Automated Market Makers (AMM) in Blockchain / Solidity - Step-by-Step Execution

Concept Flow - Automated Market Makers (AMM)

User provides Token A and Token B

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AMM Pool receives tokens

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Calculate new token reserves

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Apply constant product formula: x * y = k

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Determine output token amount

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User receives swapped tokens

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Update pool reserves for next trade

The AMM takes tokens from the user, updates reserves using a formula, and returns swapped tokens, keeping the product of reserves constant.

Execution Sample

Blockchain / Solidity

reserveA = 1000
reserveB = 1000
inputA = 100
k = reserveA * reserveB
newReserveA = reserveA + inputA
newReserveB = k / newReserveA
outputB = reserveB - newReserveB

This code swaps Token A for Token B using the constant product formula in an AMM pool.

Execution Table

Step	Variable	Value	Calculation/Action	Explanation
1	reserveA	1000	Initial reserve	Starting Token A in pool
2	reserveB	1000	Initial reserve	Starting Token B in pool
3	inputA	100	User input	User adds 100 Token A to swap
4	k	1000000	reserveA * reserveB	Constant product remains fixed
5	newReserveA	1100	reserveA + inputA	Pool now has 1100 Token A
6	newReserveB	909.09	k / newReserveA	Calculate new Token B reserve
7	outputB	90.91	reserveB - newReserveB	User receives ~90.91 Token B
8	-	-	-	Swap complete, reserves updated

💡 Swap ends after calculating output tokens and updating reserves.

Variable Tracker

Variable	Start	After Step 3	After Step 5	After Step 6	Final
reserveA	1000	1000	1100	1100	1100
reserveB	1000	1000	1000	909.09	909.09
inputA	-	100	100	100	100
k	-	-	1000000	1000000	1000000
newReserveA	-	-	1100	1100	1100
newReserveB	-	-	-	909.09	909.09
outputB	-	-	-	90.91	90.91

Key Moments - 3 Insights

Why do we multiply reserveA and reserveB to get k?

Because the AMM uses the constant product formula x * y = k to keep the pool balanced, as shown in step 4 of the execution_table.

Why does outputB equal reserveB minus newReserveB?

Because the user receives the difference in Token B reserves after the swap, as calculated in step 7 of the execution_table.

Why do we add inputA to reserveA before calculating newReserveB?

Because the pool's Token A reserve increases by the user's input before recalculating Token B reserve, shown in step 5.

Visual Quiz - 3 Questions

Look at the execution_table at step 6, what is the value of newReserveB?

A 909.09

B 1000

C 1100

D 90.91

💡 Hint

Check the 'Value' column at step 6 in the execution_table.

At which step does the pool calculate the constant product k?

A Step 3

B Step 5

C Step 4

D Step 7

💡 Hint

Look for the step where k = reserveA * reserveB is calculated in the execution_table.

If the user inputs 200 Token A instead of 100, which variable changes first in the variable_tracker?

A reserveB

B inputA

C newReserveB

D outputB

💡 Hint

Look at the variable_tracker to see which variable records the user input first.

Concept Snapshot

Automated Market Makers (AMM) use a formula x * y = k to keep token reserves balanced.
Users swap tokens by adding one token to the pool.
The pool calculates the output token amount by maintaining k constant.
Reserves update after each swap to reflect new balances.
This allows decentralized token trading without order books.

Full Transcript

Automated Market Makers (AMM) let users swap tokens by interacting with a pool of two tokens. The pool keeps the product of the token reserves constant, called k. When a user adds some amount of Token A, the pool calculates how much Token B to give back so that reserveA times reserveB stays equal to k. This process updates the reserves and completes the swap. The key steps are: starting reserves, user input, calculating k, updating reserves, and determining output tokens. This method allows smooth token swaps without needing buyers and sellers to match directly.