AMM Mechanics Deep Dive: Complete DEX Technical Reference

Last updated 10 Jan 2026, 14:09

Automated Market Makers (AMM) Fundamentals

What is an AMM?

An Automated Market Maker replaces traditional order books with mathematical formulas to determine prices. Instead of matching buyers and sellers, liquidity providers deposit assets into pools, and traders swap against these pools.

Key Innovation

  • No order matching needed - Trades execute instantly
  • Permissionless liquidity - Anyone can become a market maker
  • 24/7 trading - No market hours
  • Composability - Other protocols can integrate

Constant Product Formula (x * y = k)

The Core Math

Pioneered by Uniswap V1/V2:

x * y = k

Where:
x = quantity of token A
y = quantity of token B
k = constant (product of reserves)

Price Derivation

Price of A in terms of B = y / x
Price of B in terms of A = x / y

Trade Execution

When trading Δx of token A for token B:

New state: (x + Δx) * (y - Δy) = k
Solving: Δy = y - k/(x + Δx)

Slippage

Price impact from trade size:

Price impact ≈ Δx / x (for small trades)

Larger trades = more slippage because:

  • You're buying up the available liquidity
  • Price moves against you as you trade

Impermanent Loss Formula

IL = 2 * sqrt(price_ratio) / (1 + price_ratio) - 1

Where price_ratio = new_price / initial_price
Price Change Impermanent Loss
1.25x (25% up) 0.6%
1.5x (50% up) 2.0%
2x (100% up) 5.7%
3x (200% up) 13.4%
5x (400% up) 25.5%

Uniswap Evolution

Uniswap V1 (November 2018)

  • ETH pairs only (TOKEN/ETH)
  • No direct TOKEN/TOKEN swaps
  • Simple constant product
  • Foundation proof of concept

Uniswap V2 (May 2020)

Key Improvements:

  1. ERC20/ERC20 pairs: Any token pair possible
  2. Price oracles: TWAP (Time-Weighted Average Price)
  3. Flash swaps: Borrow without collateral (repay in same tx)
  4. Protocol fee switch: 0.05% to protocol (not activated)

Fee Structure: 0.30% to LPs

Key Contracts (Ethereum):

  • Factory: 0x5C69bEe701ef814a2B6a3EDD4B1652CB9cc5aA6f
  • Router02: 0x7a250d5630B4cF539739dF2C5dAcb4c659F2488D

Uniswap V3 (May 2021)

Revolutionary Changes:

1. Concentrated Liquidity

LPs provide liquidity within custom price ranges:

Instead of: 0 to ∞
Choose: 1800-2200 USDC per ETH

Benefits:

  • Up to 4000x capital efficiency
  • Higher fees earned per dollar
  • Active management required

2. Multiple Fee Tiers

Tier Use Case
0.01% Stablecoin pairs
0.05% Stable pairs, high volume
0.30% Most pairs
1.00% Exotic/volatile pairs

3. NFT LP Positions

  • Each position is unique NFT
  • Tracks price range, liquidity amount
  • Enables position as collateral

4. Oracle Improvements

  • Up to 65,535 price observations
  • More manipulation-resistant

Key Contracts (Ethereum):

  • Factory: 0x1F98431c8aD98523631AE4a59f267346ea31F984
  • SwapRouter: 0xE592427A0AEce92De3Edee1F18E0157C05861564
  • Universal Router: 0x3fC91A3afd70395Cd496C647d5a6CC9D4B2b7FAD

Uniswap V4 (2024)

Next Generation Features:

1. Hooks

Custom logic at key points:

  • Before/after swap
  • Before/after liquidity change
  • Dynamic fees
  • On-chain limit orders

2. Singleton Design

  • All pools in one contract
  • Gas savings from reduced calls
  • Flash accounting

3. Native ETH Support

  • No wrapping required
  • Gas savings

4. Custom Implementations

Hooks enable:

  • TWAMM (Time-Weighted AMM)
  • Dynamic fees based on volatility
  • MEV-aware pricing
  • Custom oracles

Other Major DEXs

SushiSwap

Uniswap V2 fork with additions:

  • SUSHI token incentives
  • xSUSHI staking (fee sharing)
  • Kashi lending integration
  • Trident AMM (concentrated liquidity)

PancakeSwap (BNB Chain)

Dominant BNB Chain DEX:

  • V2 and V3 (Uniswap-style)
  • CAKE token staking
  • IFO (Initial Farm Offerings)
  • Prediction market, lottery

Key Contracts (BNB Chain):

  • V2 Router: 0x10ED43C718714eb63d5aA57B78B54704E256024E
  • V3 Router: 0x1b81D678ffb9C0263b24A97847620C99d213eB14

Curve Finance

Optimized for like-kind assets:

StableSwap Invariant

Modified formula for stablecoins:

A * n^n * sum(x_i) + D = A * D * n^n + D^(n+1) / (n^n * prod(x_i))

