"Who's Taller" game with random variables I have an exercise that I cant get my head around. 
You play the game of who's taller" in class (of n people). You pick always a random
opponent among the people you haven't yet played, compare your heights, and the taller
person wins (height are never exactly the same). You continue until your first loss or until you beat everyone. By the time you are finished, you won X games. What is the mass
function of X, so what is P(X=i) for i = 0, 1, 2,..., n-1
Hint: Solve it for small class sizes first. Don't assume anything about your or other people's heights.
The thing is, it seems too simple if I solve for small classes - like size 2 or 3. I always get P(X=i) = 1/n

If you are yourself chosen uniformly randomly from the class (a feature which we will assume but that you do not explain), $[X\geqslant i]$ means that you are the tallest person from a uniform sample of size $i+1$ (you and your $i$ first "opponents"). By symmetry the probability of that event is $1/(i+1)$ hence $P(X\geqslant i)=1/(i+1)$ for every $0\leqslant i\leqslant n$. 
Surely you can deduce $P(X=i)$ from these considerations?
