The point is the pattern with a lot of information is by its very nature unlikely to occur. In fact what it means to be informative is that it’s unlikely.
Her 1925 essay, “Mathematics and Eternity,” is a remarkable document of an intellectual world in which faith and science each felt some need to justify themselves to the other. “We can practice the presence of God in an algebra class,” she writes, “better than in Brother Lawrence’s Kitchen; and in the utter loneliness of an unfashionable corner of research work, better than on a mountain top.” Every mathematician, religious or not, will understand what she means in this should-be-famous epigram:
[T]he thoughts of pure mathematics are true, not approximate or doubtful; they may not be the most interesting or important of God’s thoughts, but they are the only ones that we know exactly.
From this 3Blue1Brown video:
A girl thinks of a number which is 1, 2, or 3, and a boy then gets to ask just one question about the number. The girl can only answer “Yes“, “No“, or “I don’t know,” and after the girl answers it, he knows what the number is. What is the question?
Answer(s) at StackTrace