Result: Much lower slippage for stable pairs

Key Pools

Pool Assets Use Case
3pool DAI/USDC/USDT Stablecoin base
stETH ETH/stETH LST swaps
Tricrypto USDT/WBTC/ETH Volatile with low slippage
frxETH ETH/frxETH Frax LST

veCRV and Gauge Wars

  • Lock CRV for veCRV (voting power)
  • Vote on liquidity gauge weights
  • Protocols bribe voters (Votium, Hidden Hand)
  • Creates "Curve Wars" dynamics

Balancer

Multi-asset pools with custom weights:

Weighted Pools:

V = Π (B_i)^(W_i)

Where:
B_i = balance of token i
W_i = weight of token i (sum = 1)

Use Cases:

  • Index funds (80/20 pools)
  • LBP (Liquidity Bootstrapping)
  • Managed pools

1inch (Aggregator)

Not a DEX, but aggregates across DEXs:

  • PathFinder algorithm finds best routes
  • Splits orders across venues
  • Fusion mode: MEV-protected limit orders
  • Chi gas token savings

CowSwap

Batch auction model:

  1. Collect orders for ~30 seconds
  2. Solvers compete to find best settlement
  3. Coincidence of Wants (CoW) first
  4. Remaining via DEXs

Benefits:

  • No MEV extraction
  • Better prices from batch matching
  • Surplus to users

AMM Math Deep Dive

Virtual Reserves (Uniswap V3)

With concentrated liquidity:

L = sqrt(x * y)  // Liquidity

For a position in range [pa, pb]:
x = L * (1/sqrt(p) - 1/sqrt(pb))  when p < pb
y = L * (sqrt(p) - sqrt(pa))      when p > pa

Tick Math

Prices stored as ticks:

price = 1.0001^tick
tick = log(price) / log(1.0001)

Tick spacing by fee:

Fee Tick Spacing
0.01% 1
0.05% 10
0.30% 60
1.00% 200

TWAP Oracles

Time-Weighted Average Price:

TWAP = (cumulative_price_B - cumulative_price_A) / (time_B - time_A)

Manipulation resistance: Attacker must hold manipulated price for the entire window

Price Impact Calculation

For constant product:

Price impact = Δy/y - Δx/x
            ≈ 2 * Δx / (x + Δx)  // for large trades

For stableswap (Curve): Much lower due to amplification factor A

LP Strategy Considerations

Passive LP (Uniswap V2 / full range V3)

  • Set and forget
  • Collects fees from all trades
  • Subject to impermanent loss
  • Best for: Correlated pairs, stable markets

Active LP (Concentrated liquidity)

  • Requires rebalancing
  • Higher fee capture in range
  • Zero fees if price exits range
  • Best for: Active managers, volatile pairs where range predictable

Just-In-Time (JIT) Liquidity

MEV strategy targeting LPs:

  1. Detect large swap
  2. Add liquidity in exact tick range
  3. Capture majority of fees
  4. Remove liquidity immediately

Controversial: Extracts value from passive LPs

Impermanent Loss Mitigation

  1. Correlated pairs: ETH/stETH has low IL
  2. Stablecoin pairs: DAI/USDC minimal IL
  3. Covered calls: Options strategies
  4. Incentives: Token rewards can offset IL

DEX Selection for Trading

When to Use Each

Scenario Best DEX
Stablecoin swaps Curve (lowest slippage)
Large trades Aggregator (1inch, CowSwap)
Fast meme trades Uniswap (most liquidity)
MEV-sensitive CowSwap (no MEV)
Low-cap tokens Check liquidity on Uniswap/Sushi

Aggregator Comparison

Aggregator Specialty
1inch Best routes, Fusion mode
CowSwap MEV protection
Paraswap Good rates, gas optimization
0x API Developer-focused

MEV Extraction Points

DEX-Specific MEV

Uniswap V2:

  • Sandwich attacks (most common)
  • Simple arbitrage between pools
  • Backrun large trades

Uniswap V3:

  • JIT liquidity provision
  • Tick crossing arbitrage
  • Range order fills

Curve:

  • Stablecoin depeg arbitrage
  • Cross-pool arbitrage
  • Virtual price manipulation

Multi-DEX:

  • Cross-DEX arbitrage
  • Route optimization MEV
  • Bridge arbitrage

Flash Loan DEX Patterns

// Example: Arbitrage pattern
1. Flash loan USDC from Aave
2. Buy ETH on Uniswap (lower price)
3. Sell ETH on Sushiswap (higher price)
4. Repay flash loan + fee
5. Keep profit

Router Analysis for MEV

Monitor router transactions:

  • Universal Router (complex swaps)
  • V2/V3 specific routers
  • Aggregator routers

Key Takeaways for DarkZen

  1. Know the math: Price impact, IL formulas critical
  2. Monitor multiple DEXs: Arb opportunities across venues
  3. Understand fee tiers: Affects profit calculations
  4. Watch liquidity distribution: V3 concentration matters
  5. Track big swaps: Backrun opportunities
  6. Oracle mechanics: Flash loan manipulation risks
  7. Gas optimization: Router choice affects profitability