While I regretfully lost touch with Letterman 22 years ago after he moved his show over to CBS, I was a rabid fan during his Late Night era on NBC. 12:35AM every weeknight, right after Carson.
The joke I’ll always remember went something like this. I can’t quite remember the specifics, so I’ll just use 7-Eleven for now:
“Last February I was out in Los Angeles walking into the 7-Eleven on Cahuenga when a guy loitering out front asked me if I had any spare change. Then, just yesterday, I was walking into the 7-Eleven down on Church Street here in New York City when I ran into the exact same guy asking if I had any spare change. The exact same guy. What are the odds, Paul? So I walked up to him and I said, ‘Hey, weren’t you the guy out in Los Angeles last year in front of the 7-Eleven on Cahuenga?’ And he tells me, ‘Yes, yes I was.’ So I asked, ‘What are you doing all the way out here in New York?’ And he tells me, ‘I got transferred.'”