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So if you start with the ring gaps staggered, and they rotate randomly, what is the statistical chance that they will at some point align on their own? I'm befuddled by that question.
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Conditions on initial startup after a rebuild are not normal. If the rings are lined up, due to blow by effects, there is a higher statistical probability of the rings not starting to rotate/shift randomly. Failure of the rings to move will cause excessive wear. During normal operation, there are many times when the rings happen to be lined up. You just don't want that condition the first time a new engine is started, it's asking for trouble.
If you guys are really curious and don't mind reading through a technical paper, here is a published study of piston ring rotation using an embedded gamma ray source on a piston ring.
http://article.nuclear.or.kr/jknsfil...4803285773.pdf
Bruce