Kelly criterion calculator
Enter your estimated true probability of winning and the price you're getting. We'll compute the optimal Kelly stake plus safer fractional Kelly recommendations.
What this does
Kelly says: your edge per unit risked, scaled by the inverse of your potential loss, equals the optimal fraction of bankroll to bet. In math: f* = (b × p - q) / b, where:
- b = decimal odds − 1 (profit per unit risked if you win)
- p = your estimated probability of winning
- q = 1 − p (probability of losing)
Full Kelly maximizes long-run bankroll growth, but it's emotionally aggressive — a 60% bet on a 70% favorite still has a 30% chance of a catastrophic loss. Most pros use quarter Kelly (f*/4) or half Kelly (f*/2) which keep most of the growth while dramatically reducing drawdown variance.
Limitations
Kelly assumes you know p exactly. In practice you never do — your model has uncertainty. If you estimate p = 60% but the true probability is 55%, full Kelly will bet a size that exceeds the optimum for the actual edge, leading to long-run bankroll erosion. Fractional Kelly partially compensates by under-betting relative to your estimate.
See also: Kelly criterion glossary entry, bankroll management, expected value.
Kelly criterion calculator — FAQ
What is the Kelly criterion?+
A formula derived by John Kelly Jr. (Bell Labs, 1956) that computes the bet size which maximizes the long-run geometric growth rate of a bankroll. Given a known edge and odds, Kelly tells you what fraction of your bankroll to risk on each bet.
What's the Kelly formula?+
f* = (bp - q) / b, where b = decimal odds minus 1, p = your estimated probability of winning, q = 1 - p. The result f* is the fraction of your bankroll to wager. Example: 60% probability at +200 odds (b=2). f* = (2 × 0.6 - 0.4) / 2 = 0.4. Bet 40% of bankroll.
Should I always bet full Kelly?+
Almost never. Full Kelly produces extremely high variance — you can routinely see 30-50% drawdowns even when you're winning long-term. Most professionals use fractional Kelly (quarter or half) which trades a small reduction in long-run growth for dramatically lower drawdowns.
What if I'm wrong about my edge?+
Kelly is extremely sensitive to errors in your probability estimate. A 5pp overestimate of your true edge can swing Kelly's recommendation from a sensible bet to a catastrophic one. This is why professionals use fractional Kelly: it builds in a margin of safety against estimation error.
When does Kelly recommend zero or negative?+
If your estimated probability times the decimal odds is less than 1, Kelly returns zero or negative — meaning no edge exists, don't bet. Negative Kelly never means "bet the other side"; it means "don't bet this side."