Probability question: names in hats

[robvalue]

I have not, but I'm extremely confident in my calculations.

This isn't like a normal puzzle where you have branches or probability spaces that all have the same probability. So just counting up ways it can happen doesn't work, like for example counting the ways you can get a total of 8 on two dice.

If experiment contradicts the theory, I shall be interested and most surprised! It would cause me major concern over my mathematical abilities, if I've got this 3 person example wrong. In fact, I think actually doing the puzzle as an experiment would help you see exactly why it's 1/4. (Unless I've made some catastrophic error. Of course, that's always possible.)

I tell you what, I was going to code the 10 man puzzle anyway. So I'll code the 3 man one as well and get some data that way.

EDIT: I just realized another one I could explain it. I'm going to draw another diagram.