Do these things affect the probability of this outcome?

[BezoomnyBratchny]

This is an app called Cube Timer. It generates random (for simplicity's sake, we can just pretend that it is truly random) scrambles for Rubik's cubes. The strange looking strings of numbers, letters and apostrophes are sets of 19 moves to perform on a solved Rubik's cube to give it a completely unique scramble for a person to solve the cube again and repeat. I had a freak occurrence happen to me where I was randomly given a particular scramble by the app and then a month later, was randomly given the same scramble. There are 12 possible different moves that it can generate and it generates them as a set of 19 consecutive moves. It is also written into the app to not repeat the same move twice in a row so each move from the second one onwards has 10 possibilities (the 12 moves are 90 degree and 180 degree turns of each of the 6 sides so each move eliminates 2 possible moves from the move that comes after it). I know how to calculate the probability of me getting two of the same scramble. But if I knew (or could reasonably estimate) how many total users of this app that there were and how many solves each of these other users have performed on the app, I'm wondering if that will affect the likelihood of this freak occurrence happening somewhere to someone on the app. I have a suspicion that the probabilities are isolated from one another from user to user because of both scrambles needing to come about from the same user but I'm not sure.

 

[pbuk]

But if I knew (or could reasonably estimate) how many total users of this app that there were and how many solves each of these other users have performed on the app, I'm wondering if that will affect the likelihood of this freak occurrence happening somewhere to someone on the app. I have a suspicion that the probabilities are isolated from one another from user to user because of both scrambles needing to come about from the same user but I'm not sure.

Yes of course, the probability of anyone getting the same scramble twice is much greater than the probability of you getting the same scramble twice. But with c.10¹⁹ scrambles, that probability is still vanishingly small. There must be something else going on.

 

[FactChecker]

Although the probabilities are difficult to figure, you are correct to be extremely skeptical that those results were random. A pseudorandom number generator is started with a seed that will give the same initial result every time. I would be suspicious that the program was restarted just before both of those results and the initial seed was not changed. Actually, if you got both results at exactly the same call number after two resets, your results would be identical. I don't know what the odds of that are. It depends on how often they reset their program.