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An Automated Market Maker (AMM) is a smart contract that prices and executes trades using a mathematical formula instead of an order book.

Instead of matching a buyer with a seller, traders swap against a shared pool of tokens.

Traditional exchanges match individual buy and sell orders. AMMs replace that with a liquidity pool and a pricing curve.

• Order book: needs active market makers
• AMM: always available, prices set by formula

An AMM pool holds a reserve of two tokens, for example ETH and USDC. Traders add one token and remove the other.

The pool's reserves determine the price — the contract never needs a counterparty.

The most famous AMM (Uniswap v2) uses the constant product formula:

x * y = k

The product of the two reserves must stay equal to a constant k after every trade (ignoring fees).

To buy ETH, a trader adds USDC. The USDC reserve grows and the ETH reserve shrinks, but the product must remain k.

The instantaneous price is the ratio of reserves: price = y / x.

As one reserve shrinks, that token becomes more expensive. The curve makes large trades cost progressively more per unit.

Slippage is the difference between the expected price and the price you actually get. Big trades move along the curve and suffer more slippage.

Deeper pools (larger reserves) reduce slippage because each trade shifts the ratio less.

Each swap charges a fee (often 0.30%) that is added to the pool. This grows k slightly over time.

Fees are the reward that compensates liquidity providers for supplying capital.

If the AMM price drifts from the wider market, arbitrageurs trade against the pool until it matches.

This self-correcting pressure keeps AMM prices aligned with external markets without any oracle.

Constant product is not the only design:

• Curve uses a stableswap formula for assets that should trade near 1:1
• Uniswap v3 adds concentrated liquidity within chosen price ranges

Each curve optimizes for a different asset type.

AMMs price trades with a formula like x * y = k against a shared pool. Reserves set the price, large trades cause slippage, fees reward providers, and arbitrage keeps prices accurate.

Next we look at the liquidity pools themselves.

Test your AMM math intuition.

You learned that:

• AMMs replace order books with a formula + pool
• The constant product rule is x * y = k
• Price is the reserve ratio; big trades cause slippage
• Fees reward providers; arbitrage keeps prices honest

Next: providing liquidity to these pools.