Prices and Probabilities
Polymarket odds and Kalshi percentages connect contract prices to probabilities, helping you compare the cost of a trade with your forecast.
Following a prediction market often means asking how likely an outcome is. When you trade, you also compare that chance with the price available. Even if you expect a team to win a tournament, its contract may cost more than your forecast justifies. A less likely winner can also offer value if its price is low enough.
For a contract paying $1 on success and $0 on failure, the price in cents translates directly into an implied probability. Your own estimate can be higher or lower, and the difference affects what you would expect to earn. Fees and the price available for your order also matter because the chance quoted on the screen may differ from the chance needed to cover your costs.
What does the chance mean on Kalshi and Polymarket?
The chance shown on Kalshi or Polymarket is a Yes contract's price read as the market's implied probability of the outcome. A contract paying $1 on success and $0 on failure has an expected payment equal to its chance of success multiplied by $1. Each cent of value therefore corresponds to one percentage point of chance.
To calculate implied probability, divide the contract price by its payment on success, using the same currency unit for both. A 36¢ price divided by a 100¢ payment implies 36%. A contract paying $10 on success and nothing on failure would imply the same probability at a $3.60 price.
Suppose a hypothetical market asks whether Arsenal will win the Champions League, and a Yes contract costs 36¢. Holding one contract through ordinary settlement produces one of these results:
| Result | Money received at settlement | Profit or loss before fees |
|---|---|---|
| Arsenal wins under the contract's rules | $1 | 64¢ profit |
| Arsenal does not win | $0 | 36¢ loss |
The dollar received on success includes the 36¢ you paid. Your 64¢ profit is about 178% of that cost, while the 36% implied probability measures the chance of earning it.
A Yes contract bought at a hypothetical 36¢ pays $1 if Arsenal wins the Champions League, covering the purchase cost and leaving 64¢ in profit. The price implies a 36% chance of success, while the return on success is about 178% before fees.
A No contract applies the same logic to the opposite result. A 64¢ No price implies a 64% chance that Arsenal does not win. Although the probabilities of Yes and No add to 100%, buying both sides can cost more than a dollar because of the prices offered to buyers.
The contract's rules determine which outcome the percentage refers to. A company announcing a new phone before a deadline and shipping it before that deadline are different propositions. Evidence supporting an announcement may say little about delivery.
The cents-to-percentage reading assumes $1 or $0 at settlement. In Polymarket's documented 50-50 resolution, each side instead receives 50¢. When that result is possible, a price also includes the chance of receiving that partial payment.
How do you convert Kalshi or Polymarket prices to odds?
To convert a prediction market price to odds in decimal form, divide 1 by the price in dollars. For a $1/$0 contract at 25¢, the calculation is 1 ÷ 0.25, or 4.00. Those decimal odds mean $4 returned per dollar committed on success. American odds express the profit on $100 committed when prices are below 50¢, and the cost of making $100 profit when prices are above 50¢.
This table converts hypothetical prices before fees. Decimal and American figures are rounded where needed.
| Contract price | Implied probability | Decimal odds | American odds | Fractional odds |
|---|---|---|---|---|
| 10¢ | 10% | 10.00 | +900 | 9/1 |
| 25¢ | 25% | 4.00 | +300 | 3/1 |
| 36¢ | 36% | 2.78 | +177.78 | 16/9 |
| 50¢ | 50% | 2.00 | +100 | 1/1 |
| 75¢ | 75% | 1.33 | -300 | 1/3 |
| 90¢ | 90% | 1.11 | -900 | 1/9 |
Decimal odds and multipliers
Decimal odds and multipliers both state the total received relative to the purchase cost. At 4.00 decimal odds, or a 4× multiplier, a $20 purchase returns $80 on success. That includes the original $20, leaving $60 in profit before fees.
Converting decimal odds to probability reverses the calculation. Divide 1 by the decimal odds, then multiply by 100. Odds of 4.00 imply 25%, while 2.00 implies 50%.
