Kelly Criterion Calculator
Enter your win rate and payoff ratio to instantly compute the optimal risk per trade that maximizes long-term geometric growth. Compare full, half and quarter Kelly with the risk of ruin at each level — live, no submit, no guesswork.
Inputs
LiveShare of trades that close in profit. 0–100.
Avg win ÷ avg loss. 1.5 = win 1.5× loss.
Account balance used to contextualize position sizing.
What you currently risk per trade. Compared against Kelly.
Sequence length for the risk of ruin estimate.
Results
Full Kelly risk
Max long-run geometric growth fraction.
Half Kelly
0.0%
Quarter Kelly
0.0%
Edge
0.000R
Expectancy / trade
0.000R
Risk of ruin by Kelly level
Recommendation
Enter your inputs to see a recommendation.
How the Kelly Criterion works
Three steps turn your win rate and payoff ratio into an optimal risk fraction — and a survival check that keeps you from betting too large.
Find your edge
Edge per trade is E = p×b − q, where p is win rate, q is loss rate and b is payoff ratio. If E ≤ 0 the strategy has no statistical edge and the optimal Kelly bet is zero.
Compute Kelly fraction
The Kelly fraction f* = (p×b − q) / b is the risk percent that maximizes long-run geometric growth. Full Kelly grows fastest but with deep drawdowns.
Fraction & survive
Take half or a quarter of Kelly. You give up a little growth for a large drop in risk of ruin — the relationship is non-linear, so fractional Kelly is the professional standard.
The Kelly Criterion, explained
The Kelly Criterion is a mathematical formula for sizing a sequence of bets so that long-term wealth grows at the maximum possible geometric rate. It was published in 1956 by John L. Kelly Jr., a researcher at Bell Labs, in a paper on information theory and gambling. Kelly's insight was that the fraction of your bankroll you risk on each bet should be proportional to your edge — bet more when you have a larger advantage, and nothing when you have none.
For traders, the criterion turns two numbers — your win rate and your payoff ratio — into a single optimal risk percentage. Your win rate p is the share of trades that close in profit, your loss rate q is 1 − p, and your payoff ratio b is your average win divided by your average loss. The Kelly fraction is:
f* = (p × b - q) / b
# p = win rate, q = 1 - p, b = payoff ratio (avg win / avg loss)
# Full Kelly risk % = f* × 100
# Half Kelly = f* × 50
# Quarter Kelly = f* × 25
# Edge = p × b - q
# Expectancy (R) = p × b - q × 1
# If edge <= 0 -> f* = 0 (do not trade)Risking the full Kelly fraction maximizes the compounded growth rate of your account — but full Kelly is famously aggressive. It produces large drawdowns, sometimes 50% or more, and it assumes your win rate and payoff ratio are known with certainty. In real trading your edge is always an estimate, and a small overestimate at full Kelly pushes you past the true optimum and toward ruin. This is why almost no professional trader risks full Kelly.
The standard practice is to risk a fraction of Kelly — typically half or a quarter. Each halving gives up roughly half of the remaining growth rate, but it cuts drawdown depth and risk of ruin far more than in half. The relationship is non-linear: quarter Kelly retains about 56% of the full-Kelly growth rate while reducing risk of ruin by orders of magnitude. For noisy or uncertain edges, fractional Kelly is the rational choice.
The link between the Kelly fraction and risk of ruin is the key survival insight. Below Kelly, increasing risk grows your account faster with only a modest rise in ruin probability. Above Kelly, growth actually slows in geometric terms while ruin probability accelerates — you take more risk for less compounded return. This calculator shows the closed-form risk of ruin at full, half and quarter Kelly so you can see exactly where your sizing sits on that curve, and it compares your current risk per trade against the optimal fraction so you know whether you are under-betting, in the growth region, or over-betting into the danger zone.
In practice, treat Kelly as an upper bound, not a target. Compute it, take a fraction of it, and cap the result at a fixed-risk ceiling (0.5–2% is the professional norm). Validate your win rate and payoff ratio over a large sample of trades before trusting the number — Kelly is only as good as the inputs you feed it.
Kelly Criterion in action
Two real-world strategy profiles run through the same formula the
calculator uses. Numbers are computed live from the pure logic in
src/lib/kelly.ts.
Example 1 · High win rate
Scalper / mean-reversionA 55% win rate with a 1.5 payoff ratio — a strong, consistent edge.
Win rate
55%
Payoff ratio
1.5:1
Ruin · full Kelly
0.00%
Ruin · half Kelly
0.00%
Full Kelly is aggressive for this edge. Half Kelly (12.5%) keeps most of the growth with a fraction of the drawdown — the typical professional choice.
