Otherwise roll again, this time you succeed if you roll a 1 or a 2.
Otherwise roll again, this time you succeed if you roll a 1, 2 or 3.
Otherwise continue the pattern until you eventually win.
Let x = number of tries to success. What is the expected value of x?
Extend to an n-sided die and give a formula for E(n,x).
For any value of n there is a maximum k such that P(x≤k)≤1/2. Find a formula for this k in terms of n.
This might make an interesting casino game but I've never seen it before.