3 ms·
No, that's a common myth that a random sequence will eventually see every possible subsequence. Easy to construct a sequence of just 1 and 0 thats infinite and
by deepsun 6mo ago
No, that's a common myth that a random sequence will eventually see every possible subsequence.
Easy to construct a sequence of just 1 and 0 thats infinite and not repeating, without having a single 2 nor 3.
- hollowcelery 6mo agoBut that’s not what’s happening here - the model here is that every piece has a uniform probability of being selected next, in which case every possible subsequence appears in the limit.
- layer8 6mo agoWhile a sequence where one possible subsequence never appears has probability zero in the limit, it’s still a possible random outcome. Incidentally, every concrete infinite sequence has probability zero.
- deepsun 6mo agoYes, but "in limit" does not mean "will happen". E.g. it might be that there will never be "I" piece at all, even for infinite random sequence. Yes, probability of that happening is exactly zero, but that might happen. For example, if we select at random any number between 0.0 and 1.0 -- probability of selecting it is exactly zero. But we still selected it.