I don't think the banks shuttle coins between themselves directly. Long gone are the days when banks had their own armored cars for this purpose. But they will work through the intermediary armored car companies - the same companies which the Fed subcontracts for delivery of freshly minted coins around the country.
In essence, a bank branch which sees itself with a surplus of coins gets those surplus coins collected by the armored car companies, which then decides where to redistribute them based purely on demand and proximity. This is all done under the doctrine of moving coins around as little as possible, since coins are heavy and in the transport business, heavy = costly = less profits for the company if you have to transport them long distances. So coins from your "dump bank" aren't likely to travel far and are highly likely to end up in other bank branches in the same city or even the same suburbs that they came from, if that's where the company's demand-map says they're needed.
They're even likely to jump between altogether different banks since the armored car companies don't really care which bank gets which coins and certainly aren't going to waste time and resources keeping each bank's coins in separate streams. So even dumping your coins in TD Bank and then going to a non-TD Bank to get fresh coins isn't necessarily going to guarantee you won't be getting your own rolls given back to you again, if both banks are using the same armored car company.
In essence, a bank branch which sees itself with a surplus of coins gets those surplus coins collected by the armored car companies, which then decides where to redistribute them based purely on demand and proximity. This is all done under the doctrine of moving coins around as little as possible, since coins are heavy and in the transport business, heavy = costly = less profits for the company if you have to transport them long distances. So coins from your "dump bank" aren't likely to travel far and are highly likely to end up in other bank branches in the same city or even the same suburbs that they came from, if that's where the company's demand-map says they're needed.
They're even likely to jump between altogether different banks since the armored car companies don't really care which bank gets which coins and certainly aren't going to waste time and resources keeping each bank's coins in separate streams. So even dumping your coins in TD Bank and then going to a non-TD Bank to get fresh coins isn't necessarily going to guarantee you won't be getting your own rolls given back to you again, if both banks are using the same armored car company.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis



















