So I read some of the Kokoro Connect manga, and naturally, being a math guy, I got to wondering about whatever algorithm determines the swaps. Yeah, it says "random," but there's random and there's random. There are 119 ways for them to be out of order. 10 of those involve switching two people, 20 involve rotating three, 15 have two pairs, 30 rotate four, and 44 switch all five (24 full rotations, 20 three-and-two combos). Uh... yeah, that adds up. Most of the swaps I've seen were two people, so there has to be a probability bias toward that. Maybe it chooses a single swap randomly, then has a 50% chance of "layering" another swap on top of it? And maybe it keeps flipping the coin until it gets a negative answer.

I don't even know what the probability distributions for time-of-swap and duration would be.