Why Are Your Token Trades Always 'Fair'? The Math Magic Behind TTSWAP

About 1140 wordsAbout 4 min

2025-06-08

Why Are Your Token Trades Always 'Fair'? The Math Magic Behind TTSWAP

🤔 Ever Wondered About This?

When you swap USDC for ETH on a decentralized exchange like TTSWAP, how does the system know exactly how much ETH to give you? Why can you swap any tokens so freely, and it always feels so "fair"?

Today, let's pull back the curtain on the math magic that makes it all work.

📚 Let's Start With a Simple Story

Leo's Fruit Stand Dilemma

Leo runs a fruit stand outside his school, selling apples, oranges, and bananas. But he's got a problem:

Some classmates want to trade 2 apples for 3 oranges
Some want to swap 5 oranges for 1 banana
Others want to trade apples directly for bananas

Leo's head is spinning: How can he set prices so every trade is fair?

That's when his math teacher gives him a magical formula:

Unit price of each fruit × quantity traded = the same value

For example:

Apples: 2 yuan each, trading 2 → Value = 2 × 2 = 4 yuan
Oranges: 1.33 yuan each, trading 3 → Value = 1.33 × 3 = 4 yuan
Bananas: 4 yuan each, trading 1 → Value = 4 × 1 = 4 yuan

The magic: every trade has equal value!

🔬 From Fruit Stands to Web3: The Principle Is the Same

In Web3 decentralized exchanges, the principle is identical. Just swap:

Apples → Token A (like ETH)
Oranges → Token B (like USDC)
Bananas → Token Z (like BTC)

The Magic Formula Looks Like This:

{V_a\over Q_a} × Δa = {V_b\over Q_b} × Δb = {V_z\over Q_z} × Δz

Don't let the formula scare you! Let's break it down:

V_a = Total value of Token A in the protocol
Q_a = Total quantity of Token A in the protocol
V_a/Q_a = Unit price of Token A
Δa = Amount of Token A you want to trade

💡 Let's Use a Real Example

Scenario: You Want to Buy ETH With USDC

Suppose a pool has:

ETH pool: Total value $20 million, 10,000 ETH → Unit price = $20M / 10,000 = $2,000
USDC pool: Total value $20 million, 20 million USDC → Unit price = $20M / 20M = $1

Now you want to spend 4,000 USDC to buy ETH:

Step 1: Calculate the Value of Your Swap

Your USDC: $1 × 4,000 = $4,000 value

Step 2: Apply the Balancing Formula

ETH unit price × ETH amount = USDC unit price × USDC amount
$2,000 × ETH amount = $1 × 4,000
ETH amount = 4,000 ÷ 2,000 = 2

Result: You get 2 ETH for 4,000 USDC—totally fair!

🎯 Why Is This Formula So Important?

1. Automatic Pricing, No Human Needed

Traditional exchanges need market makers to set prices. This formula lets computers do it automatically.

2. Absolute Fairness, Guaranteed by Math

Whether you're a whale or a small trader, whatever tokens you swap, the same math applies—no discrimination.

3. Value Conservation, No Money Created Out of Thin Air

There's a hidden safeguard in the formula:

Total\ value\ before\ the\ trade\ = Total\ value\ after\ the\ trade

This means the system never creates or destroys value out of nowhere.

🔍 Digging Deeper: Why Is Value Conserved?

Let's go back to the fruit market for a deeper look:

Before the trade:

Apple pool: 1,000 × 2 yuan = 2,000 yuan
Banana pool: 500 × 4 yuan = 2,000 yuan
Total system value = 2,000 + 2,000 = 4,000 yuan

Leo's trade: 100 apples for bananas

After the trade:

Apple pool: 1,100 (added 100)
Banana pool: 450 (gave away 50)

Now, the key question: How do prices change after the trade?

📊 Price Recalculation

According to AMM logic, more supply → price drops, less supply → price rises

New apple price:

Apple count goes from 1,000 to 1,100 (supply up)
Price drops, say to about 1.82 yuan each
New apple pool value: 1,100 × 1.82 ≈ 2,000 yuan

New banana price:

Banana count drops from 500 to 450 (supply down)
Price rises, say to about 4.44 yuan each
New banana pool value: 450 × 4.44 ≈ 2,000 yuan

Total system value after trade = 2,000 + 2,000 = 4,000 yuan

🎯 Logical Reasoning: Why Must Value Be Conserved?

1. Mathematical Necessity

Leo gives 100 apples × 2 yuan = 200 yuan value
Gets 50 bananas × 4 yuan = 200 yuan value
No value created or destroyed, just exchanged

2. Prevents Arbitrage and Fake Trades If total value changed after a trade, what would happen?

3. Real-World Check Let's check the numbers:

Before trade:
Apples 1,000 × 2 yuan + Bananas 500 × 4 yuan = 4,000 yuan

During trade:
Leo gives: 100 apples × 2 yuan = 200 yuan value
Leo gets: 50 bananas × 4 yuan = 200 yuan value
Net value exchanged = 0 (no value created or lost)

After trade:
Apples 1,100 × 1.82 yuan + Bananas 450 × 4.44 yuan ≈ 4,000 yuan

Just like the law of conservation of energy, the system's total value never changes during a trade—it's just redistributed among tokens, with prices adjusting to keep the balance.

🌟 What Real-World Problems Does This Formula Solve?

Problem 1: The "Middleman" in Traditional Exchanges

Old way: Exchanges act as intermediaries, charge fees, control pricing
Web3 way: Math handles everything, no middleman needed

Problem 2: Complexity of Cross-Currency Trades

Old way: Want to swap RMB for USD, then USD for JPY? Multiple steps
Web3 way: Any two tokens can be swapped directly, formula auto-calculates the rate