# Streak!

Fascinated by the beauty of randomness, a Kaboobly Dooist asks the craftsmen to paint a linear wall consisting of $$2^{16}$$ stones in the following way:

For each stone: Flip a coin; If the toss results heads, paint the stone white; If the toss results tails, paint the stone black.

What is the expected longest contiguous streak consisting of consecutive black stones?

If the answer is $$n$$, enter your answer as $$\lfloor n \rfloor$$.

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