lottery numbers in parallel universes

Question

i have a question about how randomly generated lottery tickets. recently a woman won the lottery with a random ticket. it turns out that someone let her cut in line ahead of her and this second person was ALSO planning to get or did get a randomly generated lottery ticket. so here is my question had that person NOT let the winner cut in line would they have gotten the winning ticket number or is more likely a different random number would have been generated? it is MY opinion that unless the clerk had hit the random key at the exact same time it is highly unlikely that the winning ticket would have been generated in the theoretical "WHAT IF" universe. i hope i have made my question plain...

Answer 1

Unless the function that generates the lottery numbers is dependent on time, I don't think much can be said about what would have happened. Perhaps some multiverse theorist would claim that every possible outcome happened in a set of every imaginable parallel universes.

Answer 2

Let's do a thought experiment. Call the woman person X and the other guy person Y. Suppose whether or not person X won were not determined by a random number generator but instead by an ideal coin flip (wishful thinking, eh? :)

You probably had it drilled into you at school that the coin has no memory of what it turned up before and doesn't care who or what it's flipping for (the so-called "gambler's fallacy"). Therefore, the probability of person X winning given she flips first is exactly the same as the probability of person Y winning given that he flips first, is exactly the same for that matter as the probability of person X winning if she flips second, etc.

You will notice above I assumed the coin flip was not determined by initial conditions such as the air circulation in the room, the unique weighting of the coin, etc., which would have been the same in theory whether person X or person Y had been flipping (hence "ideal"). If it did, it could very well be that the conditions were "just right" at that moment for whoever happened to be flipping the coin to win, and so person Y would have won had he not let person X cut in line and gone first himself.

Now what are the implications for your problem? If the random number generator was a true random number generator (="ideal coin"), then no, it doesn't make a difference who went first.

However in reality the vast majority of computerized random number generators are not really random, more likely pseudorandom, depending by a convoluted yet deterministic relationship on various input conditions. A common input condition is - you guessed it - time, because the programmer can more or less exploit the randomness inherent in when an event occurs (as measured in milliseconds) to be lazy and not have to bother with something like turning static into numbers to be truly random. I would be very surprised if whoever ran the lottery bothered to install a true random number generator in the randomizer for lottery ticket numbers.

So, if the (pseudo)random number generator depended only on time, and the clerk hit the random key at exactly the same moment, the answer is, yes, had that unlucky soul not been courteous enough to let a lady cut in front of him in the queue, he might have won. It just goes to show that nice guys finish last :)

(But you could also say there was an equal probability that the next random number would have been the winner, in which case it he would win if he let someone in front of him. So you're at Nash equilibrium ;)