Kelly Criterion Calculator

Frequently Asked Questions

What is the Kelly criterion?

A formula for the bet or position fraction that maximises long-run logarithmic growth: f* = (b·p − q) ÷ b, where p is win probability, q = 1 − p, and b is the payoff ratio.

Why do people use fractional Kelly?

Full Kelly maximizes long-run growth in theory, but it produces large swings in practice and is very sensitive to errors in your win-probability estimate. Betting half or a quarter of the Kelly fraction preserves most of the growth benefit while cutting drawdowns significantly, making it more practical for real trading and investing.

What if the formula gives a negative number?

A negative Kelly fraction means the bet or trade has no mathematical edge given your inputs. The prescribed action is to take no position at all, or to consider the opposite side of the trade. Review your assumed win probability and payoff ratio, since small errors in those estimates can flip the sign.

Where is it applied?

Originally for gambling and information theory, it is now used for position sizing in trading and portfolio allocation where edge and odds can be estimated.

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This calculator provides estimates for educational purposes only and is not investment advice. Past performance does not guarantee future results. Consult with a qualified financial advisor before making investment decisions. All investments carry risk, including potential loss of principal.

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How This Calculator Works

The Kelly criterion finds the fraction of bankroll that maximizes the long-run geometric growth rate. For a bet with win probability W and win/loss payoff ratio R, the optimal fraction is f* = W − (1 − W) ÷ R. Equivalently, in the continuous investing form, f* = (expected excess return) ÷ variance - the edge divided by the risk you take to capture it. Betting more than f* actually lowers long-run growth and sharply raises ruin risk; betting less grows slower but far more smoothly. Because the formula is acutely sensitive to the inputs, practitioners almost universally use fractional Kelly - half or quarter of f* - which keeps roughly three-quarters of the growth rate while cutting volatility and drawdown dramatically. This tool reports full, half, and quarter Kelly plus a bankroll-stake example.

Worked Numeric Example

Win probability W = 55% (0.55), win/loss ratio R = 1.5. f* = 0.55 − (1 − 0.55) ÷ 1.5 = 0.55 − 0.45 ÷ 1.5 = 0.55 − 0.30 = 0.25, i.e. 25% of bankroll for full Kelly. Half-Kelly is 12.5%, quarter-Kelly 6.25%. On a $10,000 bankroll full Kelly stakes $2,500 per bet - aggressive enough that a normal losing streak produces gut-wrenching swings, which is precisely why most disciplined players would risk the half-Kelly $1,250 instead. Expected value per unit risked is 0.55 × 1.5 − 0.45 ≈ +0.375, a genuine edge.

Real-World Use

Kelly originated in information theory (John Kelly at Bell Labs, 1956) and was popularized by blackjack card counters and sports bettors and by investors such as Ed Thorp, whose hedge fund applied edge-over-variance sizing for decades. In markets the investing form, f* = (expected excess return) ÷ variance, is why concentrated high-conviction managers reference Kelly when defending large single-name weights - and also why almost all of them still scale to a fraction of it, because real-world probabilities are estimated rather than known and the penalty for overbetting is severe and one-sided. Warren Buffett and Charlie Munger have informally endorsed Kelly-like thinking (bet big when the odds are heavily in your favor, bet nothing otherwise) while being scathing about full-Kelly aggression, which captures the practical consensus: the formula is a ceiling to respect, not a target to hit.

Common Mistakes

Trusting estimated win rates - overstating W by a few points can flip a profitable system into a ruinous one.

Using full Kelly; the variance is brutal, with frequent 50%+ drawdowns even with a true edge.

Ignoring correlation across simultaneous bets - the single-bet formula assumes independence.

Applying Kelly to negative-expectation games, where the answer is simply "do not bet" - the formula returns a negative or zero fraction.

Forgetting that fees, slippage, and taxes reduce the real edge, so the honest f* is lower than the gross-number formula suggests.

Limitations & Strong Caveat

Kelly assumes you know the true probabilities, payoffs are stationary, and outcomes are independent - none of which hold cleanly in markets. It optimizes long-run growth, not comfort: full-Kelly paths are extraordinarily volatile and high variance. Always favor fractional Kelly and cap exposure with separate risk controls. This is an educational tool for understanding bet sizing - it is not investment, trading, or gambling advice, and aggressive sizing can lead to substantial or total loss of capital.

Kelly Criterion Calculator

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