Prices and Probabilities

Every contract on a prediction market carries a price, and the price does double duty. It is the amount a trader pays to open a position, and it is the market's running estimate of how likely the underlying event is. A contract trading at 34¢ can be read, with some care, as a 34% chance. Moving fluently between those two readings turns a screen full of prices into a screen full of probabilities, and it is the reason a market page can be read as a forecast at all. The care matters as much as the conversion, because a price tracks a probability closely without ever equaling it exactly.

What does a prediction market price of 34 cents mean?

Prices make sense only in light of the instrument they are attached to. The unit of trade on a prediction market is an event contract, a claim that pays a fixed settlement value, normally $1, if a defined event occurs, and nothing if it does not (CFTC: Understanding Prediction Markets and Event Contracts). There is no partial credit. The contract settles at $1 or at $0, and everything about reading prices follows from that binary structure. The Event Contracts guide examines the instrument itself; this guide is about what its price tells you.

Suppose a contract trades at 34¢. That single number supports three readings at once:

• A cost. One contract costs 34¢ to buy right now.
• An estimate. The market is collectively pricing roughly a 34% chance that the event occurs.
• A break-even point. Buying is profitable in expectation if the event's true probability is above 34%, and unprofitable if it is below.

The fixed settlement value is what welds price to probability. A claim that pays $1 when an event happens is worth, in expectation, the probability of that event expressed in dollars. A 50% chance of collecting $1 is worth about 50¢, and a 10% chance is worth about 10¢. If a contract traded meaningfully below that expected value, buying it would be systematically profitable and buyers would push the price up; meaningfully above, sellers would push it down. The price that survives this pressure is the point where the marginal buyer and the marginal seller agree, which makes it a working consensus estimate, denominated in cents.

Venues present prices in exactly these terms. Polymarket's introduction to prediction markets describes contract prices as probabilities produced by trading (What is a Prediction Market?), and Kalshi's beginner material walks new traders through reading its prices as percentages (A beginner's guide to reading probabilities). The percent figure on an event page and the price in the order form are the same number wearing different units.

One structural fact completes the picture. Every binary market has a Yes side and a No side, and the pair settles to exactly $1 combined. Whichever way the event resolves, one side pays the full settlement value and the other pays nothing. If Yes trades at 34¢, No consequently tends to trade near 66¢. When the two prices stop summing to roughly $1, traders can lock in a profit by trading the imbalance, and that activity tends to pull the pair back into line.

How do you convert a prediction market price to a probability?

With a settlement value of $1, the conversion rule fits in a sentence: the price in cents is the implied probability in percent. The formal version divides the price by the settlement value.

$$\text{implied probability} = \frac{\text{price}}{\text{settlement value}} = \frac{\$0.34}{\$1.00} = 34\%$$

Read in plain language, the formula says a price is the fraction of the eventual settlement value being paid up front. Because the settlement value is one dollar, the division is nearly invisible. A price of 34¢ is 34% of a dollar, so the implied probability is 34%. A 7¢ contract implies 7%, a 91¢ contract implies 91%, and the whole scale from impossible to certain maps onto prices from $0 to $1.

The conversion runs in both directions, and the reverse direction is where analysis begins. An independent estimate of the event converts to a fair price. If your own research puts the probability at 45%, the contract is worth 45¢ to you. A market price of 34¢ then reads as an eleven-point disagreement between you and the consensus, and the size of that gap, weighed against your confidence in your estimate, is what makes a position attractive or not. Without the conversion, a price is just a number; with it, every market becomes a comparison between what you believe and what the market believes.

Two small caveats keep the arithmetic honest. On venues where contracts trade in one-cent increments, quoted probabilities are coarse at the extremes. Every probability between roughly half a percent and one and a half percent shows up as the same 1¢ price. And the conversion inherits whatever the price itself contains, including the trading costs and structural effects discussed later in this guide, so an implied probability is the market's estimate filtered through market mechanics.

Why is the price you pay on a prediction market different from the displayed probability?

An exchange never has just one price. Buyers post the prices they are willing to pay, sellers post the prices they are willing to accept, and the exchange collects them in an order book. The highest standing buy order is the bid, the lowest standing sell order is the ask, and the gap between them is the spread. The Order Books guide covers the mechanics in full. The part that matters for interpretation is that the probability displayed on an event page is typically computed from the middle of the spread, while the prices available to you sit at its edges. Polymarket's help documentation, for example, describes the displayed price as the midpoint of the bid and the ask (How Are Prices Calculated?).

Suppose an event page shows 60%. Underneath, the best bid might be 58¢ and the best ask 62¢, and the display presents the 60¢ midpoint as a probability. A trader who buys immediately pays the ask, so the position breaks even at 62%, not 60%. A trader who sells immediately receives the bid, 58¢. Anyone who buys and then sells without the market moving pays the full 4¢ spread for the round trip. The displayed probability was accurate as a summary, and no trade was ever available at it.

