[gpvos]

If you randomize a list of numbers there will always be cycles like described (similar to how there will always be cycles if you would draw lots for Secret Santa and then reveal who drew who), and these cycles have a certain length. It might be one cycle of length 100, but more commonly there will be lots of shorter cycles. If you start with your own number, you are guaranteed to be in a cycle that will return back to you, you just don't know how long that cycle will be (could be 1, could be 100, more likely something between). And apparently you can calculate that in ~31% of cases all cycles will have a length of 50 or less. This is just a neat way to exploit a kind of structure that there always will be within the randomness.