Amplification in an Automated Market Maker

Typical Liquidity Pool

x * y = k

In constant product automated market maker: x is the first token y is the second token k is the constant x and y must always multiply to form k

A pool will start with a equal number of both tokens In this instance, we can start with 5000 Apples and 5000 Bananas

Taking Apples as x, and Bananas as y, 5000 (Apples) * 5000 (Bananas) = 25,000,000 (k) The constant is 25,000,000

APPLE-BANANA Liquidity Pool

There are currently 5000 Apples and 5000 Bananas in the pool.

Swap

From:

Apples

To:

Bananas

Amplified Liquidity Pool

ax * ay = k * a^2

In a dynamic market maker: Both x and y are amplified by a ax and ay are thus virtual balances ax and ay must always multiply to form k * a * a.

A pool will start with a equal number of both tokens In this instance, we can start with 5000 Apples and 5000 Bananas

Amplification:

Taking Apples as x, and Bananas as y, you can set amplification above accordingly. The amplified amount of Apples is: 2,000,000 (5000 Apples * 400 amplification = 2,000,000) The amplified amount of Bananas is: 2,000,000 (5000 Bananas * 400 amplification = 2,000,000) 2,000,000 (Apples) * 2,000,000 (Bananas) = 4,000,000,000,000 (k) The amplified constant is 4,000,000,000,000

APPLE-BANANA Liquidity Pool

There are currently 5000 Apples and 5000 Bananas in the pool.

Swap

From:

Apples

To:

Bananas