How LMSR prices work

Every Predictifi market is priced by a Logarithmic Market Scoring Rule (LMSR). It sounds academic, but the idea is simple: instead of matching buyers to sellers in an order book, a cost function decides the price of every trade. Here is how it works, and why it is a good fit for prediction markets.

A cost function, not an order book

The market tracks how many shares of each outcome have been bought — a vector q = (q₀, q₁, …) — and a liquidity parameter b. The total cost the market has committed is:

C(q) = b · ln( Σᵢ exp(qᵢ / b) )

To buy shares of an outcome, you pay the difference in this cost before and after your purchase. To sell, you receive the difference in reverse. There is always a number, at any size — the market never runs out of a counterparty.

Prices are probabilities

The price of an outcome is the softmax of the quantities:

price(i) = exp(qᵢ / b) / Σⱼ exp(qⱼ / b)

Because that is a probability distribution, outcome prices always sum toward $1.00. A price of $0.65 means the market's implied probability for that outcome is about 65%. Buy an outcome and its price rises; the others fall to keep the total at 1.00.

What b does

The liquidity parameter b sets the market's depth:

• A larger b means deeper liquidity — prices move less per trade, so large orders barely nudge the price.
• A smaller b means prices react more sharply — small orders move the price a lot.

The market creator funds the subsidy that backs b, and the maximum the maker can ever pay out is bounded — so the market cannot be drained beyond what was funded.

Why it fits prediction markets

LMSR gives you continuous, bounded, always-available pricing with prices that read directly as probabilities. That is exactly what you want when the whole point is to aggregate a crowd's belief about whether something will happen.

Want the full picture? The whitepaper covers the on-chain implementation, including the numerically-stable softmax the contracts use.