While every outcome is equally likely, one can say that, a-priori, the odds of an easily described outcome is small. This is formalized in Algorithmic Information Theory [1] [2].
For instance, when flipping a coin 100 times, the odds of the outcome being describable by a 40-bit program in a predetermined language are only 1 in 2^60.
Yes, good point. It's also formalized in basic probability theory. The set of number sequences a human would find interesting or surprising is smaller than the set of all number sequences. If all number sequences are equally likely, by the third axiom of probability you're more likely to draw an uninteresting number sequence than an interesting number sequence.
However that does change the problem statement; we do still expect "123456" to occur equally as often as any other sequence, interesting or not.
For instance, when flipping a coin 100 times, the odds of the outcome being describable by a 40-bit program in a predetermined language are only 1 in 2^60.
[1] https://en.wikipedia.org/wiki/Algorithmic_information_theory
[2] https://en.wikipedia.org/wiki/Algorithmically_random_sequenc...