The Kelly Criterion is the gold standard for optimal position sizing in betting, trading, and investing. Developed by John Kelly at Bell Labs, this mathematical formula tells you exactly what percentage of your bankroll to wager to maximize long-term growth while managing risk.
The Kelly Criterion is a formula for bet sizing that maximizes the expected logarithm of wealth (geometric mean return). Unlike other methods, Kelly mathematically optimizes for long-term growth rather than just expected value. The result is expressed as a percentage of your total bankroll that should be risked on a given opportunity. Kelly assumes you have an edge (positive expected value) and tells you how aggressively to bet it.
Instant Kelly Criterion calculation. Fractional Kelly recommendations (full, half, quarter). Expected value edge calculation. Risk indicators for negative EV bets. Mobile-friendly design. Formula explanation and examples. Copy results functionality. Privacy-protected calculations. Free unlimited usage. Professional-grade accuracy.
Enter your estimated win probability as a percentage. Input your win/loss ratio (average win amount divided by average loss amount). Our calculator applies the Kelly formula: f* = (bp - q) / b. Results show the optimal percentage of your bankroll to bet, along with fractional recommendations for risk management.
Sports betting bankroll management. Stock and options position sizing. Forex trading lot sizing. Poker bankroll decisions. Cryptocurrency trading allocation. Investment portfolio concentration. Business capital allocation. Trading strategy optimization. Risk-adjusted bet sizing. Long-term wealth building.
Our Kelly Criterion Calculator provides instant precise calculations with both full Kelly and fractional Kelly recommendations. Unlike basic calculators, we clearly indicate negative expected value situations and provide risk context. Whether you're betting, trading, or investing, our tool helps you size positions for optimal long-term growth.
Sports bettors managing bankrolls. Stock traders sizing positions. Options sellers allocating capital. Cryptocurrency traders. Poker players at all levels. Investment managers. Anyone making probabilistic bets with positive expected value. Risk managers. Professional gamblers. Value investors.
Estimate your win probability based on historical data or analysis. Calculate your win/loss ratio from past results. Enter both values into the calculator. Review the Kelly percentage and status. Consider using half-Kelly for safety. Apply the recommended percentage to your current bankroll. Track results and adjust estimates over time.
Use half-Kelly or quarter-Kelly to account for estimation error. Keep detailed records to refine probability estimates. Be conservative with your edge assumptions. Never bet negative Kelly. Consider transaction costs. Don't exceed Kelly even with high confidence. Diversify across uncorrelated opportunities. Reassess when conditions change. Use with proper stop losses. Maintain emotional discipline.
Requires accurate probability estimates which are difficult to obtain. Full Kelly can produce extreme volatility. Assumes infinite betting opportunities. Doesn't account for changing market conditions. Ignores transaction costs and slippage. Assumes no correlation between bets. Can recommend position sizes too large for practical risk tolerance. Doesn't prevent going broke in finite timeframes.
The Kelly Criterion is a mathematical formula developed by John Kelly at Bell Labs in 1956. It calculates the optimal fraction of your bankroll to bet on a favorable gamble to maximize long-term growth. The formula is: f* = (bp - q) / b, where p is win probability, q is loss probability, and b is the win/loss ratio.
The Kelly formula is: f* = (bp - q) / b. Where: f* = optimal fraction of bankroll to bet, b = average win divided by average loss (odds received), p = probability of winning, q = probability of losing (1-p). For example, if you have 60% win probability with 2:1 odds, Kelly = (2×0.6 - 0.4) / 2 = 40% of bankroll.
Yes, our Kelly Criterion Calculator is completely free with no usage limits, registration, or hidden fees. Calculate optimal betting and position sizes for unlimited scenarios.
Full Kelly betting can be extremely volatile and requires perfect probability estimates. Half-Kelly (betting 50% of the Kelly amount) reduces variance significantly while only slightly reducing growth. Many professional traders use quarter-Kelly or half-Kelly for safety and peace of mind.
A negative Kelly percentage means the bet has negative expected value (EV). You should completely avoid these bets as they will lead to long-term losses. The formula is specifically designed to identify favorable opportunities.
Yes! Kelly can be applied to position sizing in trading. Calculate your win rate on similar setups and your average win/loss ratio. However, many traders use half-Kelly due to uncertainty in probability estimates and the need to avoid large drawdowns.
Kelly maximizes the geometric mean of returns (long-term growth rate). Fixed fractional betting uses a fixed percentage regardless of edge. Martingale increases bets after losses. Kelly is mathematically optimal for growth but requires accurate inputs.
Kelly is sensitive to probability estimates. Being off by just 5-10% can significantly change results. This is why fractional Kelly is recommended - it provides a buffer for estimation errors. Always be conservative with your probability estimates.
Yes, but it becomes more complex. You need to calculate the optimal allocation across all opportunities simultaneously. Many bettors simply divide Kelly by the number of simultaneous bets or look for specialized multi-bet Kelly calculators.
Kelly assumes: infinite betting opportunities, accurate probability estimates, no transaction costs, no correlation between bets, and that you cannot go broke (no margin). In reality, these assumptions rarely hold perfectly, which is why fractional Kelly is so popular.