What's the probability of getting 1000 heads in a row? I'm reading The Master Algorithm by Pedro Domingos and I'm having a hard time understanding something he wrote on page 74:
"If you do a million runs of a thousand coin flips, it's practically certain that at least one run will come up all heads."
My intuition tells me this is false. My understanding of probability would indicate that the chance of encountering $1000$ heads in a row after trying $1000000$ times is:
$$\frac{1}{2^{1000}} *1000000$$ 
which is minuscule and hardly "practically certain." Is my understanding correct, or am I missing something?

For another perspective on why OP's heuristic estimate is so spot-on:
The number of successes on $n = 10^6$ trials where the probability of a success is $p = \frac{1}{2^{1000}}$ is well-approximated by a Poisson distribution with parameter $$\lambda = np = \frac{10^6}{2^{1000}}.$$
In a Poisson distribution the probability that there is at least 1 occurrence is $1 - e^{-\lambda}$. But $$1 - e^{-\lambda} \approx \lambda$$ for $\lambda \approx 0$, hence the probability is approximately $\lambda = \frac{10^6}{2^{1000}}$.
