# Two "Heads" are better than one

Probability Level 4

I toss a fair coin 100 times in a row. If the expected number of times that two Heads are tossed consecutively is equal to $N$, what is the value of $100N$?

Clarification: A run of three or more Heads in a row will contribute more than one instance of consecutive Heads. If three Heads are tossed in a row, then two Heads have been tossed consecutively twice. If six Heads are tossed in a row, then two Heads have been tossed consecutively five times, and so on. For example, two Heads have been tossed consecutively 11 times in the following sequence of 30 tosses:

$THHTHHHHTHHHTHTHHHHHTTTTHHTHTT$

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