kelly criterion / pinnacle fair odds / stake sizing

Kelly staking with Pinnacle fair odds

The Kelly criterion turns an edge into a stake: with a fair chance of 46.13% and a price of 2.25, full Kelly says 3.04% of the bankroll. Most bettors stake a quarter of that. This page gives the formula, where the fair chance comes from when Pinnacle prices arrive through the odds API, and the mistakes that turn a good edge into a drawdown.

The formulaStake fraction = (b × p − q) ÷ b, where b is the price minus one, p the fair chance of winning and q one minus p.
The examplePrice 2.25, so b = 1.25; p = 0.4613, q = 0.5387. (1.25 × 0.4613 − 0.5387) ÷ 1.25 = 3.04%.
Quarter Kelly3.04% ÷ 4 = 0.76% of the bankroll. On 1,000 that is a stake of 7.61.

The formula and a worked stake

Kelly answers one question: given an edge, what fraction of the bankroll maximises its long-run growth? The answer depends on two numbers only, the price you are offered and your estimate of the fair chance. Everything else, including how confident you are in that estimate, goes into the fraction of Kelly you choose to bet.

The example is the one the EV calculator opens with. Pinnacle prices the home side at 2.10 in a three-way market; with the margin removed the fair chance is 46.13%. A bookmaker offers 2.25. Expected value is 2.25 × 0.4613 − 1 = +3.80%, and full Kelly is 3.04% of the bankroll.

Pinnacle 2.10fair 2.17yours 2.25

Expected value at 2.25: +3.80%Positive EV at this price
Stake at quarter Kelly: 0.76%7.61 of the bankroll; full Kelly 3.04%

Where the fair chance comes from

The p in the formula is not the price's implied chance. A price of 2.25 implies 44.44%, but that figure includes the other book's margin, and a stake sized on it is sized on a number that flatters the book. Use Pinnacle's price with the margin removed instead: the margin removal guide shows the arithmetic, and the calculators do it for you.

From the Pinnacle odds API the chance is a loop away. Each event's money line arrives under its period; convert, sum, divide, and the fair chance for every selection on the board is ready before the next poll. Drop alerts carry the fair price of the moved selection in the nvp field, so a relay can print the Kelly stake next to the alert. A null nvp means unknown, and no stake should be sized on it.

Half KellyThree quarters of the growth rate with far smaller swings.
Quarter KellyThe common choice when the edge is an estimate, which it always is.
Twice KellyZero expected growth: the extra risk cancels the edge entirely.

Why almost nobody bets full Kelly

Full Kelly assumes p is exactly right. It never is: the fair chance is a market estimate, and a bettor's own view sits on top of it. Overestimate the edge by a factor of two and full Kelly becomes twice Kelly, whose expected growth is zero. Underestimate it and you merely grow more slowly. That asymmetry is the whole case for fractional staking.

Half Kelly keeps three quarters of the growth rate and roughly halves the size of the swings. Quarter Kelly gives up more growth for a bankroll curve most people can live with, and it is the fraction the calculator defaults to. The right fraction is a temperament decision as much as a mathematical one; the mathematics only says that less than full is safe and more than full is not.

Mistakes that undo the formula

Sizing on the raw implied chance rather than the fair one, which overstates p on every bet. Sizing on a stale price: a Pinnacle price that dropped five minutes ago has a new fair chance, and a stake computed before the drop is computed on the wrong p. Treating correlated bets as independent, so three Kelly stakes on outcomes of the same match add up to a position far larger than any one edge justifies. And recomputing the bankroll only monthly, when Kelly assumes each stake is a fraction of what you hold now.

A drop alert is the moment to recompute rather than to bet reflexively. The dropping odds calculator turns the two prices in an alert into the chance shift the market made, which is the input the next Kelly stake needs. Prices in American format convert first; the odds converter on pnclAPI handles that step.

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Questions about Kelly stakes

What if the Kelly fraction comes out negative?

Then the price is below the fair price and the bet has no edge. Kelly says stake nothing. The EV calculator shows the same as a negative expected value.

Does Kelly work for three-way markets?

Yes, one selection at a time. Each selection has its own fair chance and its own price, so each has its own Kelly fraction. Betting two selections of the same market at once is where the correlation mistake above appears.

How often should the bankroll figure be updated?

Before every stake, from the current balance. Kelly is a fraction of what you hold, and a figure from last month sizes bets on money that may already be lost or won.

The worked numbers follow the calculator's example prices; API field names follow the vendor's published documentation, checked on 26 September 2026. Published 29 September 2026.