Calculate the mathematically optimal fraction of your bankroll to risk using the Kelly Criterion formula.
High Kelly Fraction
Full Kelly exceeds 25%. Consider using Half or Quarter Kelly to reduce volatility and drawdown risk.
Full Kelly
Aggressive
25.00%
$2,500.00
Half Kelly
Recommended
12.50%
$1,250.00
Quarter Kelly
Conservative
6.25%
$625.00
Full Kelly Final
$964,728.82
Half Kelly Final
$312,760.14
Quarter Kelly Final
$75,718.34
Kelly Criterion calculations are estimates. Past performance does not guarantee future results.
Always use fractional Kelly in practice. Last updated: February 2026
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Input your historical win rate as a percentage (0-100%). This is the proportion of your trades or bets that result in a profit. For example, if 55 out of 100 trades are profitable, enter 55%. Accuracy here is critical since the Kelly formula is highly sensitive to win rate estimates.
Enter the average dollar amount you gain on winning trades and the average dollar amount you lose on losing trades. These values determine your win/loss ratio (the 'b' in the Kelly formula). For example, if you average $150 on wins and $100 on losses, your ratio is 1.5:1.
Provide your total available capital or bankroll. The calculator uses this to convert Kelly percentages into concrete dollar amounts for position sizing. This helps you see exactly how much to risk on your next trade or bet based on your edge.
Examine the Full Kelly, Half Kelly, and Quarter Kelly recommendations. The visual gauge shows where your sizing falls across conservative to aggressive zones. Review the expected growth simulation to understand how different Kelly fractions affect long-term compounding and drawdown risk.
Understanding optimal position sizing
The Kelly Criterion is a mathematical formula for optimal bet sizing developed by John L. Kelly Jr. at Bell Labs in 1956. Originally published in the Bell System Technical Journal under the title "A New Interpretation of Information Rate," Kelly's work addressed the problem of how a gambler with inside information on horse races (transmitted over a noisy telephone line) should size their bets to maximize the long-term growth rate of their bankroll. The formula emerged from information theory, building directly on Claude Shannon's foundational work on communication channels.
The Kelly Criterion formula is elegantly simple:
f = (bp - q) / b*
Where:
An equivalent formulation used widely in trading is: *f = p - (q / b), which can be expressed as *f = p - ((1 - p) / (avgWin / avgLoss)). This version directly shows that the Kelly fraction equals the win probability minus the loss probability adjusted by the payoff ratio.
The Kelly Criterion is the only sizing strategy that provably maximizes the geometric growth rate of capital over time. This is not a claim about any single bet. It is a theorem about the long-run compounding behavior of repeated wagers with a positive edge. Using Full Kelly, a bettor will almost surely end up with more money than any other strategy after a sufficiently long sequence of bets.
However, Full Kelly comes with significant volatility. The standard deviation of returns under Full Kelly is substantial, and drawdowns can be severe. In practice, most professional traders and gamblers use fractional Kelly. Half Kelly retains approximately 75% of the growth rate but cuts variance roughly in half. Quarter Kelly sacrifices more growth but produces far smoother equity curves.
After Kelly published his paper, the formula was quickly adopted by gamblers and then by investors. Edward O. Thorp, a mathematics professor who developed card-counting strategies for blackjack, was one of the first to apply Kelly sizing systematically. Thorp later founded Princeton Newport Partners, one of the most successful quantitative hedge funds of its era, where Kelly-based position sizing was central to their risk management.
Today, the Kelly Criterion influences portfolio construction at quantitative firms, sports betting syndicates, poker professionals, and individual retail traders. It provides a rigorous, mathematically grounded answer to the question every trader faces: "How much of my capital should I risk on this opportunity?"
The Kelly Criterion assumes: (1) you have an accurate estimate of your win probability and payoff ratio, (2) outcomes are independent, (3) you can bet any fractional amount, and (4) your edge remains constant over time. In practice, none of these hold perfectly. Estimation error in win rate or payoff ratio can lead to significant over-betting, which is why fractional Kelly (Half or Quarter) is strongly recommended as a margin of safety.
