It's been a busy day.
So, just for now, here's a very abstract experiment (and I'll give you the kit to play with the experiment)
Imagine you've got a hundred bowls in front of you.
In each bowl, you've put a hundred pennies – 99 dull ones, and one magic one.
Every day, you get to look at one random penny from each bowl. You drop the penny back in its bowl when you've looked.
If you had a hundred days, how many magic pennies might you see?
If you wanted to see all the magic pennies, how long would you plan to spend to be reasonably confident? How confident is reasonably?
If you want to work this out, do. You could find out empirically and viscerally, too, but you don't necessarily need a hundred quid in coppers and a couple of seasons: Play with the thing below. There are a hundred purple circles, that go yellow with a chance of 1:100 every tick of the red number. You can change the red number before you start. Press the arrow in the circle to set things going. Treat "work done" as "days spent" for now – no one thinks finding magic pennies is a real job.