What a Prediction Market Is

You already know how to update a belief (Bayes) and how to size a bet (Kelly). This course hands you a place to spend those skills: a market that doesn’t price companies or commodities, but probabilities themselves. On a prediction market, the thing being traded is a claim about the future — “this candidate wins,” “this rate cut happens” — and the number on the screen isn’t a dollar value of an asset. It is the crowd’s probability, in cents.

That single move — turning a probability into a price you can buy and sell — is what makes the whole machine work, and it’s the foundation everything else in this course stands on. This lesson builds that foundation from the ground up: what the contract actually is, why its price equals a probability, where your profit comes from when your number disagrees with the market’s, and why a crowd of people with money on the line tends to forecast better than the pundits who don’t.

What a prediction market is

Analogy. Think of a betting slip you can resell. You walk up to a window, put money on “it rains tomorrow,” and get a slip that’s worth $1 if you’re right and nothing if you’re wrong. In an ordinary betting shop that slip is frozen until the event settles. A prediction market does one radical thing differently: it lets you resell the slip to someone else at any moment before the event, at whatever price the next buyer will pay. The slip becomes a tradeable security, and its live market price is the headline number.

Definition. A prediction market is a market where you trade contracts whose payout is determined by the outcome of a future real-world event — an election, a sports result, an economic data release, a court ruling. You can open a position, and you can close it (sell to someone else) before the event resolves; when it does resolve, the contract pays a fixed amount to whoever holds the winning side.

The key contrast. Ordinary asset markets price a thing — a share of Apple is a claim on a real, ongoing business, and its price reflects expected future cash flows, growth, risk premia, and a hundred other moving parts. A prediction market prices a probability — the contract has no cash flows, no growth, no management team. It has exactly one job: pay $1 if a specific statement turns out true. Strip away everything an asset normally carries, and the only thing left to value is how likely the statement is. That’s why a prediction market’s price is so legible: there’s nothing else for it to mean.

The outcome share — a binary contract

Analogy. A light switch that hasn’t been flipped yet. When the event resolves it will land in exactly one of two positions — ON (it happened) or OFF (it didn’t) — and your contract pays out based on which. You can bet on either position of the switch.

Definition. An outcome share (here, a binary contract) is the atom of a prediction market. A YES share pays $1 if the event happens and $0 if it doesn’t. A NO share is the mirror image: it pays $1 if the event does not happen and $0 if it does. Together the two sides cover every possibility — exactly one of them will be worth $1 at resolution, the other worth nothing.

Worked example — buying YES at 62¢. Suppose a YES share trades at 62¢ and you buy one. You’ve now paid $0.62, and there are precisely two futures:

• The event happens. Your share pays $1. Profit = $1 − $0.62 = +$0.38.
• The event doesn’t happen. Your share pays $0. Profit = $0 − $0.62 = −$0.62.

So a single 62¢ YES share is a coin-shaped gamble: risk 62 cents to make 38, or lose the 62. Notice the two numbers, $0.38 and $0.62, are just the distances from your price to the two payout rails ($1 and $0). That geometry — price sitting on a $0-to-$1 track, with your upside and downside being the gaps on either side — is the entire payoff structure, and it’s exactly what the interactive below draws.

Price = implied probability

This is the theorem the whole course rests on, so we’ll derive it rather than assert it. Why should the price of a YES share equal the probability the event happens?

The argument. A YES share pays $1 with probability $p$ (the event happens) and $0 with probability $1 - p$ (it doesn’t). Its expected payout is therefore

$E[\text{payout}] = p \cdot 1 + (1 - p)\cdot 0 = p \text{ dollars}.$

Now imagine a risk-neutral, no-arbitrage market — traders who care only about expected value and will pounce on any mispricing. If the share traded below $p$, its expected payout would exceed its cost, so buyers would pile in and bid the price up. If it traded above $p$, holders would be overpaying for the expected $p$, so sellers would push the price down. The only price with no one-sided incentive left is the price that equals the expected payout — which is $p$ itself. The fair price of a $1/$0 share is the probability it pays out.

Worked example — reading a price as a probability. A YES share sits at 62¢. Its expected payout is $0.62 \times 1 = 0.62$ dollars, so the market’s implied probability of the event is simply 62%. No further math — the cents are the percent. Flip it around: if you believe the true probability is 62%, then 62¢ is exactly the price at which you’re indifferent to buying, because you’d be paying 62¢ for an expected 62¢.

The sum-to-one check. Because exactly one side wins, YES and NO together always pay out exactly $1. So in a clean market their prices must sum to $1:

$p_{\text{YES}} + p_{\text{NO}} = 1 \text{ dollar} \quad\Longleftrightarrow\quad \text{implied probabilities sum to } 100\%.$

If YES is 62¢, NO must be 38¢ — implied probabilities of 62% and 38%, which add to 100%, exactly as probabilities should. If they didn’t sum to one dollar, you could buy both sides for less than a dollar and pocket a guaranteed dollar — a free lunch that arbitrageurs erase instantly.

