Kelly Criterion Calculator
Calculate your optimal bet size based on your win rate and payoff ratio. See full Kelly, half Kelly and quarter Kelly recommendations.
The Kelly Criterion Formula
The Kelly criterion is a mathematical formula that determines the optimal percentage of your capital to risk on a single trade or bet. John Kelly published it in 1956 while working at Bell Labs. Ed Thorp took the formula from information theory to blackjack tables and then to Wall Street.
The formula: f* = (bp - q) / b, where b is the odds received (average win divided by average loss), p is the probability of winning and q is the probability of losing (1 - p).
Simplified: K% = W - ((1 - W) / R), where W is your win rate and R is your payoff ratio.
Example: You win 55% of your trades. Your average winner returns $200 and your average loser costs $100. Payoff ratio R = 200/100 = 2.0. Kelly% = 0.55 - (0.45 / 2.0) = 0.55 - 0.225 = 0.325, or 32.5% of your bankroll per trade.
The formula works for stocks, forex, crypto, options and sports betting. You can replicate this calculation in Excel using the formula =B1-(1-B1)/B2 where B1 is win rate and B2 is payoff ratio.
Why Half Kelly Beats Full Kelly in Practice
Full Kelly maximizes long-term growth rate. It also produces drawdowns that most traders cannot stomach. A 50% drawdown requires a 100% gain to recover. Full Kelly makes drawdowns of that magnitude probable over hundreds of trades.
Half Kelly captures roughly 75% of the growth rate with far less volatility. Warren Buffett and Ed Thorp both advocate fractional Kelly approaches because real-world conditions include estimation error, changing market regimes and correlated outcomes.
| Full Kelly | Half Kelly | Quarter Kelly | |
|---|---|---|---|
| Bet size | 32.5% | 16.3% | 8.1% |
| Risk on a $10,000 account | $3,250 | $1,625 | $813 |
| Share of maximum growth rate | 100% | 75% | 44% |
| Share of full Kelly volatility | 100% | 50% | 25% |
Bet sizes use the worked example above: a 55% win rate at a 2.0 payoff ratio, giving full Kelly of 32.5%. Growth share comes from g(f) / g(1) = f(2 − f), where f is the fraction of full Kelly. Half Kelly gives 0.5 × 1.5 = 0.75, which is the 75% figure above; quarter Kelly gives 0.25 × 1.75 = 0.44. Volatility of log growth scales as f, so halving the bet halves the swing.
Half Kelly keeps three quarters of the growth for half the swing.
See how your Kelly fraction affects your probability of account ruin with the risk of ruin calculator.
When Kelly Doesn't Work
The Kelly formula requires accurate win rate and payoff estimates. Most traders overestimate both. If you feed the formula inflated numbers, it prescribes oversized positions that accelerate losses.
Kelly assumes each trade outcome is independent of the last. Markets exhibit serial correlation, momentum and regime shifts. A strategy that wins 60% in a trending market may win 35% in a choppy one.
The formula also ignores fat tails. Flash crashes, overnight gaps and liquidity failures can produce losses larger than your planned stop loss. No formula accounts for events that fall outside your data set.
For a simpler approach based on fixed risk per trade, use the position size calculator. Track your win rate and average payoff in a trading journal, then apply Kelly sizing when you practice on the Tradicted simulator.
Kelly Against Two Simpler Rules
Kelly sizes the bet from your edge. The two rules most traders use instead ignore the edge and size from the account or from the last result.
| Half Kelly | Fixed fractional (2%) | Martingale | |
|---|---|---|---|
| Sized from | Your win rate and payoff ratio | Account balance | The last result |
| Risk on the next trade | $1,625 | $200 | $200, doubling after each loss |
| After a loss | Falls with the balance | Falls with the balance | Doubles |
| Needs an edge estimate | Yes | No | No |
| Six losses in a row | Account down about 62% | Account down about 11% | Needs $12,600 staked, more than the account holds |
Half Kelly uses the 16.3% figure from the worked example above. The martingale column doubles a $200 base: 200, 400, 800, 1,600, 3,200, 6,400. The sixth bet alone is $6,400 against a balance that has already given up $6,200.
Fixed fractional gives up growth for a rule you can follow without knowing your edge, which is why the position size calculator asks for a stop distance rather than a win rate. The martingale column is there as the boundary case: it needs no estimate and no edge, and a six-trade losing run ends the account.
Thorp (2006) reports that a Kelly-managed convertible-hedging investment partnership compounded at approximately 20 percent annually for about 28.5 years, from November 3, 1969 through May 1998, turning $10,000 into $18 million tax-exempt.From our summary of Thorp, The Kelly Criterion in Blackjack, Sports Betting and the Stock Market (2006)
Thorp ran fractional Kelly on a quantified edge with institutional execution behind it. The formula on this page gives you the same sizing arithmetic once you can put real numbers into it.
Frequently Asked Questions
The Kelly criterion is a formula that calculates the optimal fraction of your capital to risk on a bet or trade. John Kelly developed it at Bell Labs in 1956. Ed Thorp applied it to blackjack and later to financial markets, proving it could maximize long-term wealth growth when you have a quantifiable edge.
The Kelly formula is f* = (bp - q) / b. The variable b is the payoff ratio (average win divided by average loss), p is the probability of winning and q is the probability of losing (1 minus p). A simplified version: K% = W - ((1 - W) / R), where W is the win rate as a decimal and R is the payoff ratio.
Half Kelly means betting 50% of the amount the full Kelly formula recommends. Half Kelly captures roughly 75% of the full Kelly growth rate while cutting volatility and drawdowns by a large margin. Most professional traders and investors use half Kelly or less because overestimating your edge leads to overbetting.
Start by tracking your trades in a journal to find your win rate and average reward-to-risk ratio. Enter those numbers into the calculator above. The resulting Kelly percentage tells you what fraction of your account to allocate per trade. For stocks, apply this to your position size by multiplying your account balance by the Kelly fraction.
Yes. A negative Kelly percentage means you have no statistical edge on that setup. The expected value of the trade is negative. Do not trade a setup with a negative Kelly. Reassess your strategy, improve your win rate or payoff ratio, or skip the trade.
The Kelly criterion provides a rigorous framework for position sizing, but it requires accurate inputs. Your win rate and average payoff must come from real trade data, not guesses. Most professional traders use fractional Kelly (half or quarter) to build in a margin of safety against estimation error.
Fixed fractional sizing risks a constant percentage of your account on every trade regardless of your edge. The Kelly criterion adjusts position size based on how strong your edge is. Stronger edges warrant larger positions; weaker edges call for smaller ones. Fixed fractional is simpler and more forgiving of estimation errors.
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