What Is the Kelly Criterion?
The Kelly criterion is the bet fraction that maximises the long-run growth rate of capital, calculated as f = p − q/b for a payoff of b to 1. It is mathematically optimal for growth and far too aggressive in practice, because its inputs are estimates rather than known constants.
What is the formula?
f = (b × p − q) ÷ b, equivalently f = p − q ÷ b, where p is the win probability, q = 1 − p, and b is the payoff ratio.[1]
Worked example. A 50% win rate at 2:1 gives f = 0.5 − 0.5 ÷ 2 = 0.25, so full Kelly is 25% of capital per trade. A 55% win rate at 1:1 gives f = 0.55 − 0.45 = 0.10, or 10%.
Note what happens when the edge shrinks: at a 52% win rate and 1:1, f = 0.04. Kelly is extremely sensitive to p, and p is exactly the number nobody knows precisely.
Why does nobody bet full Kelly?
The inputs are estimated. If your true win rate is 50% but you estimated 55%, full Kelly at 1:1 has you betting 10% of capital on a strategy with no edge at all. Over-betting Kelly is not merely suboptimal — past 2x Kelly, expected growth is negative.
The drawdowns are brutal. Full Kelly accepts drawdowns of 50% or more as part of normal operation. It maximises growth, not comfort, and a trader who abandons the system inside that drawdown gets none of the growth and all of the loss.
Half Kelly is the usual compromise. Betting half the Kelly fraction retains roughly three quarters of the growth rate with substantially smaller drawdowns. Quarter Kelly is common among practitioners who trust their estimates less than they trust the arithmetic.
How does it relate to normal position sizing?
Common risk rules — 1% or 2% of the account per trade — are far below quarter Kelly for any plausible edge. That is not a mistake. It is an implicit admission that the edge is uncertain, and given how badly over-betting behaves, erring small is the correct direction to err in.
Use Kelly as a ceiling rather than a target: if your intended risk exceeds half Kelly on your own numbers, you are betting more than your estimated edge supports.
How does this connect to a track record?
Why almost nobody should trade full Kelly, stated from the regulatory side: ESMA restricted retail CFD leverage in 2018 after finding 74–89% of retail accounts lost money, with average losses between €1,600 and €29,000.[2] Full Kelly on a mis-estimated edge is a larger bet than the one that produced those numbers.
Kelly is only as good as p and b, and both come from your record. A metric is a summary of a record, so it inherits every weakness of that record. Computed from trades selected after the fact, it is a number about the selection. kappi commits each trade before it resolves and publishes it on a Merkle-anchored log, so PnL, RME, correlation to SPX, mean R:R and trade count over 30, 100 and 200-day windows are computed over everything that was committed, losses included. $15/month to keep a record; reading one is free.
Sources
Frequently asked questions
How do you calculate the Kelly criterion?
f = p − q/b, where p is the win probability, q = 1 − p and b is the payoff ratio. A 50% win rate at 2:1 gives f = 0.5 − 0.25 = 0.25, or 25% of capital.
Why do traders use half Kelly?
Half Kelly keeps roughly three quarters of the long-run growth rate with much smaller drawdowns, and it protects against overestimating the edge — beyond 2x Kelly, expected growth turns negative.
Is Kelly appropriate for trading?
As a ceiling rather than a target. It assumes the win rate and payoff are known constants, whereas in trading both are noisy estimates from a finite sample, so full Kelly systematically over-bets.
How does Kelly compare to risking 1% per trade?
A 1% rule is far below quarter Kelly for any plausible edge. That conservatism is a reasonable response to uncertainty in the inputs, since over-betting is punished far more harshly than under-betting.