Kelly Criterion Calculator
Optimize your stake size to balance growth and risk. The gold standard for professional bankroll management.
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Inputs locked
probability
55%
odds
1.90
Result snapshot
fullKelly
5.00%
halfKelly
2.50%
Next step
18+ where legal. Educational calculator only. Bet sizing outputs are not financial advice.
How the Kelly Criterion Calculator Works
The Kelly Criterion is a mathematical formula derived by John L. Kelly Jr. in 1956 while working at Bell Labs. Originally designed for signal transmission, it was quickly adopted by gamblers and investors as the mathematically optimal staking strategy. The core insight: bet proportionally to your edge, not a fixed amount.
The formula: f* = (bp − q) / b, where b = decimal odds minus 1, p = your estimated win probability, and q = 1 − p. The result is the fraction of your bankroll to bet. If Kelly returns 8%, you should bet 8% of your current bankroll — not 8% of your starting bankroll.
The critical caveat: Kelly requires accurate probability estimates. If you overestimate your win probability by even 3%, the formula tells you to overbet, increasing drawdown risk dramatically. This is why professional bettors use half Kelly (50% of the Kelly output) as their default. Half Kelly sacrifices roughly 25% of long-run growth but cuts variance nearly in half — a trade-off almost every professional accepts.
Quarter Kelly (25% of output) is appropriate for bettors who are less confident in their probability estimates or who are betting in highly variable markets like player props or live betting. The mathematical relationship: as you scale down from full Kelly, variance decreases faster than expected growth, making fractional Kelly a highly efficient risk management tool.
The Kelly Formula
f* = (b × p − q) / b Where: b = Decimal Odds − 1 (net profit per unit) p = Win Probability (0 to 1) q = 1 − p (loss probability) f* = Fraction of bankroll to bet Half Kelly = f* × 0.5 (recommended default) Quarter Kelly = f* × 0.25 (conservative)
Kelly Staking Examples
b=1, p=0.55, q=0.45 → f* = (0.55 − 0.45)/1 = 10% full Kelly. Half Kelly = 5%. On $1,000 bankroll: bet $50 to $100.
b=0.90, p=0.52, q=0.48 → f* = (0.90×0.52 − 0.48)/0.90 = 1.3% full Kelly. Half Kelly = 0.65%. Tiny edge = tiny bet.
Frequently Asked Questions
What is the Kelly Criterion?
The Kelly Criterion is a mathematical formula that calculates the optimal fraction of your bankroll to bet. It maximizes long-run expected log wealth — meaning it grows your bankroll faster than any other staking strategy given accurate probability estimates.
Should I use full Kelly or half Kelly?
Most professional bettors use half Kelly (50% of the full Kelly output). It reduces variance by ~50% while sacrificing only ~25% of long-run growth. Full Kelly is mathematically optimal but requires perfectly accurate probability estimates — rarely achievable in practice.
What does a negative Kelly value mean?
A negative Kelly value means the bet has no positive expected value at those odds. The calculator shows 0%, meaning you should not bet. This happens when bp − q < 0, i.e., the offered odds are lower than the true fair odds given your probability estimate.
How accurate does my probability estimate need to be?
Very accurate. The Kelly formula is highly sensitive to probability input. A 3% overestimate on a coin flip (53% instead of 50%) produces the same Kelly as a 3% overestimate on a 70% shot — but with very different real-world consequences. When uncertain, use quarter Kelly as a safeguard.