The width of the spread is itself information. Heavily traded markets tend to hold spreads of a cent or two, so the midpoint, the bid, and the ask all tell nearly the same story. Thinly traded markets can carry spreads of five cents or more, and the honest reading of such a market is a range rather than a point. The consensus sits somewhere inside the spread, and trading is not active enough to say where. A wide spread also warns that the displayed number may move sharply when any sizable order arrives.

Crossing the spread is a measurable cost rather than a rounding detail. One independent analysis of tens of millions of exchange trades found that takers, the traders who accept a standing price for immediate execution, earned systematically negative returns relative to the traders whose resting orders they filled, with the gap widest in thin, lightly traded categories (The Microstructure of Wealth Transfer in Prediction Markets). Immediacy has legitimate value, so the finding does not make taking liquidity a mistake. It does mean the cost belongs in the probability arithmetic.

How do American and decimal odds convert to implied probabilities?

Prediction market prices, decimal odds, and American odds are three notations for the same quantity. Sportsbooks and international exchanges quote the odds formats, while prediction markets quote prices. A trader comparing a contract against a sportsbook line, or reading commentary written in another notation, needs to move between them, and the conversion always passes through implied probability.

Decimal odds state the total return per unit staked, so the conversion is a single division: implied probability is 1 divided by the decimal odds. Decimal odds of 2.94 imply 1 / 2.94, or about 34%. American odds use two conventions that meet at plus and minus 100. A positive figure states the profit on a 100-unit stake, and a negative figure states the stake required to earn a profit of 100 units.

$$p = \frac{100}{A + 100} \;\;\text{for } A > 0 \qquad\qquad p = \frac{|A|}{|A| + 100} \;\;\text{for } A < 0$$

In words: for positive American odds, divide 100 by the odds plus 100; for negative American odds, divide the absolute value of the odds by that same value plus 100. A quote of +250 converts to 100 / 350, about 28.6%, comparable to a contract priced near 29¢. A quote of -400 converts to 400 / 500, or 80%, comparable to an 80¢ contract.

One structural difference keeps the notations from being perfectly interchangeable. Sportsbook odds carry the operator's margin, often called the vig, inside the quote. Convert both sides of a two-way line to implied probabilities and they will sum to more than 100%, because the book prices each side slightly in its own favor. Recovering the book's underlying probability estimate requires stripping that margin out. On a prediction market, the ask prices of the two sides also tend to sum slightly above $1, but the excess is the spread between resting orders rather than a margin embedded in every quote, and it narrows as trading deepens. The Markets vs Sportsbooks guide compares the two structures in full.

How do you read prices in a multi-outcome market?

Many events resolve to one of several outcomes rather than a simple yes or no: a nomination contest, an award, the winner of a season. Venues list these as a family of binary contracts, one Yes contract per outcome, all settling against the same event. The productive way to read the family is as a probability distribution.

Read as a set, the table describes a two-candidate race with a modest leader, a distant third, and a fourth priced close to irrelevance. Relative prices matter as much as absolute ones. A at 46¢ against B at 33¢ says the market sees A as roughly 1.4 times as likely, a closer contest than the ordering alone might suggest.

The total deserves attention, because mutually exclusive and exhaustive outcomes should in principle sum to exactly 100%. In practice the sum usually lands slightly above or below. Each outcome trades in its own order book with its own spread, displayed numbers are typically midpoints rounded to the cent, and quotes in thin outcomes can sit stale for hours. A total between roughly 99¢ and 102¢ is ordinary market texture rather than a signal.

Larger deviations tend not to survive, because they are directly tradeable. If every Yes contract in the set could be bought for a combined 96¢, a trader could buy one of each, and since exactly one contract must settle at $1, the basket guarantees $1 of proceeds against 96¢ of cost. If the set could be sold for a combined 104¢, the reverse trade locks in the excess. Automated traders watch for these inconsistencies continuously, and an academic study of a year of on-chain trading measured tens of millions of dollars of realized profit from closing them, most of it from rebalancing prices within multi-outcome sets (Unravelling the Probabilistic Forest). For a reader, the consequence is reassuring: arbitrage pressure keeps the distribution roughly coherent, so the set of prices can be trusted as a set.

When a cleaner distribution is needed, normalize by dividing each price by the total. Candidate A's 46¢ against the 101¢ sum reads as about 45.5%, and the four outcomes then sum to exactly 100%. The binary market of the earlier sections is simply the two-outcome case of the same structure, which is why Yes and No prices sum to roughly $1.

Why is a prediction market price not exactly a probability?

A market price is produced by trading, and everything that shapes trading leaves a residue in the price. Four forces account for most of the distance between a price and the probability it implies. They do not break the conversion, but they do set its margin of error.

