> For the complete documentation index, see [llms.txt](https://eigenphi-1.gitbook.io/classroom/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://eigenphi-1.gitbook.io/classroom/mev-types/arbitrage/arbitrage-involving-3-tokens-among-3-trading-venues.md).

# Arbitrage Involving 3 Tokens Among 3 Trading Venues

Sometimes an arbitrage has to employ three cryptocurrencies that have rates spread among three [liquidity pools](https://eigenphi.io/ethereum/pool/freq) to make a profit. It requires the [searcher](/classroom/users-of-eigenphi/searcher.md) to have the ability to discover the opportunities from rate changes in three liquidity pools.  

Searcher Alice detects the rate spreads of USDC, WETH, and X2Y2 amid three liquidity pools. Then, she proceeds with the arbitrage as below: 

1. Alice sells 284,427.34 $USDC for 100 $WETH in a liquidity pool--called LP1--on Uniswap with the exchange rate of 1 $WETH for 2,844.27. $USDC.
2. Alice sells 100 $WETH for 2,082,721.43 $X2Y2 in another liquidity pool--called LP2--on Uniswap with the exchange rate of 1 $WETH for 20,827.21 $X2Y2. 
3. In another liquidity pool--called LP3, Alice exchanges 2,082,721.43 $X2Y2 for 303,670.11 $USDC.

![Triangular Arbitrage](/files/vndvgMr1R1eNbCmF4lgq)

Alice's revenue from this arbitrage is 19,242.77 $USDC. The cost is the gas fees for the three transactions. Assuming it's 0.05 $WETH, an equivalent of 150 USD at the price of the time. And let's presume the exchange rate of USDC and USD is 1:1. In the end, Alice's profit is 19,092.77 USD.

Next, we will examine the arbitrage requires more tokens and trading venues.