I have a problem that can be simplified as follows:
Imagine a game where every person has either a red or green jersey with a number from 1 to 10,000 randomly printed on it. It's possible for any given number to be used 0 - n times.
The object of the game is to find a player with the closest number to your own but with opposite color (ex: you have green 4017 so ideal match would be red 4017). When two people have agreed to match, they remove themselves from the game but others keep playing. After a given time, the game is called over and players win cash prizes according to how close their numbers are (details not relevant)
Let's assume this game has already started and I need to pick one of 100 arenas given that they vary in number of players. How would I decide given that the only information I have is:
-My own number and color
-The quantity of players in each arena who have red shirts
-The quantity of players in each arena who have green shirts
For example, if I have a red shirt should I prefer...
-an arena with 50 green shirts and only 10 other red shirts OR
-an arena with 1,000,000 green shirts and 1,000,000 red shirts
I'm not sure how to quantify/rank the options. I'm trying to come up with some kind of expected value calculation that takes into account number of players with each color.
I've taken some basic stats/probability classes but that was years ago so appreciate any help/explanations here. Hoping there's a simple way to model this.