Converting Kalshi cents to American odds
American odds use a plus sign for prices below 50¢, showing the profit on $100 committed. Above 50¢, the minus sign indicates how much you must commit to make $100 in profit.
Both hypothetical purchases buy 400 contracts that return $400 on success before fees. American odds of +300 mean $300 profit on a $100 purchase at 25¢; -300 means paying $300 at 75¢ to make $100 profit.
With the contract price in cents, the conversion to American odds is:
- Below 50¢, American odds equal 100 × (100 − price) ÷ price.
- Above 50¢, American odds equal −100 × price ÷ (100 − price).
- At 50¢, the equivalent is even money, commonly written +100.
To convert American odds to implied probability, calculate 100 ÷ (odds + 100) for positive odds. For negative odds, remove the minus sign and calculate odds ÷ (odds + 100). Multiply the result by 100 to express it as a percentage. For example, +400 implies 20%, while -400 implies 80%.
Fractional odds
Fractional odds state profit divided by cost. For fractional odds of a/b, implied probability is b ÷ (a + b). The table's 3/1 means $3 of profit for every $1 committed and a probability of 1 ÷ (3 + 1), or 25%.
The spoken phrase “3-to-1” commonly uses this profit convention. Statistical odds in favor of a 25% event reverse the ratio, counting one success for every three failures, written 1:3.
For a hypothetical 25¢ contract, decimal odds of 4.00 count the $4 returned per $1 committed, while fractional odds of 3/1 count the $3 profit before fees. The same 25% chance gives odds in favor of 1:3, comparing one success with three failures.
Comparing Polymarket and Kalshi prices with sportsbook odds
Converting sportsbook odds to percentages preserves the margin included in those odds. Two opposing lines of -110 each imply about 52.38%, totaling 104.76%.
When comparing a contract with a sportsbook line, convert the price you can actually buy at and account for fees. The positions also need matching settlement conditions. A football contract on winning in regular time and a sportsbook line that includes extra time can pay differently on the same match, even when their converted odds are identical.
How much do you make when a prediction market price goes up?
If you sell, your profit per contract is the selling price minus the purchase price and fees. Divide that profit by the purchase price plus entry fees to calculate your percentage return. For a contract that settles at $1 or $0, a price move in cents also changes its implied probability by the same number of percentage points.
Suppose a hypothetical Yes contract on Arsenal winning the Champions League rises from 36¢ to 45¢. Its implied probability has risen by 9 percentage points. If you bought at 36¢ and can sell at 45¢, the 9¢ gain is 25% of your purchase cost, before fees.
A 10¢ rise doubles the value of a contract bought at 10¢, while a rise from 80¢ to 90¢ earns a 12.5% return before fees.
The 9¢ and 10¢ gains in these hypothetical trades produce different returns because each is divided by the price paid. The return before fees is 100% from 10¢ to 20¢, 25% from 36¢ to 45¢, and 12.5% from 80¢ to 90¢.
On research pages reached through the Polymarket and Kalshi screener, a +9 beside a market's chance means a rise of nine percentage points over 24 hours.
The hypothetical market puts Arsenal's chance of winning the Champions League at 45%, up from 36% over 24 hours. The +9 beside 45% measures that rise in percentage points.
A price move can follow new information or a change in the orders traders are willing to place. Connecting it to an injury report or earnings announcement requires comparing when that information became available with the timing of observations in the price chart.
Which prediction market price should you compare with your forecast?
Use the price a seller will accept when deciding whether to buy. For a contract paying $1 on success and $0 on failure, that price in cents sets the break-even percentage before fees. If you already hold the contract, compare its expected settlement value with the price a buyer offers.
A displayed probability may use the average of buying and selling quotes or the price of a previous trade.
