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Kelly criterion calculator for binary markets

A sizing rule for an edge you already have. It cannot give you one.

On a contract that pays $1, bought at price p, with your own probability estimate q, the Kelly fraction collapses to something you can hold in your head: f = (q − p) / (1 − p). That is the share of your bankroll that maximises long-run growth if q is right. The whole argument is in those last three words.

Kelly for a binary contract
Use your all-in price from the fee calculator if you are the taker.
The whole roll you are staking from, not this trade.
1 = full Kelly. Most people who use this at all use a quarter of it.
Suggested stake
Full-Kelly fraction of bankroll
f = (q − p) / (1 − p)
Fractional-Kelly fraction of bankroll
Shares that buys
Edge per share
Net odds received
b = (1 − p) / p
Expected log-growth per trade, at full Kelly
the quantity Kelly maximises — not a return forecast
Kelly assumes your probability estimate is right. It is a sizing rule for an edge you already have, not a way to manufacture one, and it is famously brutal when the estimate is wrong — which is why the fraction box exists. Read what this actually assumes before using it.

What it assumes, stated plainly

That your probability is correct. Kelly is optimal given a true probability. Given an overconfident one it does the opposite of what you wanted: overbetting past the growth-optimal fraction lowers long-run growth, and betting at twice the Kelly fraction drives it to zero. Most people who use Kelly seriously use a fraction of it — a quarter is the common choice — and the reason is not modesty, it is that estimate error is the dominant risk.

That you can bet repeatedly. The criterion maximises the expected logarithm of wealth, which is a statement about a long sequence of independent bets. One market, once, is not that sequence.

That the price you enter is the price you enter. If you are the taker, your real entry is the price plus the fee — take the all-in number from the fee calculator and put that in the price box, or Kelly will size you off a price you did not get.

That resolution is binary and prompt. A contract that voids, or resolves in fourteen months, is not the bet Kelly is modelling. The resolution calculator covers that part.

Questions

What is the Kelly formula for a prediction market?

For a binary contract paying $1 bought at price p with estimated probability q, the Kelly fraction is (q - p) / (1 - p). It is the general Kelly formula with net odds b = (1 - p) / p substituted in.

What is fractional Kelly?

Betting a fixed fraction of the Kelly stake — a quarter or a half — to reduce drawdown and to buy tolerance for a probability estimate that is wrong. It gives up some theoretical growth for a much smoother path.

What if my estimate equals the market price?

Then the formula returns zero and the correct stake is nothing. Kelly sizing zero is an answer, not an error.

Does Kelly apply to prediction markets at all?

The arithmetic applies to any bet with a known payoff and a probability you are willing to state. Whether you should trust your probability is a separate question and the more important one.

Related

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