how does this compare to the privacy afforded by whirlpool?

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It's similar, but you have to do a few rounds to get similar anonymity set. Also you don't pay any coordinator fee, just your portion of the mining fee for the coinjoin.

Keep in mind that Whirlpool also doesn't give perfect privacy, you can read this series to learn more: https://spiralbtc.substack.com/p/the-scroll-4-intersection-attacks