(March 14, 2016 at 11:12 am)robvalue Wrote: For 3 players, it's very simple. The only way to achieve is picking 2, 1, 3.
Probability = 1/2 * 1/2 = 1/4
For 4 players:
2, 3, 1, 4 = 1/3 * 1/3 * 1/2 = 1/18
or
3, 1, 2, 4 = 1/3 * 1/2 * 1/2 = 1/12
Total = 5/36
As you can see, the two probability lines for 4 players aren't equal like they often are in probability questions, due to the fact that player 2 sometimes has more names to choose from.
Imagine how screwed up that gets analyzing the possibilities for 10 players.
Yikes, my results don't agree with yours for either 3 people or 4. I believe there are only three combinations in which the first two people keep a name other than their own and only one of these has the last guy getting his own name. P = 1/3. Right?