Suppose a hypothetical Bitcoin contract has a best bid of 41¢, the highest buying offer, and a best ask of 45¢, the lowest selling offer. Their midpoint is 43¢. The useful number depends on the comparison you are making:
| Comparison | Relevant price | What it means |
|---|---|---|
| Following the quoted probability | 43¢ midpoint | The quotes imply 43%, though no trade need be available at 43¢. |
| Buying and holding to $1/$0 settlement | 45¢ ask | Success must be more likely than 45% for positive expected profit before fees. |
| Selling a contract you already hold | 41¢ bid | Selling releases 41¢ now, to compare with the expected value of holding. |
For example, at an estimated 40% chance of success, the contract's expected settlement value is 40¢. Before fees or the cost of waiting, that is less than the 41¢ available by selling. Your purchase price enters your eventual profit or loss, but it is already paid whether you sell or hold.
A hypothetical Bitcoin contract can be sold for 41¢ or bought for 45¢, with the midpoint displayed as a 43% chance. A 40% forecast puts the expected value of holding at 40¢, below the selling price, while buying needs a forecast above 45% for positive expected profit before fees.
Why can buying more contracts raise the price per contract?
The lowest asking price may cover only part of your order. Buying the rest at higher prices causes slippage, raising the average cost and the probability needed to break even. For example, equal quantities bought at 45¢ and 47¢ cost 46¢ per contract on average, requiring a 46% success rate before fees.
Only 100 contracts are offered at 45¢ in this hypothetical order book, so a buyer ordering 200 pays 47¢ for the rest. The $92 order averages 46¢ per contract and needs a 46% chance of success to break even before fees.
How do fees change a prediction market's break-even probability?
Fees increase the success rate needed to cover a trade's cost. For an ordinary contract held to $1/$0 settlement, the break-even probability after entry fees is the total upfront cost per contract divided by $1, assuming no later charges or income.
Suppose you buy 100 Yes contracts on the same outcome at 45¢ each and pay entry fees totaling a hypothetical $1. The contracts cost $45 and the fees bring the total to $46, or 46¢ per contract. The break-even probability rises from 45% to 46%.
| Settlement result | Position's net result |
|---|---|
| The outcome occurs | Receive $100 and make a $54 profit after entry fees. |
| The outcome does not occur | Receive nothing and lose the $46 spent. |
If your research puts the chance at 50%, expected profit weights each result by its probability. Half the $54 gain minus half the $46 loss leaves an expected profit of $4. At a 46% estimate, expected profit is zero.
Buying 100 Yes contracts at a hypothetical 45¢ plus $1 in entry fees costs $46 and returns $100 if the outcome occurs. Expected profit increases by $1 for each percentage point in your forecast, reaching zero at 46% and $4 at 50%.
For a $1/$0 contract, expected profit per contract simplifies to the estimated chance of success multiplied by $1, minus the total cost. The difference between your forecast and the break-even probability is how far your estimate could fall before the expected profit disappears.
If a charge instead reduced the successful contract's payment to 98¢, a 45¢ purchase would break even at 45 ÷ 98, or about 45.92%. The amount received after that charge belongs in the denominator.
The execution price already accounts for which side of the spread you traded on. Once 45¢ is the purchase price in your calculation, adding the four-cent spread from the bid-and-ask example would count it twice.
For a hypothetical Bitcoin contract, paying the 45¢ ask already covers the 2¢ difference from the midpoint displayed as 43%. A 1¢ fee raises break-even to 46%, so a 50% forecast can fall four percentage points before expected profit reaches zero.
Why are Polymarket fees highest near 50¢?
In Polymarket's documented fee formula, the price in dollars is multiplied by one minus that price. At a fixed rate, the fee per contract reaches its maximum at 50¢ and is equal at complementary prices such as 10¢ and 90¢. The documented rule charges takers, who accept existing orders, in markets with fees. It exempts makers, whose posted offers are accepted.
Suppose a hypothetical fee per contract is 0.05 × price × (1 − price), with price measured in dollars. At 50¢, the fee is 1.25¢, raising break-even to 51.25%. At 10¢ or 90¢, it is 0.45¢, raising break-even to 10.45% or 90.45%.
The hypothetical fee curve peaks at a 50¢ contract price, where a 1.25¢ fee raises the break-even chance to 51.25%. At 10¢ and 90¢, the fee is 0.45¢ in both cases, bringing break-even to 10.45% and 90.45%.
