There are tools like EuroBillTracker (https://en.eurobilltracker.com/) where you can enter the serial number of bills that you received and can watch them travel around the world. If someone else tracks them as well, that is.
I entered 31 serial numbers over the last 15 years. Those haven't been seen again so far. I guess it's not the right kind of game for me... :)
If there were money in it, someone would throw OCR at the problem. Say, attach prizes to certain bills, or finding certain patterns of bills (say, two bills whose serial numbers are mathematically related a certain way).
You can still play that game with new coins, but it’s less f visible now, as most coins are old and those already are well dispersed throughout the euro zone (and, of course, more and more people pay with a card)
If the banks track serial numbers, they could probably build a fairly complete picture of what kind of transactions are going on. With the vast amount of data, you could probably fill in a lot of the gaps.
ATMs might already be recording serial numbers
I've been wondering about this forever.Say John gets bills from the ATM then pays dealer Dylan for weed. Dylan then buys a beer at a bar.
If Dylan gets convicted, and banks collaborate with the police, then John gets subjected to - at least - parallel reconstruction.
You don’t punish someone based on chance.
There is no need for it to be trustless and distributed.
If the police arrest suspected criminals and find money that can be traced back to criminal activity, they’ll confiscate it (permanently only after a trial). “Traced back” typically need not even involve checking serial numbers. If you’ve a lot of cash, but no regular job that explains how you could have that much money or why you would keep it in cash, that’s enough to confiscate it.
If, on the other hand, they find John Doe in possession of a banknote that was paid out in a ransom or stolen from a bank, and cannot link John Doe to any crime, John Doe can keep the money (they’ll ask him whether he knows where he got it and may be able to force him to exchange it for untainted money, but that’s it)
(Counterfeit money is different. If the police finds you in possession of it they’ll confiscate it, even if they know that you’re a victim)