Bet sizing, and the arithmetic behind it.

Buy one contract at 40¢ and you have spent $0.40. If the event happens the contract settles at $1.00 and you are up $0.60. If it does not, it settles at zero and you are down the $0.40 you paid. That is the whole payoff structure, and it is why prediction markets are easier to size than most instruments: there is no leverage to unwind, no margin call, and the worst case on a long position is exactly the premium paid.

Two numbers follow from the price. The net odds you are being offered are (1 − p) ÷ p — at 40¢ that is 1.5 to 1. The break-even probability is the price itself, before costs: a 40¢ contract needs to happen more than 40% of the time to be worth buying. Kalshi's fee moves that bar, which the break-even guide works out in cents.

The Kelly criterion maximises the expected logarithm of a bankroll — equivalently, its long-run compound growth rate. For a bet with net odds b that wins with probability q, the growth-optimal fraction of bankroll to stake is f* = q − (1 − q) ÷ b.

Substitute the prediction-market odds b = (1 − p) ÷ p and the algebra collapses:

f* = (q − p) ÷ (1 − p)

That is the entire sizing rule for a binary contract. The numerator is your edge in probability points. The denominator is what you stand to gain per contract. Notice what is absent: how confident you feel, how large the market is, and how the last five trades went. The formula does not model any of them.

Each row is f* computed at a price and a believed probability, with the half-Kelly figure beside it. Read the fourth column against the third before reading anything else on this page.

A five-point edge at 50¢ returns 10% of bankroll. The same five-point edge at 90¢ returns 50%, because the denominator (1 − p) has shrunk to a dime — you risk 90¢ to make 10¢, so the formula demands size to make the growth arithmetic work. Whether a rule that stakes half a bankroll on one contract is one anybody should run is the subject of the next two sections.

The fee is not a rounding error at these sizes and it does not belong beside the formula — it belongs inside it. Kalshi's taker fee is 0.07 × p × (1 − p) per contract, peaking at 1.75¢ on a 50¢ contract. Paying it means the price you actually paid is 51.75¢, so the edge in the numerator is smaller than the one you started with.

A believed 55% chance bought at 50¢ looks like a five-point edge and sizes at 10% of bankroll. Enter it as a taker and the real entry is 51.75¢, the edge is 3.25 points, and f* falls to 6.7% — a third of the position, deleted by a fee most sizing discussions leave out. At the extremes the fee is smaller in cents but the edges are usually thinner too, so the proportion it removes rarely improves.

Full Kelly is growth-optimal and brutal. It is indifferent to the shape of the path, and the path includes drawdowns that most people cannot sit through: staking the full fraction repeatedly means halving a bankroll is an ordinary event rather than a catastrophe. Nothing in the derivation says the ride is tolerable, only that the terminal growth rate is maximised.

Worse, the formula's input is q, the true probability — and q is not observable. You have an estimate of it, and the error in that estimate does not enter symmetrically. Betting twice the Kelly fraction drives the long-run growth rate to zero even when the edge is genuinely there; so an edge you have overestimated by a factor of two is not merely a smaller edge, it is a losing strategy run at full size. Underestimating costs you growth. Overestimating costs you the bankroll.

That asymmetry, rather than squeamishness, is the usual argument for fractional Kelly. Half Kelly gives up roughly a quarter of the theoretical growth rate for roughly half the volatility, and it keeps you solvent through an edge estimate that turns out to be optimistic — which, for anyone estimating probabilities from public information, is the base case rather than the tail.

The formula sizes a single bet in isolation. Portfolios rarely are. Ten contracts across ten NFL games are close to independent; ten contracts that all resolve on one Fed decision are one position with ten tickets, and sizing each as though it stood alone stakes ten times what the arithmetic intended. Correlation is the most common way a disciplined-looking book turns out to have been a single concentrated bet, and it is covered in correlated positions.

It is not advice, and no number above is a recommendation. Kelly is a growth-rate optimiser under assumptions — a known probability, a bankroll you are willing to compound, indifference to the path — and if any of those do not describe you, the formula is answering a question you did not ask. Position sizing is a decision about your own money, made with information about your own circumstances that this page does not have and does not want.