A positive Kelly fraction requires positive expected value. The expected value per trade is calculated as: EV = (p x avgWin) - (q x avgLoss). If EV is negative, the Kelly fraction will be negative, meaning you have no edge and should not bet. The Kelly Criterion goes beyond expected value by optimizing for geometric growth rather than arithmetic gain, accounting for the asymmetric impact of losses on compounding capital.
How traders use the Kelly Criterion
Determine optimal position size for equity and options trades based on historical win rate and risk/reward ratio. Avoid over-concentrating in a single position while maximizing long-term portfolio growth. Half Kelly is the standard recommendation for equity traders due to estimation uncertainty.
Calculate optimal stake sizes for sports wagers where you have identified value (positive expected value). Convert subjective probability estimates into precise bet amounts. Critical for professional bettors managing bankrolls across multiple simultaneous wagers.
Apply Kelly sizing to volatile cryptocurrency markets where position sizing discipline is essential. The high volatility of crypto assets makes fractional Kelly particularly important. Helps prevent ruin from over-leveraged positions in a market known for extreme drawdowns.
Size bets and all-in decisions using Kelly principles when you have an estimated edge. Poker players use Kelly to determine how much of their bankroll to buy in with for tournaments or cash games, balancing growth rate against risk of ruin.
Calculate lot sizes for currency trades based on your strategy's historical performance metrics. Forex traders can convert Kelly percentages to specific pip risk and lot sizes. Particularly useful for scalping and swing trading strategies with well-documented track records.
Apply Kelly principles to startup investment decisions where win rates are low but payoffs can be enormous. Helps angel investors determine what fraction of their investable capital to allocate per deal, accounting for the power-law distribution of venture returns.
Master optimal position sizing
This calculator determines optimal position sizing using the Kelly Criterion formula. Enter your trading or betting statistics and the tool computes the mathematically optimal fraction of your capital to risk, along with conservative fractional Kelly alternatives.
Win Rate (%): Your historical winning percentage. If 55 out of 100 trades are profitable, enter 55. This must be between 0 and 100. The accuracy of your Kelly calculation depends entirely on the accuracy of this input. Use at least 30-50 trades to get a meaningful win rate estimate; fewer trades produce unreliable statistics.
Average Win Amount ($): The average profit on your winning trades. Sum all winning trade profits and divide by the number of winning trades. For example, if your last 10 winners were $200, $150, $300, $100, $250, $180, $220, $190, $270, $140, your average win is $200.
Average Loss Amount ($): The average loss on your losing trades (enter as a positive number). Sum all losing trade dollar amounts and divide by the number of losing trades. This, combined with average win, determines your payoff ratio (b = avgWin / avgLoss).
Account Balance ($): Your total trading capital or bankroll. Used to convert the Kelly percentage into a concrete dollar position size.
Full Kelly (f):* The mathematically optimal fraction that maximizes long-term geometric growth rate. However, it produces high volatility and large drawdowns. Most practitioners consider Full Kelly too aggressive for real-world use.
Half Kelly (f/2):* Retains approximately 75% of the growth rate of Full Kelly while cutting variance roughly in half. This is the most commonly recommended fraction for professional traders and serious bettors.
Quarter Kelly (f/4):* Very conservative sizing that prioritizes capital preservation. Growth is slower but drawdowns are minimal. Suitable for traders with uncertain edge estimates or those in early stages of validating a strategy.
The visual gauge displays a spectrum from conservative to dangerous:
The simulator projects expected account growth over a configurable number of trades. It shows three curves (Full, Half, Quarter Kelly) to illustrate the trade-off between growth rate and volatility. The simulation uses the formula:
Expected growth per trade = p * ln(1 + f * b) + q * ln(1 - f)
This is the Kelly growth rate, where higher fractions produce faster expected growth up to Full Kelly, beyond which growth rate actually decreases.
Everything you need to know
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