Calculate the mathematically optimal percentage of capital to allocate per trade using the Kelly Criterion. Includes half-Kelly and quarter-Kelly options with overbetting warnings.
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What is Kelly Criterion Calculator?
The Kelly Criterion is the gold standard for mathematically optimal position sizing. Developed by John L. Kelly Jr. at Bell Labs in 1956, it calculates the exact percentage of your capital that maximizes long-term wealth growth — no more, no less.
Our Kelly Criterion calculator takes your win rate, average win, average loss, and total capital to compute the Kelly percentage, optimal dollar allocation, expected growth rate, and win/loss ratio. Choose between Full Kelly (maximum theoretical growth), Half Kelly (reduced volatility, ~75% of growth), or Quarter Kelly (conservative approach).
The calculator includes an overbetting warning when Kelly exceeds 25% — a sign that the formula recommends an dangerously large position. A confidence indicator tells you whether your trade sample size is sufficient for reliable calculations. The scenario panel lets you adjust win rate and average win with sliders to see how the optimal allocation changes in real-time.
Steps:
Enter your historical win rate as a percentage.
Enter your average winning trade amount.
Enter your average losing trade amount.
Enter your total trading capital.
Optionally enter total trades for confidence assessment.
Choose Full, Half, or Quarter Kelly based on your risk tolerance.
Review the Kelly percentage, optimal allocation, and expected growth rate.
Formula
Kelly% = W − (1 − W) / R
Where:
W = Win Rate (as decimal, e.g., 0.55 for 55%)
R = Win/Loss Ratio (Average Win ÷ Average Loss)
Half Kelly = Kelly% × 0.5
Quarter Kelly = Kelly% × 0.25
Optimal Allocation = Capital × Kelly% / 100
Example: Win Rate = 55%, Avg Win = $500, Avg Loss = $300
R = 500/300 = 1.67
Kelly% = 0.55 − (1 − 0.55) / 1.67 = 0.55 − 0.27 = 28.1%
Half Kelly = 14.05%
On $50,000 capital: Full = $14,050, Half = $7,025, Quarter = $3,512
Use Cases
Stock traders optimizing position sizes based on historical edge
Forex traders sizing positions with Kelly-adjusted risk
Sports bettors calculating optimal bet sizes
Portfolio managers allocating capital across strategies
Key Benefits
Mathematically optimal position sizing
Maximizes long-term wealth growth
Built-in overbetting protection
Scenario analysis with live sliders
Pro Tips
Use Half Kelly for a balance of growth and reduced volatility
Recalculate Kelly monthly with your latest trade data
Never use Kelly if your win rate or edge is uncertain
Combine Kelly with maximum position caps for extra safety
Common Mistakes to Avoid
Using Full Kelly without understanding the volatility
Calculating Kelly with insufficient trade history
Ignoring transaction costs and slippage
Not adjusting Kelly as win rate changes over time
Key Terms Explained
Kelly Criterion: Formula for optimal bet size maximizing long-term growth
Win/Loss Ratio: Average win divided by average loss
Half Kelly: 50% of full Kelly recommendation, reduces volatility ~50%
Overbetting: Allocating more than optimal, reducing long-term growth
Related Concepts
Position Size Calculator – Risk-based position sizing
Risk-Reward Ratio Calculator – Evaluate trade quality
Drawdown Recovery Calculator – Understand recovery math
Example
You have a 55% win rate with average wins of $500 and average losses of $300. Win/Loss Ratio = 500/300 = 1.67. Kelly% = 0.55 − (0.45/1.67) = 0.55 − 0.27 = 28.1%. Since this exceeds 25%, the calculator warns of overbetting. Half Kelly = 14.05%. On $50,000 capital, the Half Kelly allocation = $7,025 per trade. Expected growth rate = 2.34% per trade.
Frequently Asked Questions
What is the Kelly Criterion?
The Kelly Criterion is a mathematical formula developed by John L. Kelly Jr. in 1956 at Bell Labs. It calculates the optimal fraction of your bankroll to bet or invest in order to maximize long-term wealth growth. The formula is: Kelly% = W − (1−W)/R, where W is your win rate (as a decimal) and R is your win/loss ratio (average win divided by average loss).
Why would I use Half Kelly instead of Full Kelly?
Full Kelly maximizes theoretical growth but produces extreme volatility — drawdowns of 50% or more are common. Half Kelly (using 50% of the Kelly recommendation) reduces volatility by about 50% while still capturing about 75% of the growth. It's the most popular choice among professional traders and investors.
What does a negative Kelly percentage mean?
A negative Kelly percentage means your edge is negative — your win rate and win/loss ratio combination doesn't produce a positive expected value. In this case, the Kelly Criterion recommends not betting at all. You should either improve your strategy or avoid trading until you have a positive edge.
How many trades do I need for Kelly to be reliable?
The Kelly Criterion assumes you know your true win rate and win/loss ratio. In practice, you need at least 30 trades for a rough estimate, 100+ trades for moderate confidence, and 300+ trades for high confidence. With fewer trades, your estimates may be skewed by luck rather than skill.
Is the Kelly Criterion used in real trading?
Yes, the Kelly Criterion is used by professional traders, hedge funds, and famous investors. Edward Thorp used it for card counting and investing. Warren Buffett and Bill Gross have referenced Kelly-like position sizing. However, most professionals use fractional Kelly (half or quarter) to reduce the extreme volatility of full Kelly.
What is the overbetting warning?
When Kelly% exceeds 25%, it means the formula recommends allocating more than a quarter of your capital to a single trade. This is extremely risky — a string of losses could devastate your account. The warning suggests switching to Half Kelly (12.5% max) or Quarter Kelly (6.25% max) for safer position sizing.
Can Kelly Criterion be used for portfolio allocation?
Yes, the Kelly Criterion can be extended to portfolio allocation across multiple assets. However, the multi-asset Kelly formula is more complex and requires estimating correlations between assets. For single-asset position sizing, the basic formula works well. For portfolios, consider using a Kelly-based optimizer or consulting a financial professional.
What are the limitations of the Kelly Criterion?
Kelly assumes: (1) you know your true win rate and win/loss ratio, (2) each trade is independent, (3) you can reinvest profits continuously, and (4) there are no transaction costs. In reality, win rates change, trades may be correlated, and commissions/slippage reduce returns. These limitations are why most traders use fractional Kelly.
How does Kelly compare to fixed fractional position sizing?
Fixed fractional sizing (e.g., always risking 2% per trade) is simpler but doesn't account for your edge. Kelly is mathematically optimal but requires accurate edge estimation. In practice, many traders use a hybrid approach: calculate Kelly to understand their theoretical optimal, then use a fixed fraction (1-3%) that feels comfortable and is well below the Kelly recommendation.
Should I recalculate Kelly after every trade?
Yes, your win rate and win/loss ratio change with each trade outcome. Recalculating Kelly periodically (weekly or monthly) keeps your position sizing aligned with your current edge. However, avoid overreacting to short-term results — use a rolling average of your last 100+ trades for stability.
Can the Kelly Criterion guarantee profits?
No. The Kelly Criterion optimizes position sizing for long-term growth given a positive edge, but it cannot guarantee profits. You can still have losing streaks, and if your edge disappears (win rate drops or losses increase), Kelly will eventually recommend reducing or stopping your bets. It's a risk management tool, not a profit guarantee.
