The math behind share prices and why the market can start with no pre-funded AMM pool. For rules of the round itself, see Trading mechanics.
Pricing uses a logarithmic market scoring rule (LMSR) — a classic automated market maker for prediction markets. There is no central person setting odds and no CLOB of resting limit orders; instead a fixed formula turns the current market state into both prices and how much you pay for the next shares.
Why there is no “seed liquidity” like an AMM pair. The market records two counters, qYes and qNo — how many YES and NO shares have been minted on the curve. When a round opens, both start at zero. Nobody pre-deposits paired assets into a pool; the rule itself defines valid prices at every state. Traders are the first source of cash: each purchase pays the incremental cost of moving those counters.
Cost function (binary LMSR)
C(qYes, qNo) = b · ln( e^(qYes/b) + e^(qNo/b) )
You always pay ΔC — the change in C — when your trade increases either counter. That is the actual cost for your new shares.
Implied “odds”. The YES/NO percentages in the UI come from the partial derivatives of C (a softmax over the two sides). They are marginal prices: always positive and summing to 100%. At qYes = qNo = 0 the curve starts at a 50 / 50 split before anyone trades.
What b does. The positive parameter b controls curvature: a larger b means the same budget moves implied probabilities less — often described as a “deeper” or more liquid book even though no separate LP stack sits at zero. A smaller b makes the book react faster. This deployment can hold b fixed or scale it with the token's reported DEX liquidity so very thin pools get a tighter curve.
Convexity. Because C is convex, buying more shares on the same side keeps getting more expensive per marginal share. That is why large bets move the line more than tiny ones.
In textbook LMSR, a market maker who starts at (0,0) has a worst-case subsidy bounded by b · ln 2 if every issued share had to settle at $1. Here, configuration also caps how large total outstanding share mass can grow per market, so the book does not grow without limits.
Everyone who buys shares pays their ΔC into the protocol flow (vault accounting in SOL mode). At resolution each winning share is worth about one unit of balance; losing shares pay zero. So visible winnings are not magic money from an empty vault — they are redistribution of funds participants already committed while minting shares: losers' stakes stay in the settlement system, winners redeem against it, and the LMSR only decided how expensive each share was along the way. You are not waiting for one specific counterparty to stay matched with you the way a bilateral bet would.
