Kelly Criterion Calculator

What is the Kelly Criterion?

The Kelly Criterion is a formula used to determine the optimal size of a series of wagers or investments to maximize the long-term logarithmic growth rate of capital. First described by John L. Kelly Jr. in 1956, the formula is widely used by sports bettors, financial investors, and traders to manage risk and prevent bankroll depletion.

The Kelly Formula

The mathematical expression for the Kelly fraction is:

where:

• $f^*$ is the optimal fraction of the bankroll to wager.
• $b$ is the net odds received on the wager (i.e. payout ratio excluding the stake).
• $p$ is the probability of winning (between 0 and 1).
• $q$ is the probability of losing, computed as $q = 1 - p$.

Fractional Kelly Sizing

While Full Kelly maximizes growth rate mathematically, it can lead to high volatility and significant temporary drawdowns (losses). To mitigate this, many investors use a fractional Kelly strategy (such as Half Kelly or Quarter Kelly), which wagers a smaller fraction (e.g. $0.5 \cdot f^*$ or $0.25 \cdot f^*$). This significantly reduces risk while retaining a large portion of the expected growth rate.

To compare this with other investment return calculators, check out our IRR Calculator or the Compound Interest Calculator.