Decisions
20 min

Kelly criterion

Size a repeated bet as a fraction of what you hold, to maximise long-run growth rather than the return on any single bet.

Time cost
20 min
Output
A position size as a fraction of current holdings.
Steps
5

Use when

  • A favourable bet repeats and you must decide how much to commit each time.
  • You can lose a fraction rather than a fixed amount.
  • You have an estimate of the edge that is better than a guess.

Do not use when

  • The bet happens once. Kelly optimises a growth rate over many repetitions and says nothing about a single event.
  • Your edge estimate is unreliable, which is the normal case — overestimating the edge makes Kelly aggressive enough to ruin you.
  • A loss cannot be taken as a fraction. If the downside is a fixed catastrophic amount, this is the wrong model.

Inputs required

  • Probability of winning
  • The payoff ratio
  • An honest view of how wrong the probability might be

Procedure

  1. 01

    Establish the edge

    Probability of winning, and what a win pays relative to a loss. Without a genuine edge the formula returns zero or negative, which is the correct instruction: do not bet.

  2. 02

    Compute the fraction

    For a bet paying b to 1 with win probability p, the fraction is (bp − q) / b, where q is 1 − p. It returns the share of current holdings to commit.

  3. 03

    Halve it

    Use a half or a quarter of the Kelly fraction in practice. Kelly assumes the probability is exactly right; halving costs a little growth and greatly reduces the damage from overestimating the edge.

  4. 04

    Resize each time

    The fraction applies to current holdings, not original ones. After a loss you bet less in absolute terms. That is the mechanism that prevents ruin.

  5. 05

    Check the assumption holds

    Kelly requires many repetitions and independent outcomes. If either fails, use a different rule.

Characteristic failure mode

Overbetting from an overestimated edge. The penalty is asymmetric: betting at twice the Kelly fraction has zero expected growth, and above that the expected growth is negative even though every individual bet is favourable.

Worked example

A recurring opportunity wins 55% of the time and pays even money.

  1. 01p = 0.55, q = 0.45, b = 1. Full Kelly = (0.55 − 0.45) / 1 = 10%.
  2. 02Half Kelly = 5% of current holdings per opportunity.
  3. 03If the true probability is 52% rather than 55%, full Kelly overbets by more than double.

Result

5% per opportunity, resized after each one. The halving is not conservatism — it is the correct response to uncertainty about the edge itself.

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