Kelly Criterion Calculator
Calculate your optimal bet size based on your win rate and payoff ratio. See full Kelly, half Kelly, and quarter Kelly recommendations.
The Kelly Criterion Formula
The Kelly criterion is a mathematical formula that determines the optimal percentage of your capital to risk on a single trade or bet. John Kelly published it in 1956 while working at Bell Labs. Ed Thorp took the formula from information theory to blackjack tables and then to Wall Street.
The formula: f* = (bp - q) / b, where b is the odds received (average win divided by average loss), p is the probability of winning, and q is the probability of losing (1 - p).
Simplified: K% = W - ((1 - W) / R), where W is your win rate and R is your payoff ratio.
Example: You win 55% of your trades. Your average winner returns $200, and your average loser costs $100. Payoff ratio R = 200/100 = 2.0. Kelly% = 0.55 - (0.45 / 2.0) = 0.55 - 0.225 = 0.325, or 32.5% of your bankroll per trade.
The formula works for stocks, forex, crypto, options, and sports betting. You can replicate this calculation in Excel using the formula =B1-(1-B1)/B2 where B1 is win rate and B2 is payoff ratio.
Why Half Kelly Beats Full Kelly in Practice
Full Kelly maximizes long-term growth rate. It also produces drawdowns that most traders cannot stomach. A 50% drawdown requires a 100% gain to recover. Full Kelly makes drawdowns of that magnitude probable over hundreds of trades.
Half Kelly captures roughly 75% of the growth rate with far less volatility. The tradeoff is worth it. Warren Buffett and Ed Thorp both advocate fractional Kelly approaches because real-world conditions include estimation error, changing market regimes, and correlated outcomes.
See how your Kelly fraction affects your probability of account ruin with the risk of ruin calculator.
When Kelly Doesn't Work
The Kelly formula requires accurate win rate and payoff estimates. Most traders overestimate both. If you feed the formula inflated numbers, it prescribes oversized positions that accelerate losses.
Kelly assumes each trade outcome is independent of the last. Markets exhibit serial correlation, momentum, and regime shifts. A strategy that wins 60% in a trending market may win 35% in a choppy one.
The formula also ignores fat tails. Flash crashes, overnight gaps, and liquidity failures can produce losses larger than your planned stop loss. No formula accounts for events that fall outside your data set.
For a simpler approach based on fixed risk per trade, use the position size calculator. Track your win rate and average payoff in a trading journal, then apply Kelly sizing when you practice on the tradicted simulator.
Frequently Asked Questions
Frequently Asked Questions
The Kelly criterion is a formula that calculates the optimal fraction of your capital to risk on a bet or trade. John Kelly developed it at Bell Labs in 1956. Ed Thorp applied it to blackjack and later to financial markets, proving it could maximize long-term wealth growth when you have a quantifiable edge.
The Kelly formula is f* = (bp - q) / b. The variable b is the payoff ratio (average win divided by average loss), p is the probability of winning, and q is the probability of losing (1 minus p). A simplified version: K% = W - ((1 - W) / R), where W is the win rate as a decimal and R is the payoff ratio.
Half Kelly means betting 50% of the amount the full Kelly formula recommends. Half Kelly captures roughly 75% of the full Kelly growth rate while cutting volatility and drawdowns by a large margin. Most professional traders and investors use half Kelly or less because overestimating your edge leads to overbetting.
Start by tracking your trades in a journal to find your win rate and average reward-to-risk ratio. Enter those numbers into the calculator above. The resulting Kelly percentage tells you what fraction of your account to allocate per trade. For stocks, apply this to your position size by multiplying your account balance by the Kelly fraction.
Yes. A negative Kelly percentage means you have no statistical edge on that setup. The expected value of the trade is negative. Do not trade a setup with a negative Kelly. Reassess your strategy, improve your win rate or payoff ratio, or skip the trade.
The Kelly criterion provides a rigorous framework for position sizing, but it requires accurate inputs. Your win rate and average payoff must come from real trade data, not guesses. Most professional traders use fractional Kelly (half or quarter) to build in a margin of safety against estimation error.
Fixed fractional sizing risks a constant percentage of your account on every trade regardless of your edge. The Kelly criterion adjusts position size based on how strong your edge is. Stronger edges warrant larger positions; weaker edges call for smaller ones. Fixed fractional is simpler and more forgiving of estimation errors.