Automated market maker (AMM)

How it works

The constant-product formula (x times y equals k) is the foundational model, from Uniswap v2. Here x is the reserve of token A, y is the reserve of token B, and k is a constant preserved after each trade (excluding fees). Deposit token A and x rises; the formula forces y down proportionally, and the buyer receives that decrease in y. Larger trades shift reserves more and move price more, which is slippage.

Concentrated liquidity AMMs, from Uniswap v3, let providers deploy capital only within a chosen tick range. Inside that range the pool behaves as if much larger, with higher efficiency and tighter spreads. Outside it, the position earns no fees and provides no depth, making range selection a strategic decision.

Design consequence

Given the opening reserve ratio, the pool depth, and the formula, you can calculate exactly how much price moves for any trade size. That is the stress-test. A Uniswap v2 pool seeded with $200K on a $10M FDV moves the price roughly 10% on a $20K market buy. That number tells the team whether pool design matches their community's trade sizes.

Common mistake

Teams treat the AMM as infrastructure rather than a model input. Those who skip the math before launch cannot say what trade size breaks their price, and they are flying blind on the most consequential decision in the launch plan.