Goals:

To journey from "Centralized Order Book Exchanges" all the way to "AMM + Curve Stablecoin Pools," and understand:

👉 Why do we need AMMs?

👉 Who are LPs?

👉 Where does Slippage come from?

👉 Why does Impermanent Loss exist?

👉 Why does Curve have low slippage and low impermanent loss?

👉 Why don't all AMMs use a "low slippage curve"?

• Examples: Nasdaq, Binance, Coinbase

• Uses an Order Book:

  • Users post "Buy Orders / Sell Orders."

  • A matching engine pairs them on a centralized server.

• Funds are Custodial: Held by the exchange.

Pros:

• Extremely fast matching speed.

• No gas fees for cancelling orders.

• High liquidity.

Cons:

• Not Censorship-Resistant: Requires KYC; accounts can be frozen.

• Single Point of Failure & Custodial Risk: Hacks, downtime, or the exchange running away with funds ("rug pulls").

• Opaque Information & Potential Front-running.

• Matching and settlement are moved on-chain (Smart Contracts).

• Users must pay Gas to place, cancel, or take orders.

Pros:

• Censorship-resistant.

• Non-custodial.

Cons:

• Slow: Limited by blockchain block times.

• Expensive: Every operation requires Gas.

• Poor Liquidity: Lack of sufficient market makers.

• Vulnerable to On-chain Front-running.

Conclusion:

Moving the Order Book model directly on-chain results in a poor user experience. We need a liquidity model that does not rely on pending orders → AMM.

AMM (Automated Market Maker) =

An automated market-making system that uses mathematical formulas rather than an order book to quote prices and provide liquidity.

The Classic Model:

• x = Quantity of Token X in the pool

• y = Quantity of Token Y in the pool

• x = Constant (Invariant)

For every transaction:

• x and y change.

• Such that x*y remains equal to k.

• Price is determined by the internal state of the pool:

  

LP = Liquidity Provider

• They deposit two assets into the pool according to a specific ratio (usually 50:50 value).

  • Example: 1 ETH + 2000 USDC.

• In return:

  • They receive LP Tokens (representing their share/equity in the pool).

  • They earn trading fee revenue based on the pool's volume.

Without LPs, there is no pool; without a pool, you cannot trade using an AMM.

Slippage = The deviation between the actual average execution price and the price you saw before placing the order.

Reason:

When you place an order, the AMM doesn't just quote a price once; the price updates continuously throughout the execution of your trade.

The more you buy, the more you push the price up yourself during the process → The average execution price ends up higher than the starting point.

Pool State:

You use 10 Y to buy X:

You originally saw a "price of roughly 1:1," but the actual execution:

• 10 Y swapped for 9.091 X

• Effective Price:

  

• More expensive than the starting 1:1 → Slippage occurred.

Slippage is not the same as the Trading Fee.

It comes from the AMM formula:

By moving the price curve, you are essentially "consuming liquidity."

• Larger trade size → Curve moves more → Higher slippage.

• Shallower pool (low liquidity) → Higher slippage for the same trade size.

For the Trader:

• High slippage → High cost → Yes, it's a disadvantage.

But for the Mechanism:

Slippage = A safety valve protecting the pool from being drained instantly.

If the curve were completely flat (ultra-low slippage):

• Arbitrarily large trades would barely change the price.

• The pool could easily be drained of "cheap assets" by arbitrageurs.

• LPs would be wiped out quickly.

The higher the volatility of the asset, the steeper the curve must be, and the higher the slippage must be.

Therefore:

• Stable Assets (Stablecoins): Curve can be flatter.

• Volatile Assets (ETH / MEME): Curve must be steeper to protect LPs.

Taking Uniswap V2 as an example:

• Every Swap is charged a 0.3% Fee.

• This 0.3%:

  • Is added to the pool, increasing the total reserves.

  • Is distributed based on LP share holdings (Pool gets larger → Each LP token represents more assets).

