I see many resources online which explain what coin mixer or tumbler services are and how they work, and why someone would or wouldn't want to use one. But what I'm having trouble finding anywhere, is data or estimates about their overall prevalence.

What fraction of the transactions on a given blockchain, are constituted by tumbler activity? Is there any way of knowing or putting bounds on this number?

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A tumbler is a centralized service, different from CoinJoin protocols like Wasabi, Samourai, or JoinMarket. Thus, deposits and withdraws from Tumblers can look like small 1-input-2-ouput transactions, or they can look like batched transactions, more similar to CoinJoins, depending on the Tumbler's design.

Combined with the fact that Tumblers operate in gray if not fully illicit legal conditions, this makes it very hard to produce data about which transactions belong to tumblers.

Measuring CoinJoin use is easier because they have many inputs and many, often equally-sized outputs.

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