Drag the sliders below. The market price slider sets the YES price (and therefore the implied probability); the your true probability slider is your private belief. Watch the implied probability track the price exactly, and watch the expected-value readouts light up when your belief disagrees with the price — the setup for the next section.

Expected value and edge

Price equals the market’s probability. But you’re not here to agree with the market — you’re here to disagree profitably. The moment your probability differs from the price, the contract has a non-zero expected value to you, and that gap is your edge.

Analogy. A used-car lot prices a car at $8,000. If you (correctly) know it’s worth $11,000, buying it is +EV — you’re paying less than its true value. A prediction market works identically, except the “true value” is a probability and the “price tag” is the share price. Buy YES whenever the market underprices the event relative to your honest belief; buy NO whenever it overprices it.

Definition. Your expected value (EV) per share is your probability of each outcome times the profit in that outcome:

$\text{EV of buying YES} = p_{\text{you}} \cdot (1 - \text{price}) - (1 - p_{\text{you}}) \cdot \text{price},$

with the payout and price both measured in dollars.

The first term is your win (you collect $1, having paid the price); the second is your loss (you forfeit the price). If your probability beats the price, this is positive — a real edge.

Worked example — you think 75%, the market says 62%. You’ve done your homework and believe the event is 75% likely. The YES share trades at 62¢. Buy one share:

$\text{EV} = 0.75 \cdot (1 - 0.62) - 0.25 \cdot 0.62 = 0.75 \cdot 0.38 - 0.25 \cdot 0.62.$

Crunch it: $0.75 \cdot 0.38 = 0.285$ and $0.25 \cdot 0.62 = 0.155$, so

$\text{EV} = 0.285 - 0.155 = +0.13 \text{ dollars per share}.$

A clean +13 cents of expected value per share — and notice the shortcut hiding in the algebra: EV of YES collapses to simply $p_{\text{you}} - \text{price} = 0.75 - 0.62 = 0.13$. Your edge is just the gap between your probability and the price. That elegant fact — edge equals belief minus price — is the engine that later lessons feed straight into Kelly to decide how many shares to buy.

Information aggregation — the wisdom of betting crowds

Here’s the part that elevates a prediction market from “a tidier betting shop” to “a forecasting instrument”: its prices tend to be remarkably well-calibrated. When a liquid market says 70%, events priced that way really do happen close to 70% of the time. Why would a pile of strangers’ bets out-forecast credentialed experts?

Analogy. Ask a crowd to guess the number of jellybeans in a jar and average their answers — the average routinely beats almost every individual, because independent errors cancel. A prediction market is that jellybean jar with a crucial upgrade: the guessers are betting their own money, so the loud-but-wrong are financially punished and the quietly-correct are rewarded, which weights the average toward whoever actually knows something.

Why it works — three forces.

• Skin in the game. Posting a price costs real money if you’re wrong. That filters out cheap talk: a pundit pays nothing for a bad take on TV, but a trader pays cash. Beliefs backed by money are, on average, more honest and better-researched than beliefs backed by nothing.
• The marginal trader. The price isn’t a vote of everyone’s opinion; it’s set by whoever is willing to trade at the margin. Informed traders with an edge keep buying the underpriced side until the price reflects their information — so the price gravitates toward the view of the best-informed money, not the average opinion.
• Prices update on news. The instant new information lands, traders who see an edge act on it, moving the price within seconds. The market is a live, continuously-revised forecast — Bayesian updating implemented by a crowd’s wallets rather than one analyst’s spreadsheet.

A real example, lightly. The Iowa Electronic Markets, run by the University of Iowa since the late 1980s, let traders bet small stakes on election outcomes — and over many cycles their prices have often tracked eventual results at least as closely as traditional polling, frequently beating it close to election day. The lesson to take isn’t a precise accuracy figure (those vary by study and election); it’s the mechanism: money-weighted, continuously-updated crowd belief is a genuinely good forecast.

Putting it together

A prediction market trades contracts that pay out on the outcome of a future event — a resellable betting slip whose live price is the headline. The atom is the outcome share: a YES share pays $1 if the event happens and $0 if not (NO is the mirror), so buying YES at 62¢ wins +$0.38 or loses −$0.62. Because a $1/$0 share has expected payout $p \times 1 = p$ dollars, a risk-neutral, no-arbitrage market prices it at exactly its probability — price = implied probability, with YES + NO summing to $1. When your probability differs from the price you have an edge equal to belief-minus-price (you think 75%, price 62¢ ⇒ +13¢ EV per share), the raw material Kelly later turns into a position size. And because the people setting the price are betting real money, updating on news, and led by the informed marginal trader, the price behaves like a well-calibrated, self-correcting forecast — a probability the whole crowd has skin in.

Next up — Inside Polymarket — we drop from theory into the actual machine. You’ll see how Polymarket runs these markets on-chain: positions are denominated in USDC (a dollar-pegged stablecoin) on the Polygon network, a full set of YES + NO shares is minted from exactly $1 of collateral and can be merged back into $1, and live trading happens through an order book of resting bids and asks. The clean “price = probability” you just learned is what all that plumbing exists to deliver.