Hong Life CalculatorsUnderstanding the Kelly criterion calculator — concept and principle
The Kelly criterion answers a sizing question: if you have a repeatable bet or trade with a known edge, what fraction of your capital should you risk each time to make it grow fastest over the long run? Traders, investors and gamblers use it as an upper limit on position size. This calculator gives the full Kelly fraction, a fractional Kelly amount you choose, and the expected return per unit staked.
How it is calculated
With win probability p, loss probability q = 1 − p and win/loss ratio b (average win ÷ average loss):
- Full Kelly f* = p − q ÷ b
- Fractional Kelly = f* × chosen fraction
- Edge (expected return per bet) = p × b − q
Equivalently, f* = edge ÷ b. If f* is zero or negative there is no edge and the calculator shows 0%.
The principle
John L. Kelly Jr. published the rule in 1956 while working on information theory at Bell Labs. Instead of maximising the expected gain of a single bet, it maximises the expected logarithm of wealth, which is the same as maximising the long-run compound growth rate. Betting too little grows wealth slowly; betting too much increases the size of losses so that the growth rate falls, and betting about twice the Kelly fraction drives long-run growth to roughly zero. Edward Thorp later applied the rule to blackjack and to investing. The formula assumes independent, repeated bets with known probabilities and payoffs.
Worked example
- Win probability 55%, win/loss ratio 1.2, using 50% of Kelly.
- q = 1 − 0.55 = 0.45.
- Full Kelly = 0.55 − 0.45 ÷ 1.2 = 0.55 − 0.375 = 17.5%.
- Half Kelly = 17.5% × 0.5 = 8.75% of capital per bet.
- Edge = 0.55 × 1.2 − 0.45 = 21% of the amount staked; check: 0.21 ÷ 1.2 = 0.175.
How to read the result
Full Kelly is the most aggressive size that still makes sense, not a recommended size. It produces deep drawdowns, and your estimates of p and b are almost never exact; overestimating them leads to overbetting, which is far more harmful than underbetting. That is why many practitioners use half Kelly or less, which in the standard approximation keeps about three quarters of the growth rate with much smaller swings.
Common mistakes
- Entering the payout odds including the stake when the field asks for net win ÷ loss.
- Estimating the win rate from a short or lucky record.
- Applying it to bets that are correlated, such as several positions in the same market.
Frequently asked questions
What does a negative Kelly fraction mean?
The bet has no positive expected value, so the rule says not to bet at all.
Why use half Kelly?
It lowers volatility and the risk of ruin from estimation errors while giving up only part of the growth.
Can Kelly be used for stocks?
It can guide maximum position size, but return distributions are uncertain, so investors usually use a small fraction of it.
Sources: J. L. Kelly Jr., "A New Interpretation of Information Rate", Bell System Technical Journal, 1956 · E. O. Thorp, "The Kelly Criterion in Blackjack, Sports Betting and the Stock Market"