> For the complete documentation index, see [llms.txt](https://docs.cleo.exchange/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.cleo.exchange/introduction-to-cleopatra/dex-functionalities/swaps.md).

# Swaps

On Cleopatra, similar to other decentralized exchanges (DEXs), users can swap tokens for others. The slippage and trade price are determined based on the total value locked in the liquidity pairs and whether arbitrage activities have balanced the pool to its market rate.

Cleopatra features two types of Liquidity Pools, each with its own swap curve:

* Volatile (UniV2-Style): This is the basic type of pool where tokens are paired with equal weights in terms of dollar value. The volatile swap curve is used to facilitate trades within these pools.
  * The volatile swap curve used is:

$$
x\*y=k
$$

* Correlated (Andre-Style): Cleopatra utilizes a stable swap curve that is an efficient implementation compared to other DEXs. The stable swap curve, originally devised by Andre, offers near-zero slippage and is designed to honor his innovative approach to stable swaps.
  * The stable swap curve used is:

$$
x^{3}y \ +y^{3}x \geq k
$$

## Graphical Representation of The ve(3,3) Swap Curves

To provide a graphical representation of the ve(3,3) swap curves, the graph below illustrates the variance between 0 and 100. It demonstrates that the Green (Correlated) curve exhibits less slippage from the mean as the K value fluctuates.

{% embed url="<https://www.desmos.com/calculator/5l0tnmuqh9>" %}
Green = StableSwap Curve, Red = Volatile Swap Curve
{% endembed %}

This visualization helps users understand the behavior of the swap curves and the corresponding slippage levels associated with different values of K. Cleopatra aims to provide an optimized trading experience with minimal slippage, enhancing liquidity provision and ensuring efficient token swaps for users.


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