polyAether
Textbook · Chapter 2
Chapter 2

Prediction markets, from scratch

~9 min read

Before we can talk about weather, or bots, or edge, we need one idea: a place where you can buy and sell a bet on whether something will happen. That place is a prediction market, and once you see how it works, a surprising amount falls into place. We'll build it from nothing — no finance background assumed — one slip of paper at a time.

01 — The simplest possible contract

Imagine a slip of paper. Printed on it is a single sentence: "It will rain in Chicago tomorrow." The slip has one magical property. If it does rain in Chicago tomorrow, whoever holds the slip can trade it in for exactly one dollar. If it does not rain, the slip is worth nothing — zero dollars. It turns to dust.

That slip of paper is a contract — just a promise, written down, about a future outcome. In a prediction market, this is the only kind of thing being bought and sold. Every contract pays $1 if the outcome happens and $0 if it does not. There is no in-between. The event either occurs or it doesn't, and the slip is worth either a full dollar or nothing. People who work with these instruments call them binary contracts, and the "$1 or $0" shape is the reason the math stays so clean — as we're about to see, it lets a price and a probability be the same number.

We call the thing being predicted the outcome, and the moment we find out the truth — did it rain or not? — is called settlement (the market "settles" the contract by paying out the winners). Settlement needs a rule everyone agrees on in advance: which weather station, measured how, rounded which way. Change the rule and the same weather can produce a different payout, so the fine print matters enormously. We'll spend a whole later chapter on settlement, because it turns out to be trickier than it sounds. For now, just picture the slip: one dollar if right, nothing if wrong.

Key idea

A prediction-market contract is a bet in the shape of a coupon: it pays $1 if a specific outcome happens, and $0 if it doesn't. That's the entire product.

02 — What would you pay for the slip?

Here's the interesting question. Before we know whether it rains, how much is that slip worth right now? What would a sensible person pay for it?

Let's make it clean with a coin flip instead of weather, so the answer is obvious. Suppose the slip says "the next coin flip lands heads." A fair coin lands heads half the time. So the slip pays you $1 half the time and $0 half the time. On average, over many flips, it's worth 50 cents.

Here's the arithmetic behind "on average," because it's the single most useful calculation in this whole book. Take the two things that can happen, multiply each payout by its chance, and add them up. Heads: $1 payout × 50% chance = 50 cents. Tails: $0 payout × 50% chance = 0 cents. Total: 50 cents. That weighted-average number has a name — the expected value — and for a binary contract it always collapses to something delightfully simple: the payout of $1 times the probability. So a slip that's 50% likely is worth 50 cents; a slip that's 20% likely is worth 20 cents; a slip that's 92% likely is worth 92 cents. The probability, in cents, is the fair value.

If someone offered to sell you that coin-flip slip for 30 cents, you'd jump at it — you'd be paying 30 cents for something worth 50 cents on average. If they wanted 70 cents, you'd refuse, and you might even want to be the seller. The number that feels exactly fair, where neither buying nor selling is obviously smart, is 50 cents. That fair number is the price.

Prices in these markets are usually quoted in cents from 0 to 100 — which is the same as saying the price runs from $0.00 to $1.00, the two possible payouts. A price of 50 cents means the market thinks the outcome is a coin flip. A price of 5 cents means the market thinks it's very unlikely. A price of 95 cents means the market thinks it's nearly certain. The price can never sensibly sit below 0 or above 100, because those are the only two amounts the slip can ever be worth — you'd never pay more than a dollar for something that pays at most a dollar, and no one would sell you a sure dollar for less than nothing.

Key idea

Because a contract pays either $1 or $0, its fair price in cents is exactly the chance the outcome happens, expressed as a percentage. 60 cents means "about 60% likely." The price is a probability wearing a dollar sign.

Why the price becomes the crowd's probability

You might ask: sure, I think it's 50 cents, but why would the actual market price land there? Because of everyone else. A market is a crowd of people all free to buy and sell. Suppose the coin-flip slip is trading at 40 cents. Lots of people notice it's worth 50 on average, so they buy — and buying pushes the price up (more demand, higher price, just like concert tickets). It keeps rising until it reaches 50, where the easy profit disappears and the buying stops.

If instead it were trading at 60 cents, people would sell it (or bet against it), pushing the price down to 50. The price gets shoved from both sides until it settles at the point where the crowd, on balance, sees no free money. That balance point is the crowd's collective best guess at the probability. Nobody votes on it; it emerges from thousands of buy and sell decisions, each made by someone with money on the line.

This is the quiet magic of prediction markets. The price is not an opinion poll and not an expert's decree. It's a number that people are literally betting their own cash to move, which tends to make it honest. If you think the price is wrong, you don't argue — you buy or sell, and your money nudges the price toward what you believe. A poll asks people what they'd say; a market asks people what they'd stake. The second question gets more truthful answers, because being wrong costs money.

A note on where prices actually come from. In a real market the price you see isn't one agreed number — it's two: the highest price anyone is currently willing to pay (the bid) and the lowest price anyone is willing to sell at (the ask). To buy right now you meet the ask; to sell right now you meet the bid. The little gap between them is the spread. When lots of people are trading on both sides, that gap is thin and the price is trustworthy. When only sellers are around, the "price" can look real while being nearly impossible to actually trade against — a subtlety that will matter a great deal once we reach how polyAether trades for real.

