It is confusing (and I am still confused) because my understanding is: 1. Person A picks 2 random #s 2. Person B picks a random split #. 3. Person B looks at o

It is confusing (and I am still confused) because my understanding is: 1. Person A picks 2 random #s 2. Person B picks a random split #. 3. Person B looks at one of the random #s. Based on its relationship to the arbitrary split # he choose, he then decides it the other random # is larger or smaller than the one he has in hand. I am confused as to how choosing a random split # has any impact on the probability of the other paper in hand. I'd normally think that each random # choice is an independent event and that my "split #" has no impact on the system as a whole. Like, you choose the numbers -500 and 250. I choose to split at 1000. Or 200. Or ten billion. Obviously the math works, but why does my picking another random # make a difference in the system as a whole? The relationship of all the #s to each other is still presumably completely random. Would this work if I am instead handed two numbers, and I have to guess if a third # is greater than the first number, and I make a choice based on the relationship of the 1st number to the 2nd number? Since the 2nd number is random, it shouldn't matter who provides it, right? So stating it that way, "Here is 200, 750, and some third number, is the third number higher or lower than 200?" Does that still work?