Expected number of rolls A fair m-sided dice is rolled and summed until the sum is at least N. What is the expected number of rolls? In other words what is the number of rolls if we roll a m-sided dice and the sum of rolls become at least N.

The naive answer of $\frac N{m/2}$ misses a couple things.  First, the expected value of a single roll is $\frac {m+1}2$ because we start counting the sides at $1$. For large $N$, the revision to $\frac {2 N}{m+1}$ is correct.  Second, for small $N$ it can't be-certainly for $N=1$ the  expected number of rolls is $1$