LP revenue isn't paid out like "daily interest"; rather:

As trading volume increases, the pool as a whole gets "fatter."

• Slippage: Caused by the mathematical curve.

• Fee: A fixed percentage charged by the protocol.

Your Actual Cost = Slippage Loss + Trading Fee

1. Incentivize LPs to provide liquidity.

2. Offset Impermanent Loss for LPs.

3. Raise the cost of arbitrage, preventing excessive exploitation of the pool.

Impermanent Loss = The difference in asset value between "being an LP" and "simply holding the two assets in a wallet."

It is not an "absolute loss," but rather:

"You could have made more profit, but because you were an LP, your gains were dampened."

Initial State:

• ETH Price = 1000

• You provide LP:

  • 1 ETH + 1000 USDC → Total Value 2000

Scenario: ETH rises to 2000.

If you HODL (don't LP):

• Assets = 1 ETH (=2000) + 1000 USDC = 3000

If you LP (Pool rebalances):

• The pool constantly "Sells ETH / Buys USDC" as price rises.

• You might withdraw:

  • 0.707 ETH + 1414 USDC 2828

Difference:

3000 - 2828 = 172 → Impermanent Loss.

• If the price returns from 2000 back to 1000:

  • The pool ratio returns to the initial state.

  • You withdraw exactly what you put in.

  • The loss "disappears."

However:

• If you withdraw your liquidity while the price is diverged → The loss becomes Permanent (Realized).

• High Volatility Assets (ETH, MEME): High IL.

• Stablecoin Swaps (USDC/USDT/DAI): Very low IL. → This leads us to: Curve's Stablecoin AMM.

• Stablecoins are expected to be 1:1.

• User psychological expectation is high:

  • Swapping 10,000 USDT for 9,900 USDC is painful.

• Uniswap's curve is too convex ("curved"), causing:

  • Significant slippage even on moderately sized orders.

• Price is anchored near $1.

• Low volatility.

• Users don't care about "speculation," only "efficient exchange."

This means:

We don't need a curve as steep as the one used for ETH.

Curve does not use:

• Pure Constant Product ( $x \cdot y = k$ )

• Pure Constant Sum ($x + y = \text{const}$)

Instead, it uses:

A Hybrid Curve between the two.

It becomes very flat near 1:1 (low slippage) and acts like a standard product curve (protective) in extreme cases.

Graphical Intuition:

Constant Sum AMM
(x + y = constant)

Stablecoin Trading
Low Slippage

Constant Product AMM
(x * y = k)

Standard Token Trading
Higher Slippage

Suitable for Stable Pairs
e.g., USDC/USDT, DAI/USDC

Suitable for Volatile Assets
e.g., ETH/USDC

• In the stable range:

  • Curve is nearly flat → Minimal slippage for large trades.

• When assets deviate significantly:

  • Curve becomes steep → Prevents the pool from being drained by arbitrage.

Because:

1. Asset volatility is naturally low (USDT / USDC / DAI).

2. Curve's design is very flat near 1:1, so large swaps don't cause massive price deviation.

3. The price change endured by LPs is limited → IL is negligible.

Therefore, risk-averse LPs love:

• Stablecoin Pools (e.g., 3pool).

Soft-pegged Asset Pools (e.g., stETH/ETH).

Your question is spot on. The core logic is:

Low slippage is not a free lunch; it is "bought" with capital efficiency and model risk.

• The flatter the curve:

  • The weaker the AMM's ability to resist price deviation.

  • The easier it is for arbitrageurs to drain one side of the assets with large capital.

• For high-volatility assets, if the curve is too flat:

  • LPs will be exploited faster and more heavily.

  • The pool becomes unsafe.

Therefore:

• High Volatility Assets (ETH/USDC): Need a steeper curve (Uniswap).

• Low Volatility Assets (Stablecoins/Pegged): Can use a flatter curve (Curve).

Different asset types → Require different AMM curves → This is the "AMM Design Space."

