Updated my dice problem collection. The new problem is problem 40: A die is rolled and summed repeatedly until the sum is 100 or more. What is the most likely last roll? What if we roll two dice at time? Three, etc.?
If one die is rolled, then 6 is the most likely last roll, while 7 is the most likely last roll when two dice are rolled. With three dice, the most likely last roll is 12, but for more dice, a very clear pattern emerges: if the number of dice rolled is odd, then the most likely last roll is the most likely roll (greater than the median), while for an even number of dice, it is one more than the most likely roll. (Here we assume a sufficiently large value for "100": for large numbers of dice, we want to extend the threshold so the analysis is smoother.)