Calculator
Kelly Criterion Calculator
Kelly Criterion Calculator
100% = Full Kelly (maximum growth, maximum volatility). Most practitioners use 25–50% to tame drawdowns.
Optimal Stake (50% Kelly)
16.25%
Sizing Analysis
The strategy shows strong edge of 65.0% per trade. Applying 50%-Kelly (the fractional setting), you would stake 16.25% of the bankroll — $8,125 of $50,000. A Kelly stake in this range is consistent with a strong edge (65.0% expected value per unit risked), where the math and the volatility are both manageable.
*The Kelly Criterion maximizes long-run geometric growth under idealized assumptions: exact knowledge of win probability and payoffs, sequential independent bets, and no psychological cost to drawdowns. Real trading edges are estimated, not known. Educational only, not trading or investment advice.
What the Kelly Criterion Solves
Most traders ask which trade to take; the Kelly Criterion answers a harder follow-up: how much of your money should go on it? In 1956, Bell Labs researcher John Kelly derived the formula for the bet fraction that maximizes the long-run growth rate of a gambling bankroll. The answer depends on just two numbers — the win probability and the win-to-loss payoff ratio — and produces a stake that is provably optimal: betting more grows the account slower in expectation and risks ruin, while betting less simply leaves growth on the table. The formula migrated from information theory into professional investing when Ed Thorp applied it to blackjack, and then to the markets, and it still underpins the sizing logic of many quantitative desks today. For US retail investors the Kelly framework is the antidote to two universal sizing mistakes: betting far too much after a winning streak and far too little on genuinely edged setups. It also exposes an uncomfortable truth — that a strategy with only a small edge deserves a small stake no matter how confident you feel, and that overbetting your edge is the fastest route to blowing up an otherwise profitable system. This calculator computes the full and fractional Kelly stakes, the expected value and breakeven win rate of your strategy, and the dollar size of the position given your trading capital, translating an abstract growth-optimal fraction into an actionable order size.
How the Kelly Formula Works
The Kelly fraction is f* = (b·p − q) / b, where p is the win probability, q is the loss probability (1 − p), and b is the payoff ratio of average win divided by average loss. The numerator b·p − q is the expected value per unit risked: what you win per dollar risked on average across many trades. Dividing by b normalizes it, and the result is the fraction of capital to stake. If the formula returns zero or less, the strategy has no edge and the correct bet is nothing — the formula refuses to size a losing game, which is one of its most valuable properties. The growth logic behind it maximizes the expected logarithm of wealth — the same objective that produces compounding at the fastest possible rate over a long series of bets. A practical consequence: the Kelly-optimal stake equals the edge divided by the payoff odds, so halving your estimated edge halves your stake. Because full Kelly stakes produce stomach-turning volatility — drawdowns of 50% or more are common even with a real edge — most practitioners bet a fraction, typically 25–50%, called fractional Kelly. Fractional Kelly sacrifices some growth for dramatically smaller drawdowns, and the calculator's geometric-growth readout shows approximately what each trade adds to the compounding rate under the chosen stake.
Expert Insights
Overbetting Punishes Harder Than Underbetting
The Kelly curve is asymmetric: betting double the optimal stake does not double growth — it halves it and beyond that turns it negative, so an overbet destroys wealth while an underbet merely slows its accumulation. If your edge estimate is uncertain (and it always is), the safer bet is to err toward half-Kelly. The calculator's fraction slider exists for exactly this reason: when in doubt, take less than the full stake.
Your Edge Estimate Is the Fragile Input
Kelly is only as honest as the win rate and payoff numbers you feed it, and real backtests overstate both: fills are worse than modeled, markets regime-shift, and sample sizes are smaller than they feel. A system that backtests at a 60% win rate may live at 52%. Halve your edge before sizing, or cut the Kelly fraction to 25% as insurance against the gap between the model and reality.
Kelly Assumes Repeated Bets, Not Single Shots
The optimality proof requires many independent repetitions with stable odds — the setting of a trading system, not a single conviction trade. Applying full Kelly to a one-off event like a merger arb or an earnings play misuses the math, because there is no 'long run' for that one bet. For single-event positions, size by the maximum loss you can tolerate instead, and reserve Kelly for the recurring setups where its assumptions hold.
Actionable Tips
- 1
Track Your Real Win Rate Before Sizing
Log every closed trade with its win/loss outcome and the dollar amounts risked and gained for at least 50 to 100 trades, then compute the actual win rate and payoff ratio. Those numbers — not your intuition — go into the calculator. Systems without a recorded history are being sized by hope, and the Kelly output will inherit whatever optimism the inputs carried.
- 2
Cap the Stake With a Hard Risk Ceiling
Even when Kelly says 15%, most risk frameworks cap single-trade risk at 1–2% of equity, and the smaller of the two should win. Enter your bankroll and check the position size output; if it exceeds your risk ceiling, override the formula with the cap. Kelly maximizes growth, but the cap maximizes survival — and surviving a bad estimate of your edge matters more than growing at the theoretical maximum.
- 3
Start at Half-Kelly or Below
Set the fraction slider to 25–50% when first deploying a system; you can increase only after live results confirm the backtest. Half-Kelly retains most of the growth while cutting drawdown depth roughly by half, and it leaves room to be wrong about the edge. As live statistics accrue and confidence grows, recalibrate the inputs and consider stepping the fraction up — never the other way around after losses.
Real-World Examples
Victor Cut His Size Before It Cut Him
Victor's futures system backtested to a 45% win rate with a 2.5:1 payoff, which full Kelly sized at 23% per trade. On paper he leveraged up, and a six-loss streak drew the account down almost 60% before the edge returned. Re-running at quarter-Kelly, the same streak would have cost about 20%. He kept his system — which was profitable — and changed the sizing, the only variable that had actually failed him.
Naomi Discovered Her System Had No Edge
Naomi plugged her discretionary trading record into the calculator: 38% win rate with winners averaging 1.2 times losers. The formula returned zero — Kelly said do not bet at all, even though the trades felt right. Confronting the negative expectancy, she rebuilt the entry rules until the payoff ratio exceeded 2:1, and only then did the Kelly stake turn positive and worth sizing.
Eli Let the Fraction Slider Decide
Eli ran his swing-trading stats — 54% win rate, 2:1 payoff — and saw full Kelly called for a 31% stake. Uncomfortable with that exposure, he dropped to 50%-Kelly (about 15%) and capped it at his 2% single-trade risk rule. Over a full year, the capped stake compounded steadily with drawdowns he could endure, and the system's real edge held close to the estimate because the stress of oversized positions never crept into his exits.
Glossary of Terms
- Kelly Criterion
- The formula f* = (bp − q)/b giving the stake fraction that maximizes long-run geometric growth for a repeated bet with known odds.
- Fractional Kelly
- Betting a set proportion of the full Kelly stake — typically 25–50% — to trade slower growth for substantially smaller drawdowns and estimation risk.
- Payoff Ratio (b)
- The average win divided by the average loss per trade; the odds the strategy gets when it wins against what it gives back when it loses.
Frequently Asked Questions
Everything you need to know about this topic.
Ivy Sinclair-Wren
Financial Chaos Analyst
Ivy Sinclair-Wren is a Financial Chaos Analyst covering investing, AI, wealth psychology, and the emotional consequences of opening finance apps during market crashes. Based in Melbourne, she specializes in demystifying the US tax code and helping users navigate the intersection of spreadsheet logic and human irrationality.