The Kelly criterion for prediction markets: how the formula sizes a position on a contract priced in cents, what fees do to it, and why most people use a fraction

Guide · Updated October 24, 2026 · 18+ · Not legal, tax or financial advice · By BetG8 Editorial · Sports

Most writing about prediction markets is about whether a price is right. The Kelly criterion answers a different question: given that you think a price is wrong by a certain amount, how much should you put on it? It is the standard reference point for position sizing in betting and trading, and on an exchange where contracts settle at $0 or $1 it takes an unusually clean form.

What the Kelly criterion is

John L. Kelly Jr. derived the rule in "A New Interpretation of Information Rate," published in the Bell System Technical Journal in July 1956. His question came from information theory: a gambler with a private, imperfect tip should bet the fraction of capital that maximises the expected logarithm of wealth, and the maximum growth rate he could achieve turned out to equal the rate of information in the tip. Edward Thorp later applied the result to blackjack, sports betting and the stock market and popularised it among investors.

For a bet that pays b units of profit per unit staked if it wins, with win probability p and loss probability q = 1 − p, the Kelly fraction is f = (b·p − q) / b. Two properties follow from maximising the logarithm. The rule never bets the whole bankroll on an uncertain outcome, because a single loss would make the logarithm minus infinity. And it bets nothing when the expected value is zero or negative, since b·p − q is then zero or less.

The formula for a contract priced in cents

A yes contract bought at price c pays $1 if the event happens, so the profit per dollar spent is (1 − c) / c, and that is b. Substituting into Kelly's formula and simplifying gives a form that needs only the price and your probability:

f = (p − c) / (1 − c)

Here f is the share of the bankroll spent on contracts, p is your probability that the event happens and c is the price in dollars. The numerator is your edge in probability points; the denominator is what the contract can still gain. The same formula works for the no side: a no contract at price 1 − c is a bet that the event does not happen, so you substitute 1 − p and the no price. A useful check is that the expected return per dollar is (p − c) / c, so Kelly bets more when the edge is larger and, for the same edge, more on contracts close to $1, where a win returns little but a loss is less likely.

The table shows that Kelly does not simply follow the size of the edge. A 10-point edge at 70 cents justifies a third of the bankroll, while a 5-point edge at 5 cents justifies about 5 percent, because the cheap contract loses far more often even when it is underpriced.

Adding the fee

On an exchange the price on the screen is not the whole cost. Kalshi's published fee schedule charges a taker, an order that fills immediately against a resting order, 0.07 × contracts × price × (1 − price), rounded up to the next cent per order; on series where a maker fee applies, a resting order that is later filled pays 0.0175 times the same term. At 50 cents the taker fee is 1.75 cents per contract on a 100-contract order, and it shrinks towards the ends of the price range. Polymarket US charges a rate on the same price-times-one-minus-price term that varies by category; our fee comparison sets out the rates.

The clean way to include the fee in Kelly is to treat it as part of the price. If the all-in cost per contract is c plus the fee per contract, the formula becomes f = (p − c_all-in) / (1 − c_all-in). Because the fee comes off the numerator, which is usually small, it cuts the Kelly fraction by far more than its share of the price: in the 60 percent, 52-cent row above, a fee of 3.4 percent of the price reduces the Kelly fraction by about a fifth. A trade whose edge is smaller than the fee has a Kelly fraction of zero, whatever the price.

A worked example with a $1,000 bankroll

Suppose you have $1,000 set aside for trading, you estimate that an event has a 60 percent chance, and the yes contract is offered at 52 cents. You would take the offer, so you pay the taker fee.

The fee is rounded up once per order, so splitting the same position into many small orders costs more. On a single contract the fee rounds up to 2 cents, which is why small orders pay a proportionally higher rate.

Why full Kelly is rarely used

Kelly maximises long-run growth only if p is your true probability. In practice p is an estimate, and the formula punishes overconfidence much harder than caution. The table below uses the example above, an all-in cost of 53.75 cents, and shows the expected growth of the bankroll's logarithm per trade, then what that implies for the median bankroll after 100 independent trades of the same kind, at different fractions of the Kelly stake.

