Kelly criterion
The Kelly criterion is a formula that gives the fraction of capital to risk on a repeated bet in order to maximise the long-run growth rate of the account, given the probability of winning and the ratio of average win to average loss. It assumes independent outcomes and a known, stable edge.
Senzoukria · Glossary · Updated September 2026
The formula
In its simplest form, with p the probability of a win, q = 1 − p, and b the ratio of the average win to the average loss, the Kelly fraction is f = p − (q ÷ b). A positive f means the bet has a positive expectancy and the formula suggests risking that fraction of current capital; a negative or zero f means there is no edge to size. The result is a theoretical optimum for growth, not a comfort level: the account that risks full Kelly experiences drawdowns that most traders would not tolerate.
- Inputs come from a sample of past trades, so f inherits the sample's error.
- Fractional Kelly (a fixed share of f) trades some growth for much smaller drawdowns.
- The formula addresses size, not entry or exit; it presupposes the edge.
Assumptions that rarely hold intraday
Kelly assumes each bet is independent of the previous one, that the win probability and payoff ratio are constant, and that the capital can be resized continuously. Within a trading session, consecutive trades share the same regime, the same news and the same trader state, so they are not independent. Futures contracts come in integer sizes, so the fraction is rounded, often coarsely for small accounts. The measured p and b also drift as the market changes.
- Correlated losses arrive in clusters and make full Kelly far riskier than the formula suggests.
- Overestimating p by a few points can turn the suggested fraction from aggressive into ruinous.
- Prop firm drawdown limits are external constraints the formula knows nothing about.
In Senzoukria
The journal's "Previous sessions" panel shows a "Kelly" statistic among its performance figures. Its hint is explicit: it is a theoretical fraction of capital that assumes independent trades, which is rarely true within a session. It sits beside "Expectancy / trade", "Profit factor", "Max drawdown" and "Recovery factor", and is computed from the closed trades of the recorded sessions. The software does not size orders from it; position size remains a manual input, and any automated strategy path requires explicit arming.
Common mistakes
- Applying Kelly to a handful of trades; the inputs are too noisy to mean anything.
- Using the formula with gross results, before fees and slippage.
- Treating the fraction as a target rather than an upper bound.
- Ignoring account rules: a Kelly fraction that breaches a daily loss limit is not usable.
Related
This page in other languages
Frequently asked questions
- Why is full Kelly considered aggressive?
- Because it maximises the expected growth rate, not the probability of a comfortable path. The drawdowns along the way are large by construction, and any error in the estimated edge pushes the fraction past the optimum, where growth falls quickly. Fractions of the Kelly value are the usual practical compromise.
- Does Senzoukria size positions with Kelly?
- No. The journal reports the Kelly figure with its assumption stated, as one statistic among others. Order size in the trading panel and in a strategy is set by the user, and automated execution runs only through the autopilot after explicit arming.
- What inputs does the formula need from a journal?
- A win rate and the ratio of average winning trade to average losing trade, both net of costs. These come from closed trades over a sample long enough to be meaningful, and they should be recomputed as the sample grows because both drift.