Calculator Tools
Kelly Criterion Calculator
Compute the optimal Kelly bet size from win probability and odds, with Half, Quarter, and Custom Kelly sizing, expected value, and growth projection.
Bet type
Use Gambling when the loss equals the full stake (sports betting, casino, prop bets). Use Trading when the upside and downside are different fractions of the staked amount (stocks, options, crypto).
Inputs
Total capital available for this strategy in USD.
Your honest estimate that this bet or trade wins. Any number between 0 and 100.
Total return per 1 unit staked, including the returned stake. 2.0 is even money (+100 American, 1/1 fractional). Implied probability 50%.
Sizing fraction
Most practitioners size at half or quarter Kelly to absorb estimation error. Full Kelly maximizes long-run growth in theory but produces deep drawdowns in practice.
Quick presets
Click any preset to load its values. Edit any field afterward to explore.
Fractional Kelly sizing
Side-by-side comparison of the four sizings most traders and bettors use. Smaller fractions trade some long-run growth for shallower drawdowns.
| Sizing | Bankroll fraction | Stake (USD) | EV per bet | Log growth / bet |
|---|---|---|---|---|
| Full Kelly (1.0×) | 10% | $1,000.00 | $100.00 | 0.00501 |
| Half Kelly (0.5×) | 5% | $500.00 | $50.00 | 0.00375 |
| Quarter Kelly (0.25×) | 2.5% | $250.00 | $25.00 | 0.00219 |
| Tenth Kelly (0.1×) | 1% | $100.00 | $10.00 | 0.00095 |
100-bet expected bankroll growth
Expected geometric growth at the chosen sizing fraction. Real results vary widely; this curve is the long-run average path implied by the per-bet log growth rate.
Start
$10,000.00
After 50 bets
$12,063.88
After 100 bets
$14,553.71
Kelly Criterion formulas
The Kelly fraction f* is the bankroll fraction that maximizes the expected logarithm of bankroll after a single bet.
Gambling form (loss equals full stake)
f* = (b·p − q) / b
p is the win probability, q = 1 − p is the loss probability, b is the net decimal odds (decimal odds − 1, the profit per 1 unit staked).
Trading form (unequal up and down moves)
f* = (p·W − q·L) / (W·L)
W is the unit gain on a winning trade, L is the unit loss on a losing trade. Both are positive fractions of the staked amount (W = 0.20 for a 20% gain, L = 0.10 for a 10% loss).
What Kelly maximizes
E[log(1 + f·X)] = p·log(1 + f·W) + (1 − p)·log(1 − f·L)
X is the per-bet return. The Kelly fraction f* is the unique value of f that maximizes this expected log return. Equivalently, Kelly is the bet size that maximizes long-run geometric growth. Sizing above full Kelly increases variance without adding long-run return; sizing above 2× Kelly produces negative expected log growth even with a positive edge.
How to use
- Pick a bet type. Use Gambling / decimal odds for bets that lose the full stake on a loss (sports betting, casino, prop bets). Use Trading / win-loss when the upside and downside are different fractions of the staked amount (stocks, options, crypto).
- Enter your bankroll and pick the currency.
- Type your win probability between 0 and 100 percent. This is your honest estimate, not the bookmaker's implied probability.
- In Gambling mode, enter the decimal odds (2.0 is even money). In Trading mode, enter the win amount and loss amount as percentages of the staked capital.
- Choose a sizing fraction. Full Kelly is the theoretical optimum; Half and Quarter Kelly are the standard practitioner choices for absorbing estimation error and reducing drawdowns. Pick Custom to enter any multiplier.
- Read the Full Kelly fraction, the recommended stake at the chosen sizing, expected value per bet, expected log growth, the fractional Kelly comparison table, and the 100-bet bankroll growth projection. Copy the full report with the Copy button.
About this tool
Kelly Criterion Calculator returns the bankroll fraction that maximizes long-run growth for a single repeatable bet or trade, plus the practical sizing most professionals actually use. Two input modes cover the two ways the formula appears in the wild. Gambling mode takes a win probability and decimal odds (the total return per 1 unit staked, including the returned stake) and applies the classic Kelly formula f* = (b·p − q) / b, where b is decimal odds minus 1 and q is 1 − p. Trading mode takes a win probability with separate win and loss amounts as percentages of the staked capital and applies the asymmetric form f* = (p·W − q·L) / (W·L), the version that fits stock, options, and crypto trades where the up move and down move are different sizes. The headline shows Full Kelly, the recommended stake at the chosen bankroll, expected value per bet in currency, and the per-bet expected log growth rate, which is the quantity Kelly mathematically maximizes. A fractional Kelly table side-by-sides Full, Half, Quarter, and Tenth Kelly with stake, expected value, and log growth so you can see the standard practitioner tradeoff: smaller fractions give up some long-run return for shallower drawdowns and tolerance for estimation error in your inputs. A 100-bet expected bankroll growth chart plots the geometric path implied by the chosen sizing, the curve that explains why most experienced bettors and traders cap sizing at half or quarter Kelly. Built-in warnings flag negative-edge bets (Kelly returns zero, the bet should be skipped), oversized Full Kelly (above 25%, 50%, and 100%), decimal odds of 1.0 with no profit potential, and a win probability that exactly matches the odds' implied probability. Useful for sports bettors sizing parlays and singles, blackjack and poker players managing bankrolls, retail and proprietary stock traders sizing asymmetric trades, options sellers balancing premium against tail loss, crypto traders managing high-variance positions, and quantitative finance students working through textbook Kelly problems. All math runs locally in your browser; bankroll, probability, and odds inputs never leave your device.
Free to use. Works in your browser. No signup, no login.
Related tools
You may also like
Position Size Calculator
Risk-based position sizing with stop, take-profit, and R-multiple math.
Open tool
ConverterBetting Odds Converter
Convert between American, decimal, fractional, and implied-probability odds with payout and EV.
Open tool
CalculatorProbability Calculator
Five modes for P(A), P(A and B), P(A or B), P(A | B), Bayes, independent trials, and odds.
Open tool
CalculatorLottery Odds Calculator
Exact odds, tier-by-tier probabilities, and expected value for any lottery format.
Open tool
CalculatorStock Profit Calculator
Single-trade P&L with fees, dividends, capital gains tax, break-even, and annualized return.
Open tool
CalculatorCompound Interest Calculator
Future value, time to goal, and required contribution with annual schedule.
Open tool