reduce the swings.
- Optionally enter a bankroll to see a dollar amount. Read the share of your bankroll and the expected profit per dollar. Copy, Print or share the result.
Formula
f = (b x p - q) / b
p = chance of winning, q = 1 - p, b = net payout per $1 risked
expected profit per $1 = b x p - q
stake = bankroll x f x fraction used
When b x p - q is zero or negative the formula gives 0, which means do not bet. The break-even chance of winning is 1 / (b + 1). The fraction setting scales the answer down without changing the formula.
A 55% chance at even money
With p = 0.55, q = 0.45 and b = 1, the expected profit per dollar is 1 x 0.55 - 0.45 = $0.10 and the Kelly fraction is 0.10 / 1 = 10% of the bankroll. At half Kelly with a $2,000 bankroll the amount is 2,000 x 0.10 x 0.5 = $100.
With a 40% chance and a payout of 2 to 1, the fraction is (2 x 0.4 - 0.6) / 2 = 10%. With a 40% chance at even money the edge is negative (0.4 - 0.6), so the answer is 0%.
What the formula assumes
The Kelly criterion picks the bet size that maximizes the long-run growth rate of a bankroll when you repeat a bet with a known edge. It assumes you know the true chance of winning, the payout never changes and you can bet any fraction of your bankroll. In real life you almost never know the true chance, and an overestimate can lead to a stake that is far too large.
That is the reason many people use a fraction of the full amount. Using half of the Kelly stake cuts the swings a lot while giving up a modest share of the growth in the ideal case.
Limits and risk
This page is a mathematical illustration. It does not tell you whether a bet or an investment is a good idea, and it does not account for taxes, fees, other bets or your need to spend the money. You can lose money, including all of the amount you put at risk.
Related tools include the expected value calculator, the probability calculator, the position size calculator and the pot odds calculator.
Assumptions and limits
- The chance of winning is a percent from 0 to 100 that you estimate. The page cannot check it.
- The payout is the net profit per dollar risked on a win, and a loss costs the full stake.
- Bets are repeated and independent, and the amount can be any fraction of the bankroll.
- This is not betting, trading or investment advice. Nothing is stored or uploaded.
Frequently asked questions
What is the Kelly criterion?
It is a formula for the share of a bankroll to risk on a bet with a positive expected profit, so that the bankroll grows as fast as possible over many repeated bets. It is (b times p minus q) divided by b.
What does it mean when the answer is zero?
The expected profit is zero or negative at the numbers you entered, so the formula says not to risk anything on that bet. It does not suggest betting the other side.
Why do people use half Kelly?
Because the full amount depends on your estimate of the chance of winning being exactly right, and because full Kelly can swing a lot. A fraction trades some growth for steadier results.
Does this work for investing?
The idea has been applied to investing, but real returns do not fit the simple win or lose model used here. Treat this page as a math illustration and not as advice.