Sometimes when I’m bored and out walking, I play this game with cars. I pretend I’m allowed to keep any one of the next ten cars that go past, but I need to accept or reject it the moment I see it.

If the second car is a Volvo do I pick it, or hold out waiting for a Mercedes? If I pick that Mercedes, am I going to regret it in thirty seconds when a Rolls rolls past? Am I going to get stuck with an old Hyundai due to my inability to settle?

Wouldn't this be different since we know the maximum number and the distribution?

The solution wouldn't be to still skip 1/e if you got something like googol - 1 on the first try.