How automated market makers work for binary prediction markets
A binary prediction market lets you bet on a yes-or-no outcome. Will the Federal Reserve cut rates by September? Yes or no. Will a specific candidate win the election? Yes or no. Each outcome is represented by its own token, and the price of that token is meant to reflect the market’s estimate of the probability. But under the hood, that price comes from a mathematical rule, not from a human setting odds.
The most common rule is the fixed-product automated market maker (AMM). It is the same formula that powers many decentralized exchanges. For a binary market, the pool holds exactly two tokens: the “yes” token and the “no” token. Let’s call them Y and N. The rule is simple: the product of the quantities of Y and N in the pool must always remain constant. That constant is usually written as k.
So if the pool starts with 100 Y tokens and 100 N tokens, k = 100 × 100 = 10,000. If someone buys Y tokens, they add N tokens and remove Y tokens. The pool’s Y balance goes down, its N balance goes up. The product must stay 10,000. That forces the ratio to shift, and the price changes with every trade.
Polymarket uses exactly this mechanism. Consider a market on a yes/no question. The pool’s AMM quotes a price for each token based on the current balances. The price of the yes token is N / (Y + N). The price of the no token is Y / (Y + N). Notice they always sum to 1. Multiply either price by 100 and you get something that looks like a percentage. That is the implied probability.
But here is the key point: price is not precisely probability. The AMM price is a function of the pool’s current reserves, not of anyone’s genuine belief. It is a mechanical output of the constant product formula. If the pool has 80 Y and 120 N, the yes token price is 120 / (80 + 120) = 0.6, or 60%. That number can diverge from what any informed trader actually thinks. The formula does not contain any model of the real world. It only enforces that Y × N stays fixed.
Walk through a trade. Suppose the pool is at 100 Y and 100 N. Yes token price is 0.50. You want to buy 10 yes tokens. You must add no tokens to the pool. How many? The new Y balance will be 90 after your purchase. For k to remain 10,000, the new N balance must be 10,000 / 90 = 111.11. That means you need to add 11.11 N tokens. Your effective price per yes token is 1.111 N tokens. That is higher than the starting price. That difference is slippage.
If you buy a large amount, the shift becomes bigger. Buy 50 yes tokens from the same starting pool. New Y = 50, so new N = 10,000 / 50 = 200. You must add 100 N tokens. Your average price is 2 N per yes token. The first token cost roughly 1.0 N; the last token costs much more. Slippage grows nonlinearly. The constant product formula is convex. That is why large orders move the implied probability dramatically.
The pool has no oracle. It has no external information about the real event. All it does is enforce the product rule. If someone thinks the implied probability is wrong, they can trade against the pool. That arbitrage action is what keeps the price roughly aligned with the real probability - but only roughly. The formula itself never guarantees convergence.
One consequence is that thin liquidity pools are highly sensitive. A small trade can swing the implied probability by several percentage points. On the other hand, deep pools absorb larger bets with less slippage. The design is a trade-off. You get continuous liquidity without an order book, but you pay for it in slippage and systematic divergence from true probability.
The constant product AMM for binary markets is elegant precisely because it is simple. It reduces a complex forecasting problem to a single arithmetic constraint. Yet it is also an approximation. Anyone trading in these markets should understand that the price they see is a mechanical ratio, not a poll of informed opinion. The market can be gamed. It can be wrong. The formula does not care about being right. It only cares about the product.
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