Explains how to exploit Polymarket's LMSR pricing formula for profitable position sizing.

My brother started OpenClaw with $200 on Polymarket

Called me 3 weeks later from a new apartment. Here's the formula he used

$200 → $8,400

C(q) = b × ln( Σ e^(qi / b) )

One equation controls $2 billion on Polymarket.

Most traders don't know it exists. 

The ones who do are printing money off the ones who don't.

Every price on Polymarket isn't set by traders. It's calculated by a formula - LMSR, published in 2002 by economist Robin Hanson

That's the entire pricing engine. Every dollar. Every market.

The price function? It's softmax - the same function GPT uses to pick the next word

Polymarket prices beliefs the same way AI outputs probabilities

Not a metaphor. The math is identical

Market shows 34 cents on "Fed cuts rates." Crowd thinks 34%.

CME FedWatch says 51%. Your model says 52%.

That's an 18-cent edge

But you can't just dump money in. Every share you buy moves the price against you. First share - $0.34. The 50th - $0.46.

Position sizing matters more than direction

The move - ladder in. Stop when your average fill hits 80% of your estimated true probability. 18 cents of edge becomes 10 real, executable cents

Then there's b - the most underappreciated number in prediction markets

Small b - prices move wildly. Thin markets. Easy to extract edge

Large b - deep markets. You need serious capital

Max market maker loss: b × ln(n)

Binary market, b = 100,000 → exactly $69,315. That's the cost of running one market

You don't predict the future. You predict the market is wrong about the present

The formulas are on Wikipedia. The code runs on any laptop. The API is free

The edge isn't access. The edge is doing the math