The number of times you have to roll a set of 3 die to see a 6 on each die appears to be around ~10.555 according to a implementation of this in c++ and c#. How would this be statistically proven as instinct would suggest it should be 6 ?
Each die has 6 sides that are evenly distributed. All three die are thrown at the same time counting as one roll. Once all three die have displayed 6 at least once you can stop.
What I am looking for is the statistical proof that you are required on average to roll the set 10.555 times to have seen 6 on each of the 3 die at least once.