Probability Basics: From Chance to a Market’s Real Cost

Probability measures how likely a defined event is to happen. In a prediction market, keep three numbers separate: your probability estimate, the market’s quoted price, and the total cost of buying a contract. They can differ enough to change the calculation.

Read a probability correctly

Probabilities run from 0 to 1, or 0% to 100%. Zero means impossible; one means certain in the model. Fractions, decimals and percentages are different ways to express the same number: 3/5 = 0.60 = 60%. These are the basic conventions described in OpenStax’s probability guide.

A 60% forecast means the event is more likely than not, but failure remains a substantial possibility. It does not promise six successes in the next ten cases.

The probability of an event not happening is its complement:

P(not A) = 1 − P(A)

Here, P means “probability of.” If Yes and No cover every possibility, a 60% Yes estimate implies a 40% No estimate. This follows from the complement rule, not from whatever prices happen to appear on a trading screen. Check for cancellation or alternative settlement provisions before treating a contract’s Yes and No outcomes this way.

Two possible outcomes also do not automatically mean a 50–50 chance. Counting favorable outcomes and dividing by all possible outcomes works only when those outcomes are equally likely.

Define the event before estimating it

Consider this entirely hypothetical market:

Will Station A’s reported daily maximum temperature be at least 80°F on the specified date?

Assume its rules identify the reporting agency, station, local-day boundaries and which published temperature record determines settlement. Assume that record will be available. Exactly 80°F qualifies; a reading from another station does not.

Those details define what you are forecasting. “It will feel hot” is a different claim. Kalshi’s market-rules guidance explains that each market has its own criteria for a Yes resolution and an outcome-verification source.

For an invented teaching dataset, suppose 12 of 20 comparable past days reached the threshold:

Historical frequency = 12 ÷ 20 = 0.60 = 60%

That is a starting estimate, not a known probability for the upcoming day. The usefulness of the comparison depends on what makes the days comparable and how current conditions differ. For the arithmetic below, assume your final estimate remains 60%.

Translate probability into a payout value

Assume a simple binary contract pays $1 if Yes wins and $0 if it loses, with ordinary settlement and no cancellation. The CFTC describes this common structure in its event-contract explainer, while noting that other payout structures exist.

At your estimated probability, the expected payout is:

(0.60 × $1) + (0.40 × $0) = $0.60

That makes 60 cents your break-even purchase price if there are no other costs. “Expected” means a probability-weighted average—not a payout you receive on this single contract.

A 57-cent market quote can be read as roughly a 57% market-implied probability for a $1 binary payout. But it reflects traders’ perceived likelihood, not a verified fact about the future, as the CFTC explains.

Check the spread and fees

Keep the same example, with these hypothetical order-book prices and costs:

Item	Amount per Yes contract
Best bid: highest price a buyer is offering	55¢
Best ask: lowest price a seller is offering	59¢
Midpoint of bid and ask	57¢
Assumed purchase fee	2¢

The midpoint is a reference, not the price available for an immediate purchase. Polymarket’s order-book documentation distinguishes the lowest ask for buying, highest bid for selling, and their midpoint.

The spread is 59¢ − 55¢ = 4¢. Assume enough contracts are available at the ask to fill your purchase. Your entry cost is then:

59¢ + 2¢ = 61¢

The fee is illustrative, not a current platform fee quote. Assume you hold to settlement and incur no other costs; taxes and the time value of money are excluded.

Your possible net results are:

• Yes wins: $1 − $0.61 = +$0.39.
• Yes loses: $0 − $0.61 = −$0.61.

Your expected net result is:

(0.60 × $0.39) + (0.40 × −$0.61) = −$0.01

You judged Yes more likely than not—and more likely than the midpoint suggested—yet the purchase has a negative expected result under your estimate. Its break-even probability is 61%, because 0.61 × $1 equals the 61-cent entry cost. The spread is already reflected in the ask; do not add it again as a separate fee.

Before risking money, write down the exact event, your estimate and its basis, the executable price, and all applicable costs. A small change in your estimate could reverse this expected-result calculation; correct arithmetic does not establish forecast accuracy. Use the broader pre-trade checklist to check the remaining risks.