Everything is a claim on one dollar.

A Polymarket share is the simplest financial instrument ever issued. It pays exactly $1.00 if its event happens, and exactly $0.00 if it doesn't. There is no coupon, no duration, no counterparty spread to model. That single fact collapses all of pricing theory into one line: if the share costs q, the market is asserting that the event happens with probability q.

So your profit per share is just outcome − q, and your expected profit, if you believe the true probability is p, is:

Everything else in this course is a refinement of "find a market where p ≠ q and you're the one who's right." The refinements matter enormously — but never lose the thread. There are only two questions: how far is q from the truth, and how much should I bet on that.

One asymmetry deserves early attention. Return on capital is (p−q)/q, which explodes as q gets small. A 2¢ contract that's really worth 4¢ returns 100%. This is why longshot markets feel intoxicating and why they are where inexperienced money goes to die: the percentage return is enormous, the probability of collecting it is tiny, and the estimation error on a 2¢ fair value is frequently larger than the entire edge. Drag the sliders and watch the two columns diverge.

Before any strategy, absorb the accounting. A binary market is a closed pot. Every share that redeems for $1 was paid for by someone, and the market cannot pay out more than was put in. Before costs the game is exactly zero-sum. After costs — spread paid, gas, and the opportunity cost of capital frozen until resolution — it is negative-sum for the average participant.

That is not a reason to stay away. It's a reason to be specific. If you cannot name which of these four buckets your profit comes from, you don't have a strategy, you have exposure:

• Information — you know something the price doesn't, because you gathered it, paid for it, or noticed it first.
• Computation — you and the market see identical information, but you extract more structure from it: logical consistency across markets, joint distributions, correct sizing.
• Liquidity — you are paid a spread (and, on Polymarket, a rewards subsidy) for standing ready to trade with people who need immediacy.
• Speed — same information as everyone, arriving at your machine sooner.

And two counterfeits that feel like edge and aren't. Risk premium disguised as skill: loading up on longshots or heavily correlated positions raises returns and variance together; it's leverage, not alpha. Crossing the spread repeatedly: a strategy with a 1¢ true edge that pays a 2¢ spread has a negative edge, and no amount of being right fixes it.

Notice how the four buckets rank by durability. Speed decays fastest — the moment someone colocates a faster feed, your edge is arithmetic that runs on their machine instead of yours. Information is durable but expensive and doesn't scale. Computation is the strange one: it's the only bucket where the barrier is a hardness result rather than a resource, which is exactly why Chapter 04 is the longest in this course.

If you cannot answer that second question, the honest default is that you are the answer. On a venue where a measured $40M of pure arbitrage was harvested in twelve months, someone paid that $40M — and it was not the arbitrageurs.

Chapters 01 and 02 are the substrate: what a price is, and where trading profit actually comes from. They are free, and they stay free.

The other eight are where the theory earns its keep — the ones that tell you how much to bet, which prices contradict each other, and what the clock is doing to a position while you hold it.