Lottery fairness problem I'm wondering if this scheme is fair or not. I'm not an expert in math so I have no clue. When lottery room starts the winning number is set by random integer between 0-999. Every player enters the lottery also given random integer between 0-999, there is no duplicate. After lottery ends the payer closest to the winning number is the winner.
For example:
Winning number is 500
Player 1: assigned random number 123
Player 2: assigned random number 789
Player 3: assigned random number 456
So the winner is Player 3.

Is there any problem with this, can I call it fair? In my opinion it seems fair because everything is random, but then again there is something that disapproves its fairness.
Thank you.
 A: Assuming the numbers are picked fairly, it is fine. One way to make it appear more fair is to make the distance cyclic, so that $999$ is distance $1$ from $0,$ $300$ is distance $400$ from $900.$ But that is just appearance - each person is just as likely to win the lottery as anybody else in the original scheme, as long as all choices of numbers are uniform.
The appearance of unfairness assumes the process goes like this: each person is assigned a random number known only to himself. Then the winning number is revealed.
A person who gets $999$ or $0$ as a number knows that his only chance of winning are the numbers less than halfway to the nearest other number to one side, while a person who gets $500$ knows that she can win on one side or the other. So at this point, to the guy with $999,$ it doesn’t look fair.
And, indeed, this guy now has a lower probability of winning that the woman with $500.$ But this process is still fair because the draw of $999$ was fair - the man who got it could have gotten $500.$ So, right now he has a lower chance of winning, but before he got his number, he was just as likely as anybody else to be assigned $500.$
The “cyclic distance” approach alters that perception of fairness, because, after being assigned a number, not knowing anybody else’s number or the winning number, a person knows his estimate of his odds are the same as anybody else’s.
However, the cyclic distance is unnecessary if, while entering, before getting their draw, the man is told “the winner will be the closest to $326.$” Now, the man perceives his draw as the actual random process of the lottery, and when he gets $999,$ he knows he lost on that draw.
