Given a favourable bet you can repeat, there is a fraction of your capital that maximises long-run growth. Bet less and you grow more slowly than you could. Bet more and — this is the part that surprises people — you grow more slowly too, and past a certain point you go broke with probability one despite having the edge.
A farmer with good land can plant more seed each year and harvest more. Plant every last grain and one failed monsoon leaves nothing to sow next season. The optimal amount is not the maximum — it is the largest amount that still survives a bad year.
Kelly formalises exactly that. It finds the bet size that grows capital fastest over many repetitions, which is always less than the size that maximises any single outcome.
The formula, and what it needs
- f*
- The fraction of capital to risk
- p
- Probability of winning
- q
- Probability of losing, equal to 1 − p
- b
- Win size divided by loss size — the payoff ratio
Example: A 45% win rate with winners twice the size of losers: f* = (0.45 × 2 − 0.55) ÷ 2 = 0.175. Kelly says risk 17.5% of capital on every trade.
Why overbetting destroys the edge
Why the inputs are the real problem
- You do not know p. A 45% win rate measured over sixty trades has a confidence interval wide enough to include 35%, and Kelly at 35% says do not trade at all.
- The edge is not stationary. A rule that worked for two years may be working less well now. Kelly assumes the parameters hold; markets do not offer that.
- Overestimating the edge overbets savagely. If your true win rate is 40% and you believe it is 50%, Kelly tells you to risk roughly twice what you should — and the growth curve past the peak falls steeply.
- Trades are not independent. Kelly assumes one bet at a time. Six correlated positions sized individually at Kelly are one position at six times Kelly.
- Ruin is not the only failure. Quitting is. A drawdown that is mathematically survivable but psychologically unbearable ends the system just as completely.
The confident number
Your journal shows 68 trades: 41 wins averaging +6.2%, 27 losses averaging −3.1%. Kelly on those figures suggests risking about 29% of capital per trade.
You have a genuine edge and bet three times the Kelly fraction. What happens over many repetitions?
Achhi zameen hai toh zyada beej bo sakte ho. Par saara beej bo doge aur ek baarish dhokha de gayi, toh agle saal bone ko kuch nahi bacha. Sabse zyada nahi — utna, jitna kharab saal ke baad bhi bacha rahe. Kelly ka formula yahi kehta hai, aur uska jawaab itna bada aata hai ki koi jhel nahi paata.
- Kelly gives the bet size that maximises long-run compounded growth.
- The output is far larger than any human tolerates, and the maths is not wrong.
- Growth falls away past the Kelly peak — overbetting a real edge still leads to ruin.
- Half-Kelly captures most of the growth for about half the volatility.
- An absurd Kelly output means your edge estimate is too high, not that you should bet more.
Mark it done to track your progress through the curriculum.
Common questions
Short, direct answers to what people ask about this topic.
- kelly criterion meaning in trading
- The Kelly criterion is a formula that gives the fraction of capital to risk on a repeatable favourable bet so that long-run compounded growth is maximised. It is written f* = (p × b − q) ÷ b, where p is the win probability, q is 1 − p and b is the payoff ratio. Bet less than f* and you grow more slowly; bet more and you also grow more slowly, and far enough past it you go broke despite having the edge.
- what does kelly say to risk with a 45% win rate and winners twice the size of losers
- About 17.5% of capital. Putting p = 0.45, q = 0.55 and b = 2 into f* = (p × b − q) ÷ b gives (0.9 − 0.55) ÷ 2 = 0.175. That number is not a typo, and it is also why almost nobody trades full Kelly: four losses in a row at that size — which a 45% system produces regularly — takes the account down by roughly half.
- why do traders use half kelly instead of full kelly
- Half-Kelly captures roughly three-quarters of the growth rate for about half the volatility, and it is far more forgiving of the error that actually occurs — an over-optimistic estimate of your own edge. Since the growth curve falls away steeply past the Kelly peak, deliberately sitting below it costs little and protects against inputs that were never as reliable as they looked.
- betting more than the kelly fraction on a favourable bet results in
- Lower compounded growth than betting the Kelly fraction, and past a threshold, eventual ruin despite holding a positive expectation on every individual bet. Growth plotted against bet size is an inverted curve rather than a straight line, so twice the optimum is worse than half of it. That is how people with a genuine edge still blow up.
- what does it mean if my kelly calculation says risk 29% per trade
- It means the edge estimate feeding the formula is too generous, not that 29% is a sensible size. Kelly is exquisitely sensitive to its inputs, and a win rate measured over sixty or seventy of your own recent trades has a confidence interval wide enough to change the answer completely. An absurd output is diagnostic — it confirms the sign of an edge, not the size of a bet.