Kelly Criterion Calculator

Compute the optimal fraction of your bankroll to bet or invest based on your edge and the odds. Supports American, decimal, and fractional odds plus fractional-Kelly sizing.

Kelly Criterion – Main Calculator

Use positive (e.g. +150) or negative (e.g. -120) odds.

%

This is your model or subjective probability, not the implied probability from the odds.

$

Total capital allocated to this strategy or market.

100%

Use 100% for full Kelly, 50% for half-Kelly, 25% for quarter-Kelly, etc.

Kelly Results

If your edge is negative, the Kelly fraction will be ≤ 0 and the calculator will recommend not betting.

Full Kelly fraction (f*)
0.10 (10%)
Scaled Kelly fraction
0.10 (10%)
Recommended stake
$1,000.00
Half-Kelly stake
$500.00
Quarter-Kelly stake
$250.00

Kelly Criterion formula

The Kelly Criterion gives the fraction of your bankroll to risk on a bet when you have an edge. For a simple win/lose bet with fixed odds:

Let:
b = net odds in decimal form (profit per 1 unit staked)
p = your probability of winning
q = 1 − p = probability of losing

Kelly fraction: f* = (b·p − q) / b

If f* <= 0, the bet has no positive edge under your assumptions and Kelly says you should not bet. If f* > 0, you can stake that fraction of your bankroll to maximize long-run growth.

Converting from different odds formats

The calculator accepts American, decimal, and fractional odds and converts them internally to the net odds b:

  • Decimal odds D: b = D − 1
  • Fractional odds n/d: b = n / d
  • American odds A:
    • If A > 0: b = A / 100
    • If A < 0: b = 100 / |A|

Example: Kelly bet for a value wager

Suppose a sportsbook offers +150 (decimal 2.50) on an outcome you believe has a 55% chance of winning.

  • American odds: +150 → b = 150 / 100 = 1.5
  • Your probability: p = 0.55, so q = 0.45
  • Kelly fraction:
    f* = (b·p − q) / b = (1.5·0.55 − 0.45) / 1.5 = (0.825 − 0.45) / 1.5 ≈ 0.25

Kelly suggests betting about 25% of your bankroll. In practice, most professionals would use a smaller fraction (e.g. half-Kelly ≈ 12.5%) to reduce volatility and protect against model error.

Full Kelly vs. fractional Kelly

The full Kelly fraction maximizes the asymptotic growth rate of your bankroll, but it also produces large swings and deep drawdowns. To manage risk, many traders and sports bettors use a scaled-down version:

  • Half-Kelly: bet 0.5 · f*
  • Quarter-Kelly: bet 0.25 · f*

Fractional Kelly sacrifices some theoretical growth in exchange for much smoother equity curves and less sensitivity to errors in your probability estimates.

Common pitfalls when using the Kelly Criterion

  • Overconfident probabilities – If you overestimate your edge, Kelly will tell you to bet too much and you can lose quickly.
  • Ignoring correlation – Kelly assumes independent bets. Highly correlated positions (e.g. multiple bets on the same game or factor) should be sized more conservatively.
  • Limited bankroll in practice – Real-world constraints (margin calls, withdrawal needs, psychological limits) mean you rarely want to risk the full Kelly amount.

Treat the Kelly result as an upper bound on position size, then adjust for diversification, liquidity, and your personal risk tolerance.

Kelly Criterion FAQ

Is the Kelly Criterion always optimal?

Kelly is optimal if your probability estimates are correct, you can bet repeatedly under the same conditions, and you care only about maximizing long-run logarithmic growth. If those assumptions do not hold, a more conservative approach may be better.

Can Kelly Criterion be negative?

Yes. If the expected value of the bet is negative under your assumptions, the Kelly fraction will be ≤ 0. In that case, the strategy is to bet nothing (skip the wager or position).

How does Kelly compare to flat betting?

Flat betting uses a fixed stake per bet regardless of edge. Kelly dynamically adjusts stake size based on both edge and odds, which can significantly improve long-term growth when you truly have an edge, but it also increases variance if your estimates are noisy.