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 expected value of any roll of a fair die is the sum of the possible rolls divided by the number of sides, thus an $m$-sided die would have an expected value of $\frac{\frac{m(m+1)}{2}}{m}=\frac{m+1}{2}$ for each roll. From there is should be simple to calculate the expected number of rolls to reach any value.