03 — A worked example

Let's walk one all the way through, with a weather flavor since that's polyAether's world. A market asks: "Will the high temperature in Miami tomorrow be above 90°F?" The contract pays $1 if the high tops 90, and $0 if it doesn't. Right now it's trading at 70 cents.

1
Read the price as a probability
70 cents means the crowd thinks there's roughly a 70% chance Miami's high beats 90°F tomorrow.
2
Decide if you disagree
Say you have good reason to think it's actually more like 85% likely. In your eyes the slip is worth about 85 cents, but you can buy it for 70. That gap is your opportunity.
3
Buy the contract
You buy one slip for 70 cents. If Miami's high beats 90°F, you get $1 back — a 30-cent profit. If it doesn't, you get $0 and lose your 70 cents.
4
Wait for settlement
Tomorrow the official high comes in. The market checks it, pays $1 to every "above 90" slip, and $0 to the rest. Done.

Let's put real numbers on why this is a good buy, using the expected-value trick from section 02. You pay 70 cents. If your 85% estimate is right, then 85% of the time you collect $1 (a 30-cent gain) and 15% of the time you collect nothing (a 70-cent loss). Weighing those: 0.85 × (+30¢) + 0.15 × (−70¢) = 25.5¢ − 10.5¢ = +15 cents of expected profit per slip. Another way to see the exact same thing: the slip is worth 85 cents to you and costs 70, so buying it is worth 85 − 70 = 15 cents on average. That 15-cent gap between "your value" and "the price" is what a trader means by edge. Buy a hundred such slips and you'd expect roughly $15 of profit — even though plenty of the individual bets will lose.

Notice that you can be right about the temperature and still, on a single bet, lose money — if this particular day happens to stay at 89°F. That's fine and expected. A 15% chance of losing is exactly that: something that happens about one time in seven. The point isn't to win every bet; it's to buy slips for less than they're truly worth, over and over, so that the wins outweigh the losses in the long run. This is the same reason a casino doesn't need to win every hand — a small, repeated edge, played enough times, is what turns into money. We'll make that precise in Chapter 4 when we talk about calibration and edge.

One more honest wrinkle worth planting now: that 15-cent edge only exists if your 85% is actually better than the crowd's 70%. If you're kidding yourself — if the true chance really was 70% and you just felt lucky — then you paid a fair price for a fair bet and, after the market's own frictions, you'll slowly lose. So the entire enterprise rests on a single hard question: can you produce a probability that is genuinely more accurate than the price? For most events, most of the time, the answer is no, and the disciplined move is to not trade at all.

Key idea

You make money in a prediction market by finding contracts whose price is wrong — priced at 70 cents when the true chance is 85% — and taking the cheaper side. The whole game is spotting a better probability than the crowd, and betting the difference. No better probability, no trade.

04 — Where this is heading

So a prediction market gives us two gifts. First, it hands us the crowd's probability for free, printed right there as a price. Second, it lets us profit whenever we can beat that probability with a better one of our own.

That raises the obvious question: where would a better probability come from? For polyAether, the answer is weather. Weather is one of the few things in the world that science can forecast with real, measurable skill — yet the crowd, as we'll see, tends to misprice it in a specific and repeatable way, systematically overpricing uncertainty by roughly 1.3× rather than getting the direction of tomorrow's weather wrong. The next chapter builds the weather half of the story from scratch, exactly as we just built the market half.

A preview of the messy reality. The clean picture above — "spot a wrong price, take the cheaper side" — is true, but the real weather markets add friction that this chapter has been quietly simplifying. Most of them are not empty: each has tens to hundreds of thousands of dollars of resting sell orders. But that depth is lopsided — big one-sided walls of asks with thin bids underneath — and wherever prices are genuinely live (roughly 10–92 cents) the market is already priced efficiently, leaving no gap. Many apparent "edges" are only against a fraction of a cent of leftover interest on unlikely tail outcomes, which a sensible system refuses to trade. The genuinely two-sided, tradeable window tends to be about a day before the weather is known; nearer to settlement the price collapses toward 0 or 100 as the answer becomes obvious. The practical upshot, which we'll be honest about throughout: expect few trades. Often zero trades is the correct, disciplined outcome — not a failure. Chapters on how it runs and on risks return to this in detail.

It's worth being equally plain about what the "edge" is not. It is not a claim to forecast the weather better than a national weather service, and it is not a race to be a nanosecond faster than everyone else. For weather, new information arrives in seconds to minutes — a fresh forecast run, an hourly observation — not in nanoseconds, so speed mostly serves to avoid being picked off and to react to new information first, rather than being the source of profit itself. The edge, where it exists at all, is calibration: producing probabilities that are honest and well-tested (scored over time so we can prove they're trustworthy) against a crowd that reliably overprices how uncertain the weather is. That, and nothing more magical, is the thesis.

If you want to see how these two halves click together into an actual trading system — including a paper-trading engine that now opens positions on a cleared edge, holds them across cycles, and settles them against the real observed weather so simulated profit and loss flows through end-to-end — that picture lives in Chapter 1. It is still paper only: no real money, and no track record to point to yet. Here, the takeaway is smaller and sturdier: a market price is a probability, and a wrong price is an opportunity.