LMSR: The Right AMM for Prediction Markets

When you're creating 22,000+ prediction markets per day, you need an AMM that doesn't bleed the treasury dry. Constant product (Uniswap-style) AMMs are great for token swaps. They're terrible for binary prediction markets.

Here's why we chose LMSR.

The Problem with CPMM

A constant product market maker (x × y = k) has unbounded loss. As price approaches 0 or 1 in a binary market, the LP's loss grows without limit. If the market resolves at the extreme (which prediction markets do by definition), the LP always loses.

For a platform creating thousands of markets daily, unbounded loss per market means unbounded risk for the treasury.

LMSR: Bounded Loss by Design

The Logarithmic Market Scoring Rule, designed by Robin Hanson, has a crucial property: maximum loss is bounded at b × ln(2), where b is a parameter you control.

For our Tier 1 markets (BTC, ETH), b = 200. Maximum loss per market = $138.63. That's the worst case; it only happens if the market starts at 50/50 and resolves at 100/0 with no trading volume.

How LMSR Pricing Works

The cost to buy Δq YES shares:

cost = b × [ln(e^(q_yes + Δq)/b + e^(q_no)/b) - ln(e^(q_yes)/b + e^(q_no)/b)]

The implied YES probability at any point:

P(YES) = e^(q_yes/b) / (e^(q_yes/b) + e^(q_no/b))

As traders buy YES shares, q_yes increases, pushing the price toward 1.00. As they buy NO, it pushes toward 0.00. The b parameter controls liquidity depth: higher b means more shares need to trade to move the price.

OU Model Seeds the Starting Position

We don't start every market at 50/50. The OU model provides a prior probability, and we initialize the share quantities to match:

q_yes = b × ln(p / (1-p)) / 2
q_no  = -q_yes

If the model says 73% YES, the market opens at 73¢/27¢. The first dollar of trading already has the model's prediction baked in. Uninformed traders who bet against the model pay the spread.

Why This Matters at Scale

• 22,000 markets/day × $34.66 max loss = $762K theoretical max daily exposure
• But with 89% model accuracy, most markets start well-calibrated
• Expected LP profit = +$21/market at current accuracy
• Net expected daily P&L: positive $460K (at scale)

The LMSR's bounded loss property is what makes this possible. No other AMM lets you safely seed thousands of markets per day from a single treasury.

The math works. The model works. Now we're proving it with real money.

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Related reading:

• How the OU Model Predicts Rates — the prediction model that seeds LMSR prices
• Funding Rates Are Prediction Markets — why this market exists
• Why We Built Settled — the origin story
• Browse Live Markets — see LMSR pricing in action across 3,700+ markets
• Binance BTC/USDT Funding Rate — the flagship market LMSR prices every 8 hours
• SIREN/USDT Funding Rate — high-volatility market with extreme rate swings
• All Funding Rate Data — compare rates across 2,400+ pairs