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How prices move: the LMSR pricing formula
Every GADUIN market is priced by a logarithmic market scoring rule (LMSR): a pricing formula that quotes every outcome at all times and prices every trade itself. A trade costs the change in one cost function, so buying an outcome raises its price, lowers the others, and the prices always add up to 100%.
This guide sets out the formula, how the depth of each market is chosen, why no trade waits for another trader, and a worked example with the real numbers.
Published September 29, 2026 · last updated September 29, 2026
Why no trade waits for another trader
On an exchange, an order waits until another trader takes the other side. On GADUIN nothing waits: every trade is priced by the formula against the market itself, not matched with another trader, so it fills straight away, at a price you see before you confirm, however few other people are trading that market.
The cost function
The LMSR tracks qᵢ, the number of shares of each outcome i sold so far, and keeps one number for the whole market:
C(q) = b · ln( e^(q₁/b) + e^(q₂/b) + … + e^(qₙ/b) )
Buying Δ shares of outcome i costs C(q after the trade) − C(q before it). Nothing else enters the price: no markup and no trading commission.
Where each price comes from
The price of an outcome is the slope of the cost function in its direction:
pᵢ = e^(qᵢ/b) ÷ ( e^(q₁/b) + … + e^(qₙ/b) )
Every price sits between 0 and 1, and together they always add up to 1, which is why a price reads as a chance. Buying outcome i raises qᵢ, so its price rises and every other price falls in proportion.
The depth parameter b, and how GADUIN sets it
b sets how deep a market is. With a small b a modest trade moves the price a long way; with a large b the same trade barely moves it. GADUIN does not choose b by feel: it derives it from a limit on what one market can pay out beyond the money traders put in.
For an evenly priced market with n outcomes, the most the LMSR can pay out beyond the money traders put in is b · ln(n). GADUIN sets that limit at $100.00 per market and solves for b:
b = L ÷ ln(n)
| Market | Outcomes | Depth b | Most the market can pay beyond traders’ money |
|---|---|---|---|
| Yes/No count markets (airport arrivals, shipping passages) | 2 | 144.27 | $100.00 |
| Flight, train and voyage markets | 3 | 91.02 | $100.00 |
| Strait of Hormuz, Suez Canal and Bosporus weekly markets | 2 | 1,500 | $1,039.72 |
The three busiest shipping passages are deliberately deeper: their depth is fixed at 1,500 and the limit follows from it.
Worked example: $10.00 on Delayed
Take a flight market at depth b = 91.02 whose prices stand at On time 70%, Delayed 24% and Cancelled 6%. You put $10.00 on Delayed.
- At the screen price of 24¢, $10.00 would buy 41.67 shares.
- On the curve it buys 35.92 shares, because each share makes the next one dearer: an average price of 27.8¢.Δ = b · ln( 1 + (e^(amount/b) − 1) ÷ pᵢ )
- After the trade Delayed stands at 31.9%, On time at 62.7% and Cancelled at 5.4%. They still add up to 100%.
- If the flight arrives more than 15 minutes late, the 35.92 shares pay $35.92. If it arrives on time or is cancelled, they pay $0 and the $10.00 is gone.
Where the $100.00 payout cap comes in
One account can be paid at most $100.00 on one outcome of one market, which is $100.00 shares. In the market above, $100.00 Delayed shares cost $35.69, so a larger amount on Delayed is refused and the trade panel names the largest amount that still fits.
Why the same amount moves some markets more
Depth is fixed for each market when it opens. On a Yes/No shipping-passage market at b = 1,500 with Yes at 24%, the same $10.00 lifts Yes only to 24.5%.
Where a market starts
Each market opens with a starting price on every outcome, set before any trade. From then on only trades move it, so a price on GADUIN is what traders have been willing to pay, not a forecast from GADUIN.
LMSR pricing, in brief
- Does an LMSR match my trade with another trader?
- No. An exchange pairs buyers with sellers, and a trade waits until someone takes the other side. An LMSR is a single formula that prices every trade itself, against the market, so there is always a price and nothing to wait for.
- Can I sell shares back before the market settles?
- No. On GADUIN a trade only buys: you choose an outcome and an amount, and the shares are held until the market settles.
- Why do the prices always add up to 100%?
- Each price is one outcome’s share of the same sum in the cost function, so the shares of that sum always total 1. Exactly one outcome happens, so the prices read as chances.
- Does GADUIN add a markup or a fee on top of the price?
- No. There is no trading fee and no settlement fee; what you pay is the change in the cost function. Withdrawals carry a 5% commission.
See the curve on a live market
Every trade ticket shows the average price and exact payout before you confirm. A position can settle at $0, so only put in what you are comfortable seeing go to zero.
Keep learning
Start with the basics: What a prediction market is and how it works
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