Kelly Criterion Calculator
Calculate optimal bet size using the Kelly Criterion for trading and prediction markets
Payout for $1 risked (e.g. 2.0 = even money)
Kelly % = (p(b+1) - 1) / b
Edge = p(b+1) - 1
p = win probability
b = decimal odds - 1
Growth = p*ln(1+f*b) + (1-p)*ln(1-f)
The Kelly Criterion is negative (0.00%), which means this bet has a negative expected value. The odds do not compensate for the risk. No amount should be wagered on this outcome.
Risk Warning
Full Kelly is mathematically optimal but extremely volatile. Most professional traders use Half Kelly or less. Overestimating your edge leads to overbetting — the most common mistake.
What Is the Kelly Criterion?
The Kelly Criterion is a mathematical formula that determines the optimal size of a series of bets to maximize the logarithm of wealth (long-term growth rate). It was developed by John L. Kelly Jr. at Bell Labs in 1956, originally for optimizing signal-to-noise ratios in long-distance telephone communications. The formula was quickly adopted by gamblers and investors who recognized its power for capital allocation. In essence, Kelly answers the question: "Given an edge, how much of my bankroll should I wager to grow my wealth as fast as possible without going broke?"
The Math Behind Kelly
For a simple binary bet with win probability p and net odds b (the profit per dollar risked on a win), the Kelly fraction is: f* = (p(b+1) - 1) / b. This is equivalent to f* = p - q/b where q = 1-p is the probability of losing. The formula maximizes the expected logarithm of wealth, E[ln(W)], which is the growth rate of capital. When applied over many independent bets, Kelly betting leads to the highest terminal wealth with probability 1, by the law of large numbers. The geometric mean of returns is maximized, which is why Kelly is sometimes called the "geometric mean maximizing" strategy.
Why Fractional Kelly Is Recommended
While full Kelly maximizes long-term growth, it comes with extreme volatility. The standard deviation of returns under full Kelly is very high, and drawdowns of 50% or more are common even with a genuine edge. In practice, most professional traders and investors use Half Kelly (50% of the full Kelly fraction). Half Kelly achieves approximately 75% of the growth rate of full Kelly while cutting variance in half. Quarter Kelly is even more conservative, achieving about 56% of full Kelly growth with dramatically smoother equity curves. The key insight is that the growth rate curve is relatively flat near the Kelly peak — reducing your bet size modestly below full Kelly costs very little in expected growth but substantially reduces the pain of drawdowns.
Kelly for Crypto Trading vs Prediction Markets
In prediction markets (Polymarket, Kalshi), Kelly is straightforward: you know the price (implied probability), you estimate the true probability, and you calculate the edge. The bet is binary — you win or lose. In crypto trading, Kelly is more nuanced. Outcomes are not binary — you can win or lose varying amounts depending on where you exit. The "Win Rate & Payoff" mode approximates Kelly for trading by using your historical win rate, average win, and average loss. This gives you a sense of optimal position sizing, but remember that trading outcomes are continuous distributions, not binary bets. Kelly works best when your edge estimate is based on a large sample of trades and the underlying process is stationary.
Common Mistakes
Overestimating your edge is the most dangerous mistake. If you think your win probability is 60% but it is really 52%, full Kelly will have you betting far too much, potentially leading to ruin. Always be conservative in your edge estimates and use fractional Kelly as a buffer.
Ignoring correlation is another common error. Kelly assumes independent bets. If your positions are correlated (e.g., multiple long crypto positions that all drop together), your true risk is much higher than Kelly suggests for each individual bet.
Betting above Kelly is mathematically worse than betting below it. Overbetting not only increases variance but actually reduces expected growth. At 2x Kelly, your expected growth rate drops to zero. Beyond 2x Kelly, you have negative expected growth — guaranteed ruin in the long run.
When Kelly Doesn't Apply
Kelly assumes you know your true edge, which is rarely the case in practice. It assumes bets are independent, which breaks down with correlated positions. It assumes you can tolerate any drawdown, which ignores the psychological reality of trading. It also assumes you can bet any fractional amount, which may not be possible with minimum position sizes. Finally, Kelly optimizes for long-term geometric growth, which may not align with your goals if you have a short time horizon or specific financial targets. Use Kelly as a ceiling for position sizing, not a floor — and when in doubt, bet less.