I am not a professor, and I don't know how old the princess will be when she is twice as old as the prince was when he was half their combined age, but I think the Bernoulli trial probability math gets pretty simple for the case of a single repeated outcome. If you have a random 50% chance to hit each time, then I believe the probability of missing 14 times in a row is (0.5)¹⁴ = 6.1 × 10⁻⁵, which I interpret as not something you should not expect to see very often, even after thousands of hours of play.

Last edited by Argyle; 19/10/20 12:34 AM. Reason: ha ha, forgot the word "not"!