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Standard Pools

Overview​

Standard pools are best suited for volatile asset pairs or speculative trading environments. Their simple and elegant mechanism allows for continuous liquidity provisioning across all price ranges, including extreme market conditions.

How It Works​

Standard pools operate under the following invariant:

    x * y = k

Where:

  • x: Reserve of Token X
  • y: Reserve of Token Y
  • k: A constant that remains unchanged during trades

This invariant ensures that after each trade, the new reserves must still satisfy the equation x * y = k. As a result, the price dynamically adjusts based on supply and demand.

Trading​

When a user swaps Δx of Token X into the pool, they receive Δy of Token Y. The values are calculated to maintain the invariant:

    (x + Δx) * (y - Δy) = k

Rearranging this, we get the amount out:

    Δy = y - (k / (x + Δx))

A swap fee is typically deducted from the input (Δx) before applying the above formula.

Price Slippage​

Due to the nature of the constant product formula, larger trades result in disproportionately higher slippage. This is a feature, not a flaw, as it disincentivizes front-running and protects liquidity providers from excessive losses.

Price is implicitly given by the ratio of reserves:

    P = y / x

After a swap, the reserves shift, thus updating the price dynamically.

Liquidity Provision​

To add liquidity, providers must deposit tokens in the same ratio as the current price:

    deposit_x / deposit_y = x / y

Doing so increases the size of the pool (and hence k), allowing for:

  • More capital for traders to use
  • Reduced slippage on trades
  • Increased pool depth and stability

In return, liquidity providers (LPs) receive LP tokens representing their share in the pool. They can redeem these later for a proportional amount of the pool's assets.

Advantages​

  • Simplicity: Easy to implement and understand
  • Constant liquidity: Always available at every price point
  • Permissionless: Anyone can trade or add/remove liquidity
  • Effective for volatile assets: Encourages speculation and arbitrage

Limitations​

  • High slippage for large trades: Not ideal for low-volatility, stable pairs
  • Impermanent Loss: LPs can suffer losses compared to simply holding the assets
  • No concentrated liquidity: Capital is spread thinly across all price ranges

Use Cases​

  • New token launches: Ideal for price discovery
  • Volatile or speculative assets: Encourages active trading
  • Cross-chain assets: Where price volatility is expected due to bridging risks

Conclusion​

Standard AMMs revolutionized DeFi by democratizing liquidity and trading. While they are no longer the most capital-efficient design for all use cases, they remain a foundational mechanism and are still preferred in specific market conditions—especially where simplicity, decentralization, and volatility handling are key.