• Trading costs. Fees and the spread move the break-even probability away from the raw price.
• The cost of committed capital. Money locked in a contract until resolution cannot be used elsewhere, which can hold prices away from probabilities on long-dated markets.
• Who shows up to trade. Prices reflect the beliefs of participants, weighted by their capital and conviction, rather than a census of everyone with an opinion.
• Behavior at the extremes. Contracts priced in single-digit cents have historically tended to trade rich relative to how often they resolve Yes.

Trading costs are the mechanical wedge. The spread already separates the executable price from the midpoint, and on venues that charge trading fees the break-even moves again. A contract bought at 34¢ with a fee attached needs the event to occur slightly more than 34% of the time before the position is profitable. Fee structures differ across venues and change over time, so the practical habit is to check the venue's published schedule (Polymarket's fee documentation is one example) and fold it into the arithmetic rather than reading the raw price as the full cost.

Committed capital matters most at long horizons and near the ends of the price range. A contract at 97¢ that resolves in a year returns about 3% over that year if everything goes right, while tying up the full purchase price and bearing the risk of an upset the whole way. Many traders decline that trade even when they agree the probability is above 97%, and their absence can let the price sit below where probability alone would put it. Vitalik Buterin's first-person account of trading an election market describes this dynamic from the inside. Prices he regarded as clearly wrong stayed wrong for months, in part because correcting them required locking substantial capital into a near-certainty for an uncertain stretch of time (Prediction Markets: Tales from the Election).

Composition is the subtler force. A market price is not a poll; it is the equilibrium of whoever chose to trade, weighted by how much they traded. The canonical theoretical treatment of this question finds that under fairly general conditions prices land close to the average belief of the traders in the market, while risk preferences and the distribution of beliefs and capital among them can push price and average belief apart (Interpreting Prediction Market Prices as Probabilities). Why an aggregate of self-interested traders is worth listening to at all is its own subject, taken up in Wisdom of Crowds.

At the extremes, the record shows a persistent lean, known in the research literature as the favorite-longshot bias. Very cheap contracts attract buyers out of proportion to their chances, since a few cents can feel like a small price for a large potential return, and the microstructure analysis cited earlier found that the cheapest contracts delivered deeply negative average returns to their buyers (Microstructure of Wealth Transfer). A 3¢ price says the market treats the outcome as very unlikely, but whether the fair number is 3% or 1% is a distinction the price alone may not settle.

A clean way to see the combined effect of these forces is to watch two markets price the same event. A working paper comparing crypto threshold contracts against the probabilities implied by exchange-traded options on the same thresholds found persistent gaps of several percentage points that decayed over hours rather than seconds (Do Prediction Markets Match Option Prices?). One event carried two prices, so at least one of them sat some distance from the true probability.

None of this argues against reading prices as probabilities; it argues for reading them with error bars. The empirical record supports the practice. Across five US presidential elections, prices on the Iowa Electronic Markets finished closer to the final vote than contemporaneous polls 74% of the time, in a comparison spanning 964 polls (Prediction Market Accuracy in the Long Run), and an independent review that scored several thousand resolved markets with standard forecast-accuracy measures found real accuracy alongside real limits (Are Prediction Markets Good for Anything?). A 34¢ price is a serious estimate near 34%, produced by people risking money on being right. It is not a certified measurement, and the forces above set the width of the uncertainty around it.

Are high-probability prediction market contracts low risk?

A contract at 92¢ implies a 92% probability. Whether that makes it a low-risk position is a separate question. Probability describes the event; risk describes what happens to capital in each outcome. At 92¢, a buyer risks 92¢ per contract in order to earn 8¢ per contract. The frequent outcome is a small gain, and the rare outcome is a loss more than eleven times as large. A single miss erases the proceeds of eleven and a half wins at the same price. The position wins often, which is a statement about frequency, not about safety.

Expected value makes the point precisely. For a contract with a settlement value of one dollar:

$$\text{expected value per contract} = p \times (\$1 - \text{price}) - (1 - p) \times \text{price} = p - \text{price}$$

The algebra collapses to one term: expected profit is your probability minus the price. If your estimate of the event matches the market's, expected value is zero before costs, at 92¢ exactly as at 8¢. A high price does not make a position profitable in expectation; only a probability estimate above the price does, and that holds at every price level.

Costs sharpen the asymmetry near the top of the range. The spread and any fees are paid against a maximum possible gain of 8¢, so a cent of round-trip cost consumes a far larger share of the upside at 92¢ than it would at 50¢. High-probability positions can absorb very few errors, in the estimate or in the execution, before a thin edge inverts. The mirror-image error at the bottom of the range treats cheap contracts as small risks. The loss per contract is indeed small, but the previous section's evidence suggests the cheapest prices have tended to overstate their outcomes' chances, so frequent small losses can accumulate into the same result as a rare large one.

Reading a market well means holding both views at once: the price states the chance the market assigns, while the payoff structure determines what acting on that chance costs, and what it can return.

Related guides

The ideas in this guide connect directly to several neighboring topics.