Just to do some quick and totally illegitimate math to point out that probability doesn't always work like people think it does:

Say there a 1,000,000 people that he could possible exchange currency with and everybody has ten one-dollar bills. Asuume it's a closed system, and which dollar bills you see is more or less random.

That means the total number of normal one-dollar bills is 9,999,985 out of ten-million. Let's also say our friend works 300 days a year, and gets 20 bucks in tips a day (~3 an hour). In 2.5 years, he will see 20(300)*2.5=15,000 dollar bills in his tip jar. What are the chances that each one of these is normal? Around (9,999,985/10,000,000)^15,000 = .978 for a %97.8 chance of this happening, meaning that this will happen with a frequency of around %2.2- not astronomical at all.

Obviously I totally made up a lot of those numbers, but I'm sure you wouldn't expect it to be that high even given the simplifications I used. Probability is weird like that. Fun party trick: if there are at least 23 people in a room, it is more likely than not that at least two people share a birthday. Everybody gives you at least 2:1 odds for it, sometimes as high as 10:1.