Constant Product Formula
The rule x times y equals k, which sets a pool's price by keeping the product of its two balances constant through every trade.
If a pool holds quantity x of one asset and y of another, the contract requires that their product stay at least equal to a constant k after each swap, with the trading fee added on top. The implied price is the ratio of the two balances, so removing one asset makes the remaining units of it more expensive along a smooth curve. Because the curve approaches but never touches either axis, the pool can never be fully drained of either asset; it simply quotes ever worse prices. Larger trades relative to pool size travel further along the curve and therefore receive worse average prices.
In der Praxis
A swap that removes a large fraction of one side of a pool receives a much worse average rate than a small swap, purely because of the curve, not because of any fee.
Das häufige Missverständnis
The formula guarantees a deterministic price, not a fair one; a thin pool can quote far away from prices on deeper venues until arbitrage corrects it.