What is the expected number of times 3 consecutive heads or tails will appear when flipping a coin 1000 times?

Question

If I take a coin and flip it 1000 times, what is the expected number of times I see a series of three heads or three tails in a row appear?

So for example the results: hhtttthhh contains 2 series of tails in a row (which overlap on the four tails) as well as one series of three heads in a row.

Answer 1

After any flip, the probability that the next two flips are the same is $\frac{1}{4}$. Since $998$ flips are possible starts, the expectation is $\frac{998}{4}=249.5$.