Weighted liquidity pools: why every AMM is not fifty-fifty

Normalize balances before comparing

Suppose a hypothetical pool contains 80 A and 20 B with weights 80% and 20%. The normalized balances are 80 ÷ 0.8 = 100 and 20 ÷ 0.2 = 100. Their ratio gives a fee-free marginal price of one A per B under this convention.

The raw balance ratio is four, which would be the wrong shortcut. This is a marginal price, not the average price of a large swap; execution changes balances.

Weights change how inventory responds

For two assets, the invariant is A raised to weight A multiplied by B raised to weight B. Equal weights reduce to a transformation of the familiar constant-product relationship. Unequal weights alter how much of each asset is held at a given relative market price.

The weights describe the pool’s mathematical arrangement, not a promise that depositors avoid losses or can sell any amount at the quoted marginal price.

Read the pool and join method

A proportional deposit and a deposit containing only one asset have different effects on balances. Non-proportional actions can include swap-like costs. Identify the actual pool implementation, weights and add/remove-liquidity method before comparing a displayed pool-token value with a wallet’s starting assets.