There is an important nuance that makes it ~n+4/5 for large n (instead of n+1), but I’d have to think a bit to remember what it was and give a nice little explanation. If you can decipher this comment thread, it’s somewhat explained there: https://old.reddit.com/r/mathriddles/comments/17kuong/you_roll_a_die_until_you_get_n_1s_in_a_row/k7edj6l/
I thought of the reason independently: it’s that if the number before 66 is not odd, but even instead, it must be either 2 or 4, since if it was 6 then the sequence would have had a double 6 one digit earlier.
There is an important nuance that makes it ~n+4/5 for large n (instead of n+1), but I’d have to think a bit to remember what it was and give a nice little explanation. If you can decipher this comment thread, it’s somewhat explained there: https://old.reddit.com/r/mathriddles/comments/17kuong/you_roll_a_die_until_you_get_n_1s_in_a_row/k7edj6l/
I thought of the reason independently: it’s that if the number before 66 is not odd, but even instead, it must be either 2 or 4, since if it was 6 then the sequence would have had a double 6 one digit earlier.