The smaller fee at 90¢ takes 4.5% of the contract's possible ten-cent profit. At 10¢, the same fee takes only 0.5% of the possible 90¢ profit.
The Kalshi fees page says fees vary by market and that some markets charge makers when their resting orders execute.
Do prediction market prices equal probabilities?
Prediction market prices are estimates of probability. They combine traders' forecasts with what it costs to trade and hold a position, so the implied percentage can differ from the event's underlying chance. Evidence from settled markets shows how the relationship varies with the venue, price range, and time remaining.
Implied probability vs true probability
Implied probability translates a contract price into a percentage, while true probability refers to the event's underlying chance. A 60¢ price for a $1/$0 contract implies 60%, even if your research supports a 70% estimate. At that estimate, its expected settlement value is 70¢ and its expected profit is 10¢ before costs.
Whose beliefs does a price reflect?
The price can approximate the average forecast among traders, with more influence from those who have more money to commit. Wolfers and Zitzewitz found this relationship held closely in their models between 20¢ and 80¢. When forecasts were fairly close together, prices typically came within about one percentage point of the average. Gaps grew when views were farther apart or prices approached 0¢ and $1.
Two people assigning Arsenal a 45% and a 60% chance of winning the Champions League could both buy a hypothetical Yes contract at 36¢. A seller reducing an existing position can also retain a favorable view of the team's chances.
Two buyers pay the same hypothetical 36¢ for Yes on Arsenal winning the Champions League, despite estimating its chance at 45% and 60%. Those forecasts give expected profits of 9¢ and 24¢ per contract before fees, while both transactions record a price of 36¢.
Hedging and risk-neutral probability
A risk-neutral probability is the probability that makes a contract's expected payment, discounted for the wait, equal its market price. It can differ from a real-world forecast because the price also reflects how valuable the payment would be if that outcome happened.
A business exposed to rising inflation might buy a contract that pays when inflation is high to help cover its rising costs. Using a position to protect against another risk in this way is called hedging. Buyers willing to pay extra for that protection can push the implied chance above their forecast. A Federal Reserve staff paper on Kalshi macroeconomic markets uses the risk-neutral interpretation and finds some evidence of prices overstating the chance of high inflation and unemployment.
The contract beside the supplier bills pays when inflation is high, helping the business cover the extra costs.
Why don't Polymarket percentages add up to 100%?
Probabilities add to 100% when the list covers every possible result exactly once. Market prices can miss that total because the prices sellers ask include spreads, separate markets update at different times, or the listed outcomes overlap or leave possibilities out.
Kalshi Yes and No prices
For a Kalshi Yes and No pair, or an ordinary binary contract on Polymarket, exactly one side pays $1 at settlement. Their probabilities are complementary, but buying both uses two asking prices.
Suppose Yes is offered at 45¢ and No at 59¢. Buying both costs $1.04, with the spread included in those asking prices. Receiving $1 at settlement leaves a four-cent loss before fees.
Buying at the hypothetical asking prices of 45¢ for Yes and 59¢ for No costs $1.04 for a pair that pays $1. The 4¢ overlap between the bars marks the loss before fees.
The phrase “Kalshi vig” borrows the sportsbook term vig, meaning the bookmaker's margin or commission. With these paired Yes and No quotes, the four cents comes from accepting both asking prices. An explicit transaction fee is a separate cost.
How do you read prices in a multi-outcome prediction market?
A complete field with exactly one winner has probabilities totaling 100%. Each outcome has its own market, however, and adding the prices sellers ask can produce a higher total. Suppose an imaginary Champions League market offers these Yes contracts:
| Outcome | Available asking price | Share after normalization |
|---|---|---|
| Arsenal | 36¢ | 35.3% |
| Barcelona | 30¢ | 29.4% |
| Bayern Munich | 24¢ | 23.5% |
| Any other team | 12¢ | 11.8% |
| Total | $1.02 | 100% |
Buying one of each costs $1.02 for a combined $1 payment, assuming the tournament produces exactly one winner under matching rules.
