Kelly Criterion Calculator
Find the optimal bet or position size from your win probability and win/loss ratio — with Full, Half, and Quarter Kelly stakes.
Bet Sizing Inputs
Your historical win rate for this trade or bet type
Average win ÷ average loss (or net decimal odds − 1 for bets)
Total capital allocated to this strategy
Recommended Position Size
Full Kelly Stake
25.00%
$2,500.00 of bankroll
Half Kelly
12.50%
$1,250.00
Quarter Kelly
6.25%
$625.00
Breakdown
Why Fractional Kelly?
Full Kelly maximizes long-run growth but produces large drawdowns. Half Kelly captures roughly 75% of the growth rate with about half the volatility, which is why most practitioners size down from the full formula.
Complete Guide to the Kelly Criterion
What Is the Kelly Criterion?
The Kelly Criterion is a bet-sizing formula developed by John L. Kelly Jr. in 1956 to maximize the long-run geometric growth rate of a bankroll. Instead of betting a fixed amount every time, it scales your stake to your statistical edge — bet more when the edge is large, bet nothing when there is no edge at all.
It is widely used in sports betting, poker, and — with adjustments — trading position sizing. Pair it with our Trade Risk Calculator to translate the Kelly percentage into an actual share or contract count.
Formula
Kelly Fraction:
f* = (b × p − q) / b
Where: p = probability of winning, q = 1 − p = probability of losing, b = win/loss ratio (average win ÷ average loss)
Expected Growth Rate (per bet):
g = p × ln(1 + b·f) + q × ln(1 − f)
Where: f = fraction of bankroll staked (Full, Half, or Quarter Kelly)
Benefits of Kelly-Based Sizing
Maximizes Long-Run Growth
Mathematically proven to maximize the compound growth rate of capital over a long sequence of bets or trades, beating any fixed-fraction strategy.
Prevents Ruin
Because the stake is a fraction of current bankroll rather than a fixed amount, it is mathematically impossible to go to zero from a single Kelly-sized bet.
Scales With Edge
A bigger statistical edge automatically means a bigger recommended stake — no manual guessing about how much conviction should change position size.
Pairs With Reward-to-Risk Tools
Use the win/loss ratio alongside our Sharpe Ratio Calculator to sanity-check whether a strategy's risk-adjusted return supports the edge you're assuming.
Tips for Applying Kelly Sizing
Use a Large Sample: Estimate win probability from at least 50–100 historical trades or bets. Small samples produce unstable, unreliable Kelly outputs.
Default to Half or Quarter Kelly: Because your win rate and payout ratio are estimates, not certainties, sizing down protects against estimation error while sacrificing little long-run growth.
Recalculate Periodically: Win rate and reward-to-risk drift as market conditions or your strategy change. Re-run this calculator as new trade or bet data comes in rather than using one fixed percentage forever.
Common Mistakes
Overestimating Win Probability
A small overestimate of p compounds into a much larger recommended stake. Overconfident inputs are the single most common cause of Kelly-driven blowups.
Betting Full Kelly on Correlated Trades
The formula assumes independent bets. Sizing multiple correlated positions (e.g. several tech stocks) each at full Kelly stacks correlated risk far beyond what any single Kelly calculation assumes.
Ignoring Drawdown Tolerance
Full Kelly can produce drawdowns of 50% or more even with a real, positive edge. Use our Trading Profit Calculator to model how a drawdown of that size affects your account before committing to full Kelly sizing.
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OpenFrequently Asked Questions
What is the Kelly Criterion?
The Kelly Criterion is a formula for sizing bets or trades to maximize long-run geometric growth of capital. Developed by John Kelly at Bell Labs in 1956, it answers exactly what fraction of your bankroll to risk given a known win probability and payout ratio. It is used across sports betting, poker, and position sizing in trading.
How is the Kelly percentage calculated?
f* = (bp − q) / b, where p is your win probability, q = 1 − p is the loss probability, and b is your win/loss ratio (average win divided by average loss). For example, a 55% win rate with a 1.5 win/loss ratio gives f* = (1.5 × 0.55 − 0.45) / 1.5 = 25% of bankroll.
Why use Half Kelly or Quarter Kelly instead of Full Kelly?
Full Kelly maximizes expected growth but assumes your win probability and payout ratio are known exactly — in practice they are estimates, and overestimating either causes oversized bets and severe drawdowns. Half Kelly captures roughly 75% of full Kelly's growth rate with about half the variance, which is why most traders and professional bettors size down.
What common mistakes do people make applying the Kelly Criterion?
The two biggest errors are overestimating win probability (a small overestimate compounds into an oversized stake) and treating a single trade's Kelly output as fixed forever instead of recalculating as win rate and payout ratio drift. Betting the full Kelly fraction on correlated trades simultaneously also multiplies risk beyond what the formula assumes.
Does the Kelly Criterion apply to trading, not just betting?
Yes — in trading, b is the average winning trade divided by the average losing trade (your reward-to-risk ratio) and p is your historical win rate over a large enough sample. Many traders cap position size well below even half Kelly because trading edges (unlike fixed-odds bets) are noisy and change over time.
How does this compare to the Trade Risk Calculator?
The Trade Risk Calculator sizes a position from a fixed risk percentage and stop-loss distance, independent of your win rate. The Kelly Criterion instead derives the optimal risk percentage itself from your win rate and reward-to-risk ratio, so it answers a different question: not 'how many shares fit my 1% risk rule' but 'what risk percentage maximizes my long-run growth.'