Goals:

To journey from "Centralized Order Book Exchanges" all the way to "AMM + Curve Stablecoin Pools," and understand:

👉 Why do we need AMMs?

👉 Who are LPs?

👉 Where does Slippage come from?

👉 Why does Impermanent Loss exist?

👉 Why does Curve have low slippage and low impermanent loss?

👉 Why don't all AMMs use a "low slippage curve"?

• Examples: Nasdaq, Binance, Coinbase

• Uses an Order Book:

  • Users post "Buy Orders / Sell Orders."

  • A matching engine pairs them on a centralized server.

• Funds are Custodial: Held by the exchange.

Pros:

• Extremely fast matching speed.

• No gas fees for cancelling orders.

• High liquidity.

Cons:

• Not Censorship-Resistant: Requires KYC; accounts can be frozen.

• Single Point of Failure & Custodial Risk: Hacks, downtime, or the exchange running away with funds ("rug pulls").

• Opaque Information & Potential Front-running.

• Matching and settlement are moved on-chain (Smart Contracts).

• Users must pay Gas to place, cancel, or take orders.

Pros:

• Censorship-resistant.

• Non-custodial.

Cons:

• Slow: Limited by blockchain block times.

• Expensive: Every operation requires Gas.

• Poor Liquidity: Lack of sufficient market makers.

• Vulnerable to On-chain Front-running.

Conclusion:

Moving the Order Book model directly on-chain results in a poor user experience. We need a liquidity model that does not rely on pending orders → AMM.

AMM (Automated Market Maker) =

An automated market-making system that uses mathematical formulas rather than an order book to quote prices and provide liquidity.

The Classic Model:

• x = Quantity of Token X in the pool

• y = Quantity of Token Y in the pool

• x = Constant (Invariant)

For every transaction:

• x and y change.

• Such that x*y remains equal to k.

• Price is determined by the internal state of the pool:

  

LP = Liquidity Provider

• They deposit two assets into the pool according to a specific ratio (usually 50:50 value).

  • Example: 1 ETH + 2000 USDC.

• In return:

  • They receive LP Tokens (representing their share/equity in the pool).

  • They earn trading fee revenue based on the pool's volume.

Without LPs, there is no pool; without a pool, you cannot trade using an AMM.

Slippage = The deviation between the actual average execution price and the price you saw before placing the order.

Reason:

When you place an order, the AMM doesn't just quote a price once; the price updates continuously throughout the execution of your trade.

The more you buy, the more you push the price up yourself during the process → The average execution price ends up higher than the starting point.

Pool State:

You use 10 Y to buy X:

You originally saw a "price of roughly 1:1," but the actual execution:

• 10 Y swapped for 9.091 X

• Effective Price:

  

• More expensive than the starting 1:1 → Slippage occurred.

Slippage is not the same as the Trading Fee.

It comes from the AMM formula:

By moving the price curve, you are essentially "consuming liquidity."

• Larger trade size → Curve moves more → Higher slippage.

• Shallower pool (low liquidity) → Higher slippage for the same trade size.

For the Trader:

• High slippage → High cost → Yes, it's a disadvantage.

But for the Mechanism:

Slippage = A safety valve protecting the pool from being drained instantly.

If the curve were completely flat (ultra-low slippage):

• Arbitrarily large trades would barely change the price.

• The pool could easily be drained of "cheap assets" by arbitrageurs.

• LPs would be wiped out quickly.

The higher the volatility of the asset, the steeper the curve must be, and the higher the slippage must be.

Therefore:

• Stable Assets (Stablecoins): Curve can be flatter.

• Volatile Assets (ETH / MEME): Curve must be steeper to protect LPs.

Taking Uniswap V2 as an example:

• Every Swap is charged a 0.3% Fee.

• This 0.3%:

  • Is added to the pool, increasing the total reserves.

  • Is distributed based on LP share holdings (Pool gets larger → Each LP token represents more assets).