Two patterns stand out. Betting twice the Kelly amount produces no growth even when your estimate is right, which is a general property: growth falls to roughly zero at twice the Kelly fraction. And if the true probability is 55 percent rather than the 60 you assumed, the full Kelly stake loses money over time while the quarter stake still grows slightly, because a 55 percent chance is barely above the 53.75-cent cost. Half Kelly gives about three-quarters of full Kelly's growth rate with roughly half the volatility, which is the trade-off Thorp and later researchers describe and the reason fractional Kelly is the common practice. The figures are medians; individual paths vary widely, and a run of losses at full Kelly can cut a bankroll in half well before the long run arrives.

Several positions at once

The single-bet formula assumes one position at a time. When you hold several, Kelly fractions computed one by one can add up to more than the bankroll, and positions on related events, such as a team winning and the same team covering the spread, behave like one larger position. The usual practical adjustments are to scale all positions down so their total stays well below the bankroll, and to treat correlated positions as a single bet. Contracts that settle months away also tie up capital that cannot be used for other trades, which Kelly in its simple form ignores. None of this changes the core result: a stake should grow with the edge and shrink with the uncertainty.

What this guide does not cover

This guide covers the single-bet Kelly formula for binary contracts and the effect of a per-contract fee. It does not cover the multi-asset version, which needs a covariance estimate, selling or closing positions before settlement, the bid-ask spread, which adds to the fee for a trader who crosses it, or taxes. Fee figures are from Kalshi's fee schedule as of October 2026; schedules change, and some series carry different multipliers. The growth figures are calculated, not observed, and assume independent trades at the same price and probability. Nothing here is legal, tax, financial or betting advice, and nothing here suggests that any particular trade has an edge.

Frequently asked questions

What is the Kelly criterion formula for a prediction market contract?

For a contract that costs c and pays $1, with your probability p that the event happens, the Kelly fraction of the bankroll is (p - c) / (1 - c). At p = 60 percent and c = 52 cents that is 16.7 percent before fees. If p is not above c, the Kelly fraction is zero.

How do fees change the Kelly fraction?

Add the fee per contract to the price and use the all-in cost in the formula. On Kalshi a taker pays 0.07 times price times one minus price, rounded up per order, about 1.75 cents at 52 cents, which lowers the Kelly fraction in the example from 16.7 to 13.5 percent.

Why do people use half Kelly?

Because the probability is an estimate. Half Kelly keeps about three-quarters of the growth rate with about half the volatility, and it loses far less when the edge has been overstated. In the worked example, if the true chance is 55 percent instead of 60, full Kelly shrinks the median bankroll by about 38 percent over 100 trades while quarter Kelly still grows slightly.

Does the Kelly criterion guarantee a profit?

No. It maximises expected long-run growth if the probability estimate is correct. With a wrong estimate it can lose money, and even with a correct one the bankroll can fall sharply in the short run.

Related

• Implied probability explained: odds to percent, vig out
• Kalshi fees explained: the taker formula and maker fees
• Sportsbook vs exchange price comparison tool
• Kalshi vs Polymarket fees compared
• Is Kalshi legal in your state? The 50-state tracker

Sources

• J. L. Kelly Jr., A New Interpretation of Information Rate, Bell System Technical Journal 35(4), July 1956, for the original derivation and the log-growth criterion.
• Edward O. Thorp, The Kelly criterion in blackjack, sports betting and the stock market, 2006, for the general formula, the zero-growth point at twice the Kelly fraction and the case for fractional Kelly.
• Kalshi, Fee schedule, as of October 2026, for the taker and maker formulas and the rounding rule.
• BetG8, Kalshi vs Polymarket fees, for the Polymarket US category rates. Growth and median figures in the tables are BetG8 calculations from the formulas above.

18+ only. Betting and prediction market contracts carry real financial risk and you can lose what you stake. This page explains arithmetic; it is not legal, tax, financial or betting advice. If gambling stops being fun, help is available at 1-800-GAMBLER.