Normalization divides each price by the total, preserving the quotes' proportions while making the percentages sum to 100%. Arsenal's share becomes 36 ÷ 102, or about 35.3%. Its purchase price remains 36¢ and the buyer's break-even probability remains 36% before fees.
Buying one Yes contract on each outcome in the hypothetical Champions League field costs $1.02 for a combined $1 payment. Dividing each price by the $1.02 total gives percentages adding to 100%, with Arsenal at 35.3% even though its asking price remains 36¢.
The normalized shares can help compare the teams' relative chances if the price differences are informative. They apply the same proportional adjustment to every team, without correcting for one team's price being more distorted than another's. A display using separate midpoints or past trades can also total above or below 100%, particularly when those observations come from different times.
If a hypothetical market has a 1¢ minimum price, ten outsiders each contribute at least one percentage point to the displayed total. At an estimated 0.2% chance each, their combined chance would be only 2%, against the prices' total of at least 10%.
Pricing ten outsiders at a hypothetical 1¢ minimum implies a combined 10% chance, five times the 2% total from estimates of 0.2% each.
Using only Arsenal and Barcelona's prices, Arsenal accounts for 36 ÷ 66, or about 54.5%, of their combined total. Read as a probability, that estimate assumes one of those two teams wins.
In a Polymarket negative risk market, a No share can convert into one Yes share on every other outcome. With exactly one winner, the replacement shares have the same combined settlement value as the original No.
If a complete set could be bought for 96¢ and would return exactly $1, it would leave four cents before costs. The calculation needs available purchase prices for the required quantity of every contract, with rules that make the set complete.
Overlapping thresholds
Bitcoin finishing above $100,000 and above $120,000 are overlapping outcomes. A finish above $120,000 satisfies both, so adding their probabilities counts those outcomes twice.
For matching deadlines and price sources, the difference between two markets' chances estimates the probability of landing in the range between their thresholds. Subtracting a hypothetical 20% chance above $120,000 from a 55% chance above $100,000 gives 35% for a finish above $100,000 and at or below $120,000. The higher threshold should have no greater probability than the lower one because it covers a subset of the same results.
In this hypothetical example, Bitcoin has a 55% chance of finishing above $100,000, including a 20% chance of finishing above $120,000. The difference is the 35% chance of a finish above $100,000 and at or below $120,000.
How does time to settlement affect a prediction market price?
A dollar received later can be worth less than a dollar available today because money committed to the position could earn a return elsewhere. Traders therefore have a reason to pay less for a distant payment, even when the event is highly likely to happen.
Suppose an alternative investment could earn a hypothetical 5% over a year. Dividing $1 by 1.05 values a certain dollar received in a year at about 95.24¢ today.
For an uncertain payment, the same method discounts its expected value. A 60% chance of receiving $1 in a year would be worth about 57.14¢ at that rate. This comparison accounts for the wait, before trading costs, compensation for risk, or income received while holding the contract.
If money can earn a hypothetical 5% elsewhere over a year, a certain $1 due in a year is worth about 95.24¢ today. Discounting only for the wait also reduces the 60¢ expected from a 60% chance of that payment to about 57.14¢.
A contract bought at 97¢ that returns $1 earns about 3.09% on its cost. If settlement takes a year, that is also its annual return. If settlement takes 30 days, compounding the same return over a 365-day year produces an annualized figure of about 44.9%. That calculation raises 1 ÷ 0.97 to the power of 365 ÷ 30, then subtracts 1 and converts to a percentage. It assumes repeated opportunities to earn the same return, which a single trade cannot supply.
Selling early releases money at the price a buyer will pay then. If the reason for buying was to collect the final dollar, a future buyer may also want a discount for the remaining wait. A plan relying on an early sale needs an estimate of that sale price as well as the final outcome.
Long waits can discourage buyers of expensive contracts with little remaining profit, one proposed explanation for Intrade's stronger favorite-longshot bias far from settlement.
How does interest affect a Kalshi position's return?
Interest earned on an eligible Kalshi position adds to any gain or loss between its purchase price and settlement value. To compare an interest-earning position with holding cash elsewhere, include what each would earn over the same period.
