Kelly Criterion Calculator
Calculate the optimal stake size to maximize long-term bankroll growth while managing risk.
What Is the Kelly Criterion?
The Kelly Criterion is a mathematical formula that determines the optimal size of a series of bets to maximize long-term wealth growth. Developed by John L. Kelly Jr. at Bell Labs in 1956, it was originally designed for information theory in telecommunications, but was quickly adopted by gamblers and investors — including Warren Buffett's partner Charlie Munger.
The formula answers a deceptively simple question: given a bet with a known edge, what fraction of your bankroll should you stake? Bet too large and you risk ruin through variance. Bet too small and you leave growth on the table. Kelly finds the mathematically optimal middle ground.
The formula is: f* = (bp − q) / b, where f* is the fraction of bankroll to bet, b is the net odds (decimal odds − 1), p is the probability of winning, and q is the probability of losing (1 − p).
How the Kelly Calculator Works
Input three values: the odds being offered, your estimated probability of winning, and your current bankroll. The calculator applies the Kelly formula to determine the optimal fraction and dollar amount to wager.
The calculator also provides fractional Kelly recommendations. Many professional bettors use half-Kelly (50% of the recommended stake) or quarter-Kelly to reduce volatility at the cost of slightly slower growth. Research shows that fractional Kelly outperforms full Kelly for most bettors due to estimation errors in probability assessment.
Additionally, the tool shows what happens if your probability estimate is wrong. A sensitivity analysis reveals how much the optimal stake changes for small errors in your estimated win probability — critical for real-world application where true probabilities are never known exactly.
Why Bet Sizing Matters
Even if you consistently find +EV bets, poor bet sizing can turn a winning strategy into a losing one. Overbetting (staking more than Kelly) leads to catastrophic bankroll swings and potential ruin. Underbetting leaves profit on the table.
Consider this: if you have a 55% edge on an even-money bet, Kelly says to bet 10% of your bankroll. If you instead bet 25%, your expected growth rate actually decreases despite betting more, and your risk of ruin skyrockets. At 50% of bankroll per bet, your expected long-term growth rate is zero — you're coin-flipping your entire bankroll.
This is why understanding Kelly isn't optional for serious bettors. It's the mathematical foundation of sustainable bankroll growth.
Worked Example: Sizing a +EV NFL Bet
You have a $5,000 bankroll. You find a bet at +150 odds and estimate a 45% win probability. How much should you bet?
- Odds: +150 (decimal: 2.50, net odds b = 1.50)
- Win probability (p): 0.45, Loss probability (q): 0.55
- Kelly fraction: f* = (1.50 × 0.45 − 0.55) / 1.50 = (0.675 − 0.55) / 1.50 = 0.0833
- Full Kelly bet: $5,000 × 8.33% = $416.67
- Half-Kelly bet: $5,000 × 4.17% = $208.33 (recommended)
- Quarter-Kelly bet: $5,000 × 2.08% = $104.17 (conservative)
Full Kelly suggests $417, but most professionals would use half-Kelly ($208) or quarter-Kelly ($104) to account for uncertainty in the probability estimate. Over time, half-Kelly achieves 75% of full-Kelly growth with significantly less volatility.
Frequently Asked Questions
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