How many rolls of a single die gives you an even chance of rolling, say, a six? Does this problem, as stated, even have a unique answer? Three rolls gives you a less than even chance, while four rolls gives a greater than even chance. It is tempting to solve (5/6)^x = .5 and get x = ln 2 / ln (6/5) ~ 3.8 But since the rule that the probability of several independent events is just the product of their individual probabilities only applies for an integral number of events, this answer isn't really justified. All it tells you is that the answer, if there is one, is between 3 and 4.