Are high-probability prediction market contracts low risk?
A high chance of success alone does not make a contract low risk. Buying close to $1 leaves a small possible gain alongside a loss of nearly the whole dollar if it fails.
Suppose you buy 50 contracts at a hypothetical 96¢ each. Success returns $50 on a $48 cost, making $2 before fees. Failure loses the $48. One failed position cancels the profit from 24 successful positions bought at the same price and size.
A position of 50 Yes contracts bought at a hypothetical 96¢ costs $48 and earns $2 if successful. Profits from 24 successful positions total $48, exactly matching the loss on one failed position and leaving $0 before fees.
At a true success probability of exactly 96%, the expected profit before costs is zero. Positive expected value needs a chance above the break-even probability after fees. Lowering your forecast from 96% to 92% doubles the estimated chance of failure, from 4% to 8%, while the contract still offers only four cents of profit on success.
Is always buying No profitable?
Buying No offers a positive expected return only when its expected settlement value exceeds the purchase price and fees. If a $1/$0 No contract costs 73¢ and succeeds 73% of the time, its average settlement value is 73¢. Expected profit is zero before fees and negative after them.
Are cheap contracts better value?
A cheap contract offers value when its expected settlement value exceeds its price and fees. If a one-cent contract has a 0.5% chance of paying $1, its expected settlement value is half a cent. Paying a cent for it means an expected loss of half a cent before fees. A minimum tradable price can prevent such a contract from becoming cheap enough to match its estimated chance.
Buying 10,000 contracts at 1¢ commits $100 to a single outcome. All of them settle together, so buying more increases the amount at risk without adding independent chances of success.
Every contract in the bundle depends on the same football result, so a larger holding increases the money at risk while keeping the same chance of success.
A sharp Bitcoin fall could also defeat Yes positions on several higher price thresholds at once, exposing different contracts to the same development.
What is the favorite-longshot bias on Kalshi and Polymarket?
The favorite-longshot bias occurs when low-priced outcomes succeed less often than their prices imply, while favorites succeed more often. It has been documented on Kalshi and Intrade, with mixed findings on Polymarket.
In a hypothetical favorite-longshot pattern, 10¢ contracts succeed 5% of the time and 90¢ contracts succeed 95% of the time. Holding them to settlement gives an average loss of 50% on the 10¢ purchases and an average gain of about 5.6% on the 90¢ purchases, before fees.
For Kalshi, Bürgi, Deng, and Whelan's working paper found average losses above 60% for contracts priced at 10¢ or less, with small positive returns above 50¢. The study covered 2021 through April 2025 and calculated returns from buying at sampled prices and holding to settlement, including fees for purchases that accepted existing orders.
On Polymarket, Reichenbach and Walther's study of November 2022 through September 2025 found no general longshot bias when comparing market prices with outcome frequencies.
Qin and Yang's Polymarket-v1 preprint, covering November 2022 through April 2026, found a pattern consistent with the bias when grouping individual trades by price. In the lowest group, contracts bought at an average 5.2¢ returned 0.23¢ less per token at settlement before costs, a shortfall of about 4.4% of the average purchase price. Groups from 40¢ upward showed positive differences.
These loss figures cannot be compared directly across venues. The Kalshi study averages percentage returns at sampled prices from each market's final ten days and includes taker fees. The Polymarket figure divides the average loss per trade by the average purchase price, using trades throughout a contract's life before costs.
On Intrade, Page and Clemen's study of 1,787 markets opened between 2002 and 2007 found that the bias weakened as settlement approached. Their model showed that a long wait could deter buyers of expensive contracts offering little potential profit. The authors also noted that new information arriving closer to settlement could help explain the improvement.
Calibration tests whether outcomes happen as often as their assigned probabilities imply. Across many outcomes assigned about a 70% chance, roughly 70% should occur if the forecasts are well calibrated.
For a particular trade, evidence about accuracy in similar markets at a similar distance from settlement is more relevant than an average across unrelated contracts.