Implied probability

Every venue in this catalogue sells a contract that pays a dollar if something happens and nothing if it does not, and nearly every screen that shows one prints its price as a percentage. The conversion is one division. What it hides is the reason the number on one screen rarely matches the number on the next.

How it works

The arithmetic. A contract that pays $1 and costs $0.37 breaks even, before costs, if it wins 37 times in 100. So the price divided by the payout is the probability at which buying is a fair price, and that is what "implied" means: the probability the price implies, not one anybody measured. Polymarket's documentation puts it in a table — $0.25 is a 25% chance, $0.50 a 50% chance. Kalshi writes the same idea into its fee schedule, defining the expected earnings on a contract as the maximum earnings times "the implied probability" of making them, which it sets equal to the price divided by $1.

Which price. A contract with a bid and an ask has at least three candidate prices, and the screen picks one. Polymarket's documentation says its displayed price is the midpoint of the bid and the ask, and that when the spread is wider than 10 cents the last traded price is shown instead. Its own worked example has a bid of 34 and an ask of 40: the screen says 37%, you pay 40 to buy and receive 34 to sell. Neither of the prices you can actually trade at is the one printed.

Which unit. The same quantity arrives in at least three scales. Kalshi's API returns prices as fixed-point dollar strings with up to four decimal places, and its documentation warns that the older integer-cent fields cannot represent sub-cent prices on markets whose tick grid goes below a cent — some grids step by a tenth of a cent near the ends of the range. Polyrama normalises both of its venues to 0–1, Adjacent to 0–100. A tool that reads 0.37 as 37 cents in one feed and 37 as 37 dollars in another is not making a rounding error; it is reporting a contract at a hundred times its price.

Odds are the same number upside down. Decimal odds are the payout divided by the price, so a 37-cent contract is odds of about 2.70, and a "multiplier" display is the same thing. The conversion is exact only when nothing is taken out. The Limitless card records its Packs carrying a 10% vig already baked into the displayed multiplier, so the probability you would back out of that multiplier is not the one the product is priced on.

Why it matters here

The fee moves the break-even, not the screen. Paying 37 cents plus a fee means the contract has to win more than 37 times in 100 to break even. On a schedule like Kalshi's, where the fee scales with price times one minus price, that extra is largest in cents near 50 and largest as a share of the stake on cheap contracts. The catalogue normalises fees to one unit for this reason — see effective fee at fifty cents and what a trade actually costs.

Mutually exclusive outcomes do not sum to exactly 100%. On a multi-outcome event the percentages printed beside the outcomes add up to something near 100 and almost never to 100 — spreads, thin books on long shots and the midpoint-or-last-trade rule all leave a gap. On Polymarket the neg-risk page shows how far apart they were on one day. Normalising them to sum to one is a modelling choice, and a tool that does it silently is showing you its model, not the market.

Two venues are pricing two contracts. A 61% on one venue and a 57% on another for "the same" event are often not a disagreement about the world. The rule texts name different settlement sources and close times, the fees are charged on different bases, the collateral differs, and one side may be a last trade from an hour ago. The full breakdown is in why the same contract costs two different prices. Treat a cross-venue gap as a list of differences to account for before treating it as an opportunity.

It is a probability of settlement, not of the event. The contract pays on what its rules say and what its resolver decides. Where the wording, the source or the resolver could go another way, the price includes that, and a reader using it as a forecast of the underlying event is reading in something the price never promised. Calibration is the measure of whether those percentages have, over many contracts, come true as often as they said.