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As I'm trying (unsuccessfully) to explain, this has nothing to do with probability. You just crank out the first 1000 digits, and inspect them for the sequences you're interested in. The digits are deterministic. If you run this experiment a million times it will come out exactly the same every time.

It's like saying, if if put the number 5 into the function f(x) = x^2, what's the probability that the answer is 12? You can't say that "all answers are equally likely" just because you haven't actually calculated the result. The answer is deterministic. It's 25, with probability 1.

It makes sense to ask what is the probability of a given sequence appearing in 1000 random digits. But it does not make sense to ask what is the probability of a given sequence appearing in the first 1000 digits of, say, 2^2^10. You just calculate it out. The sequence is either there or not. There's no concept of probability because there's no random event.

I understand what you're saying, and I'm sure everybody here does. I simply don't care to word it differently because everybody here understands what I mean.