Probability question: names in hats

[robvalue]

The remaining sequences just have to bring the total up to 1, they don't have to all be the same probability. Let's see:

2, 3, 1 = 1/2 * 1/2 * 1 = 1/4

3, 1, 2 = 1/2 * 1 * 1 = 1/2

Note how the second line here happens half the time. If player one takes number 3, the other two picks are forced.

So these are the remaining two legal combinations. Total probability, along with the "winning" one: 1/4 + 1/4 + 1/2 = 1