Example 2 · Trend follower
Low win rate / high payoffA 40% win rate with a 2.5 payoff ratio — profitable through large wins, not frequent ones.
Win rate
40%
Payoff ratio
2.5:1
Ruin · full Kelly
0.00%
Ruin · half Kelly
0.00%
The lower win rate makes full Kelly volatile. Quarter Kelly (4.0%) is the safer growth option for trend-following strategies with long losing streaks.
f* = (p * b - q) / b # Kelly fraction (0-1)
fullKelly = f* * 100 # percent risk
halfKelly = f* * 50 # percent risk
quarterKelly = f* * 25 # percent risk
edge = p * b - q # statistical edge
expectancy = p * b - q * 1 # R multiples per trade
# Risk of ruin (closed-form, fixed-fractional):
edgeFraction = (p*b - q) / (p*b + q)
unitsToRuin = ln(ruinFraction) / ln(1 - riskFraction)
riskOfRuin = ((1 - edgeFraction) / (1 + edgeFraction)) ^ unitsToRuin
# If edgeFraction <= 0 -> riskOfRuin = 1Kelly Criterion, explained
Common questions about the Kelly Criterion, fractional Kelly, edge and risk of ruin.
What is the Kelly Criterion in trading?
The Kelly Criterion is a formula for sizing bets so that long-term geometric growth is maximized. For traders it tells you the optimal fraction of your account to risk per trade based on your win rate and payoff ratio: f* = (p × b − q) / b, where p is win rate, q is loss rate and b is payoff ratio (average win ÷ average loss). Risking the full Kelly fraction grows your account as fast as mathematically possible — but with large drawdowns.
Why is full Kelly too aggressive for most traders?
Full Kelly maximizes the long-run growth rate, but it also produces severe drawdowns and high volatility. The formula assumes your win rate and payoff ratio are known exactly, which is never true in real trading — estimates are noisy. A small overestimate of your edge at full Kelly can push you past the true optimal fraction and into ruin territory. Most professionals risk half or a quarter of Kelly to trade a small slice of growth for a dramatic reduction in drawdown and ruin probability.
What is half Kelly and quarter Kelly?
Half Kelly means risking 50% of the full Kelly fraction, and quarter Kelly means risking 25% of it. If full Kelly is 20%, half Kelly is 10% and quarter Kelly is 5%. Each step down roughly halves your growth rate but cuts drawdown depth and risk of ruin far more than in half — the relationship is non-linear, so fractional Kelly is far more survival-friendly per unit of growth given up.
How is risk of ruin related to the Kelly fraction?
Risk of ruin rises sharply as you approach and exceed the Kelly fraction. Below Kelly, every increase in risk grows your account faster with modest ruin risk. Above Kelly, growth actually slows (in geometric terms) while ruin probability accelerates — you are taking more risk for less compounded return. This calculator shows the closed-form risk of ruin at full, half and quarter Kelly so you can see the trade-off directly.
What win rate and payoff ratio do I need for a positive Kelly?
Kelly is positive whenever p × b > q, i.e. your win rate times your payoff ratio exceeds your loss rate. A 55% win rate with a 1.5 payoff gives 0.55 × 1.5 = 0.825 > 0.45, a clear edge. A 40% win rate with a 2.5 payoff gives 0.40 × 2.5 = 1.0 > 0.60 — also profitable, the classic trend-following profile. If p × b ≤ q, Kelly is zero or negative and the optimal action is not to trade.
Should I use Kelly or a fixed risk percentage like 1%?
They serve different goals. A fixed 0.5–2% risk per trade is a robust survival rule that works even when your edge is uncertain. Kelly tells you the mathematically optimal fraction given a known edge, but it is sensitive to estimation error. A common approach is to compute Kelly, then risk a fraction of it (quarter or half) and cap the result at your fixed risk ceiling — you get growth-optimized sizing with a survival backstop.
Does the Kelly Criterion guarantee profits?
No. Kelly maximizes the geometric growth rate of your account assuming your win rate and payoff ratio are accurate and stable. It does not guarantee you will be profitable over any finite number of trades — variance still produces losing streaks. If your inputs are wrong, Kelly sizing can be far too aggressive. Always combine Kelly with a fixed-risk cap and validate your edge with a long sample of trades.
What is the difference between Kelly and optimal f?
Ralph Vince's optimal f is the fixed fraction that maximizes terminal wealth on a specific historical trade sequence, while Kelly maximizes the expected log-growth rate given probability inputs. For a strategy with stable win rate and payoff, the two converge to the same fraction. Kelly is forward-looking (based on probabilities); optimal f is backward-looking (based on a realized trade list). This calculator uses the Kelly formula.
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