if p is the X-risk in a year, then: (1-p)^100 = 1- 1/6 = 5/6 i.e. p=1-(5/6)^(1/100) = 0.00182 And expected years left = 1/0.00182 = 548.98 I think your formula should be: century_to_year(x) = 1-(1 - x) ^ (1/100) - Ismam