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I was reminded of this counting rhyme the other day when it popped up in a book that I was reading. The protagonist used it to decide which one of the three canned dinners to eat. It seems a reasonable way of choosing among three or more equally attractive, or repugnant, choices. For two choices a simple coin flip would do. And yet, there is nothing random about the outcome of a counting rhyme. It is completely determined by the choice of the first item we count. Because the counting goes on for a while, we get a perception of randomness, and it seems like it's the chance that governs it. It probably has to do with our innate psychological perceptions and our ability to hold only about seven items in our short-term memory. It is doubtful that counting rhymes that are shorter than seven words would ever be popular.

It is quite reasonable to imagine, that many events in our lives that require holding eight or more facts at the same time in our mind, would appear equally random. It would be a fallacy to assume randomness of events only based on our limited perception capacity.