Mike,
I just listened to
your interview on AgoristRadio, which was fun. A question for you: something that would be useful--nay, essential--in a laundering service is the assurance that one will receive
new coins and not receive back
any of the same coins of the original lot.
Actually I think it would be unwise to put that condition on a mixer.
It reminds me of the method eventually used to break the enigma machines. The breakers worked out that the enigma machine would never encode a letter to itself. That gave them enough of a statistical hole that they could begin breaking.
In the same way, one could simply look at which output coins a person received that contained none of a particular input and voila, the connection is made from input to output.
The correct solution is that coins are completely randomly mixed.