LP revenue isn't paid out like "daily interest"; rather:

As trading volume increases, the pool as a whole gets "fatter."

• Slippage: Caused by the mathematical curve.

• Fee: A fixed percentage charged by the protocol.

Your Actual Cost = Slippage Loss + Trading Fee

1. Incentivize LPs to provide liquidity.

2. Offset Impermanent Loss for LPs.

3. Raise the cost of arbitrage, preventing excessive exploitation of the pool.

Impermanent Loss = The difference in asset value between "being an LP" and "simply holding the two assets in a wallet."

It is not an "absolute loss," but rather:

"You could have made more profit, but because you were an LP, your gains were dampened."

Initial State:

• ETH Price = 1000

• You provide LP:

  • 1 ETH + 1000 USDC → Total Value 2000

Scenario: ETH rises to 2000.

If you HODL (don't LP):

• Assets = 1 ETH (=2000) + 1000 USDC = 3000

If you LP (Pool rebalances):

• The pool constantly "Sells ETH / Buys USDC" as price rises.

• You might withdraw:

  • 0.707 ETH + 1414 USDC 2828

Difference:

3000 - 2828 = 172 → Impermanent Loss.

• If the price returns from 2000 back to 1000:

  • The pool ratio returns to the initial state.

  • You withdraw exactly what you put in.

  • The loss "disappears."

However:

• If you withdraw your liquidity while the price is diverged → The loss becomes Permanent (Realized).

• High Volatility Assets (ETH, MEME): High IL.

• Stablecoin Swaps (USDC/USDT/DAI): Very low IL. → This leads us to: Curve's Stablecoin AMM.

• Stablecoins are expected to be 1:1.

• User psychological expectation is high:

  • Swapping 10,000 USDT for 9,900 USDC is painful.

• Uniswap's curve is too convex ("curved"), causing:

  • Significant slippage even on moderately sized orders.

• Price is anchored near $1.

• Low volatility.

• Users don't care about "speculation," only "efficient exchange."

This means:

We don't need a curve as steep as the one used for ETH.

Curve does not use:

• Pure Constant Product ( $x \cdot y = k$ )

• Pure Constant Sum ($x + y = \text{const}$)

Instead, it uses:

A Hybrid Curve between the two.

It becomes very flat near 1:1 (low slippage) and acts like a standard product curve (protective) in extreme cases.

Graphical Intuition:

Constant Sum AMM
(x + y = constant)

Stablecoin Trading
Low Slippage

Constant Product AMM
(x * y = k)

Standard Token Trading
Higher Slippage

Suitable for Stable Pairs
e.g., USDC/USDT, DAI/USDC

Suitable for Volatile Assets
e.g., ETH/USDC

• In the stable range:

  • Curve is nearly flat → Minimal slippage for large trades.

• When assets deviate significantly:

  • Curve becomes steep → Prevents the pool from being drained by arbitrage.

Because:

1. Asset volatility is naturally low (USDT / USDC / DAI).

2. Curve's design is very flat near 1:1, so large swaps don't cause massive price deviation.

3. The price change endured by LPs is limited → IL is negligible.

Therefore, risk-averse LPs love:

• Stablecoin Pools (e.g., 3pool).

Soft-pegged Asset Pools (e.g., stETH/ETH).

Your question is spot on. The core logic is:

Low slippage is not a free lunch; it is "bought" with capital efficiency and model risk.

• The flatter the curve:

  • The weaker the AMM's ability to resist price deviation.

  • The easier it is for arbitrageurs to drain one side of the assets with large capital.

• For high-volatility assets, if the curve is too flat:

  • LPs will be exploited faster and more heavily.

  • The pool becomes unsafe.

Therefore:

• High Volatility Assets (ETH/USDC): Need a steeper curve (Uniswap).

• Low Volatility Assets (Stablecoins/Pegged): Can use a flatter curve (Curve).

Different asset types → Require different AMM curves → This is the "AMM Design Space."