How an Automated Market Maker Sets Prediction-Market Odds

An automated market maker (AMM) is a mechanism that quotes trading prices using a mathematical rule and takes the other side of trades. In a prediction market, that means someone can buy or sell outcome shares without waiting for another trader to post a matching order. The mechanism supplies liquidity; it does not independently discover the event’s true probability. Chen and Pennock’s review of prediction-market design explains this distinction between an auction that matches traders and a market maker that accepts trades itself.

For readers using markets as forecasts, the key question is not simply whether an AMM exists. It is how much trading moves its quoted probability—and what that movement actually demonstrates.

How a formula becomes a probability quote

Consider a binary contract: YES pays $1 if the specified event occurs and $0 otherwise. A 60-cent price can be read as a 60% implied probability under a simplified, fee-free interpretation. It is a market estimate, not a guarantee. The reasoning and practical qualifications are covered in how prediction-market prices become probabilities.

One established prediction-market AMM is the logarithmic market scoring rule, or LMSR, developed by Robin Hanson. It tracks outstanding shares for each outcome and calculates the cost of a trade from the change in a cost function. For a binary market:

C(qYES, qNO) = b × ln(exp(qYES / b) + exp(qNO / b))

Here, qYES and qNO are the outstanding share quantities, and b > 0 is a liquidity parameter. ln denotes the natural logarithm, and exp(z) means e raised to the power z. Buying shares costs the new value of C minus its old value. The instantaneous YES price is:

pYES = exp(qYES / b) / (exp(qYES / b) + exp(qNO / b))

The corresponding YES and NO prices sum to $1 in the standard model. David Pennock’s implementation explanation describes both the calculation and its relationship to quoted prices.

Buying YES raises its marginal price. Crucially, the quote applies to an infinitesimally small trade: a larger purchase moves along the pricing curve, so its average execution price is higher than the starting quote.

Worked example: identical buying, different odds

Suppose two fee-free binary LMSR markets begin with no shares outstanding and a YES quote of 50 cents. A trader buys 100 YES shares in each. The only difference is the liquidity parameter.

Measure	Lower liquidity: b = 100	Higher liquidity: b = 1,000
Starting YES quote	50.00¢	50.00¢
Cost of 100 YES shares	$62.01	$51.25
Average price paid per share	62.01¢	51.25¢
YES quote after the purchase	73.11¢	52.50¢

These are illustrative calculations from the standard LMSR cost and price functions, rounded to two decimal places—not observations from a live market. Pennock’s explanation supplies the underlying formulas.

The same share purchase creates a 23.11-percentage-point move in one market and a 2.50-point move in the other. Neither movement, by itself, tells us whether the trader had valuable information.

A larger b makes prices harder to move, but requires a larger potential subsidy. For a standard binary LMSR initialized at equal probabilities, the market maker’s worst-case loss is bounded by b × ln(2): about $69.31 and $693.15 in these examples. That bound concerns the market maker’s loss, not a trader’s loss or the forecast’s error. Chen and Pennock explain the trade-off between price sensitivity and the loss bound.

Not every AMM uses the same rule

The familiar crypto AMM often uses a pool of token reserves and a constant-product rule, commonly written x × y = k. Trades change the reserves and therefore the relative price; larger trades relative to pool depth have greater price impact. Uniswap’s documentation describes that structure.

That is not the same mechanism as LMSR. “AMM” does not identify a unique pricing formula, and prediction-market AMMs need not run on a blockchain.

An automated trader posting bids and asks on an order book is another distinct arrangement. As of October 11, 2026, Polymarket’s documentation describes its international platform as a central limit order book with offchain matching and onchain settlement. Its market-making guidance discusses maintaining and canceling resting orders. Automated quoting does not turn that exchange into a formula-priced liquidity pool.

What forecasters should check

Before treating an AMM quote as evidence, identify:

• The price measure. Is it the marginal quote, an average execution price, or the post-trade quote? The example shows why they are not interchangeable.
• Liquidity and initialization. How sensitive is the curve, and was the starting probability chosen by the operator rather than established through trading?
• All-in costs. Fees can change the price at which a trade becomes worthwhile; see fees versus quoted price.
• Outcomes across comparable forecasts. Calibration asks whether events quoted near 70%, for example, occur about 70% of the time over a suitable sample. That requires timestamped forecasts and resolution records, not merely a smooth pricing curve.

An AMM provides a counterparty without requiring another trader to arrive at the same time. Whether the resulting prices are useful forecasts remains a separate, measurable question.