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All of it!WWGD said:@PeroK : What part are you skeptical about?

How is this a "sure" way, given that your attempt just gets immediately bogged down?WWGD said:There's always the non-elegant-but-sure way:

How are you going to calculate ##P_n##?WWGD said:1)It can be done after n throws, with probability $$P_n$$ with expected value $$ \Sigma n*P_n $$

Given the expected value is ##18## throws, how can the probability become negligible after ##15## throws?WWGD said:. It may get somewhat messy, but after 15 or so throws, $$ n*P_n $$ is small-enough that you can ignore it.

"Some sort of recursion". Easy to say, but where's the attempted calculation?WWGD said:And it seems some sort of recursion would help compute $$P_n$$.

Calculating ##P_n = \frac 1 {16}## is something we can all see. It's trying to progress that method that's the problem.WWGD said:For $$n=4$$, the expected value contribution is :$$ 4*2^{-4}$$; for $$n=5: 5*2^{-5}$$. Then it becomes a bit more complicated, since you need to exclude the substring HHT at the beginning.

It seems to me that you've been unable to make any progress with this "sure" method of calculation.