The Kelly criterion in prediction markets
A formula for how much, given that you already know how likely. That second half is the hard part.
Kelly answers one question: given a bet with known payoff and a probability you trust, what fraction of your bankroll maximises long-run growth? On a binary contract that pays $1 the answer is unusually clean.
The formula, and why it is so simple here
General Kelly is f = (q(1 + b) − 1) ÷ b with b the net odds. On a contract bought at price p that pays $1, the net odds are b = (1 − p) ÷ p. Substitute and everything cancels: f = (q − p) ÷ (1 − p).
Read it once and the intuition arrives: the numerator is your edge, the denominator is what you stand to gain per share. Buy at 38¢ believing 45% and full Kelly is (0.45 − 0.38) / 0.62 = 11.3% of the bankroll. That is a very large position, which is the first warning.
The four assumptions
- Your probability is rightKelly is optimal given a true probability. Given an inflated one it overbets, and overbetting past the growth-optimal point reduces growth rather than increasing it — at twice the Kelly fraction, the long-run growth rate goes to zero.
- You get to repeatThe criterion maximises expected log wealth over a long sequence of independent bets. A handful of correlated positions on the same election is not that sequence.
- The price is the price you gotFees and spread move your real entry. Put the all-in number in, or the sizing is built on a price you never paid.
- Resolution is clean and promptA contract that voids, or settles in fourteen months, is not the payoff Kelly is modelling.
Why almost everyone uses a fraction of it
Because assumption one fails constantly and quietly. Half Kelly gives up a quarter of the theoretical growth and roughly halves the volatility; quarter Kelly gives up more and buys a lot of tolerance for being wrong about q. If your estimate came from a model you have never backtested, the honest fraction is small.
And if the formula returns zero or less, the position is zero. That is not the calculator failing to find you a trade — it is the answer. Run it.
Questions
What is the Kelly criterion?
A bankroll-sizing rule that maximises the expected logarithm of wealth over repeated bets. It tells you what fraction to stake given an edge, not whether you have one.
What is the Kelly formula for a binary contract?
For a contract paying $1 bought at price p with probability estimate q, the Kelly fraction is (q - p) / (1 - p).
Why do people use half or quarter Kelly?
Because full Kelly assumes your probability is exactly right, and it punishes overestimation severely. Fractional Kelly trades theoretical growth for tolerance of estimate error.