Kelly Criterion Position Sizer
Optimal bet size from win probability and payoff odds: full, half, and quarter Kelly fractions.
How It Works
Enter the net odds received on a win b, the probability of winning p, and your total bankroll. The calculator computes the Kelly fraction f star as b times p minus q divided by b, where q equals one minus p. When f star is positive, it shows dollar amounts for full Kelly, half Kelly, and quarter Kelly position sizes. Use this when evaluating a repeatable strategy with known payoff odds and estimated win rate from backtests or historical samples. Map each trade setup to a single b by dividing expected profit by maximum loss at risk. Update p when your edge changes across market regimes.
Geometric growth rates show expected log wealth increase per bet at each Kelly fraction. Full Kelly maximizes long run compound growth but produces severe drawdowns. Half Kelly and quarter Kelly sacrifice some growth for much lower volatility and better survival through losing streaks. Professional gamblers and quantitative traders rarely use full Kelly in live capital because small errors in p or b cause massive overbetting. Compare growth rates side by side before choosing a fraction. Expected value per unit risked displays separately so you confirm positive edge before sizing.
Professional gamblers and quantitative traders rarely use full Kelly in live capital because small errors in p or b cause massive overbetting. Compare growth rates side by side before choosing a fraction. Expected value per unit risked displays separately so you confirm positive edge before sizing.
Use Kelly Criterion Position Sizer whenever inputs change: after new backtest results, revised win rates, or updated payoff structures. Bookmark the page for quick reruns without installing software.
Step by step
- Open Kelly Criterion Position Sizer and enter win probability, odds b, and bankroll.
- Review Kelly fraction, dollar sizes, and geometric growth rates for each fraction.
- Adjust assumptions and compare full versus fractional Kelly before committing capital.
Worked example
Example scenario for Kelly Criterion Position Sizer: 55% win rate, 1:1 odds, $10,000 bankroll. Enter those values above to reproduce the walkthrough described in How it works.
Adjust one input at a time to see sensitivity.
When to use this calculator
Reach for Kelly Criterion Position Sizer when optimal bet size from win probability and payoff odds: full, half, and quarter Kelly fractions.
Common mistakes
Confirm tickers, percentages, and dates before acting.
Running a single baseline scenario ignores tail risks.
The Formula
f* = (b × p − q) / b
where p = win probability, q = 1 − p
b = net profit per $1 risked
g = p × ln(1 + b × f) + q × ln(1 − f)
Full Kelly maximizes geometric growth but assumes accurate p and b estimates. Fractional Kelly reduces ruin risk from estimation error. Never bet more than you can afford to lose. Independent bets are assumed; correlated outcomes require adjusted sizing.
Limitations and assumptions
Full Kelly maximizes geometric growth but assumes accurate p and b estimates. Fractional Kelly reduces ruin risk from estimation error. Never bet more than you can afford to lose. Independent bets are assumed; correlated outcomes require adjusted sizing. Kelly Criterion Position Sizer does not replace personalized advice.
Key terms
- What is the Kelly Criterion
- The Kelly Criterion is a formula that calculates the optimal fraction of capital to risk on a positive expected value bet.
- How do I convert my trade payoff into odds b
- Odds b represent net profit per dollar risked on a winning outcome.
- Model assumption
- Half Kelly bets half the Kelly fraction, capturing most growth with lower variance.
Compare alternatives
Pair with Position Sizing Calculator when translating Kelly output into share counts for a specific stock price. Use Risk Reward Ratio to confirm the odds input matches your actual payoff structure before sizing.
FAQ
What is the Kelly Criterion?
The Kelly Criterion is a formula from information theory that calculates the optimal fraction of capital to risk on a positive expected value bet to maximize long term geometric growth. Full Kelly maximizes compound growth rate but produces high volatility and large drawdowns. Most professional traders and investors use half Kelly or quarter Kelly in practice because estimation error in win rate and payoff ratio makes full Kelly dangerously aggressive. A small error in p or b can recommend betting far more than optimal.
How do I convert my trade payoff into odds b?
Odds b represent net profit per dollar risked on a winning outcome. If you risk $100 and win $150 total return, profit is $50 so b equals 0.5. If you risk $100 and receive $200 on a win, profit is $100 so b equals 1.0 even money. For stock trades, compute b as expected gain divided by expected loss from entry to stop and target. Options and spreads require mapping max loss and max gain into a single b per contract or per unit of capital at risk.
Why use half Kelly or quarter Kelly instead of full Kelly?
Half Kelly bets half the Kelly fraction. It captures roughly 75 percent of the optimal growth rate with dramatically lower variance. Quarter Kelly captures about half the growth with even smoother equity curves. The tradeoff is slower compounding versus survivability through losing streaks. When win probability is estimated with error, fractional Kelly acts as a safety margin against overbetting and ruin.
When does Kelly say not to bet?
When f star is zero or negative, expected value per dollar risked is not positive enough to justify a bet at any size. The tool displays a no bet recommendation. This protects against marginal edges that disappear after fees, slippage, and taxes. Even slightly positive theoretical edges can become negative after transaction costs, so always compare Kelly output to your real world breakeven.
What does geometric growth rate mean?
Geometric growth rate g equals p times ln of one plus b f plus q times ln of one minus f, where f is the fraction of bankroll wagered. Higher g means faster compound growth of wealth over many independent bets. Full Kelly maximizes g but at the cost of extreme path volatility. Compare g across full, half, and quarter Kelly to see how much growth you sacrifice for smoother outcomes.
Related Tools
Pair with Position Sizing Calculator when translating Kelly output into share counts. Use Risk Reward Ratio to validate the odds input matches your trade structure. Review Probability of Ruin for retirement drawdown context when applying Kelly logic to portfolio withdrawal rates.