I have a question that I can't quite categorize, which is why I'm putting it in the General Math section, and even the question title doesn't do a very good job of describing it. So here goes: We have a game involving a group of N people seated in a circle. Each person has their own "magic number" K, which is some natural number that's unique to them. The game starts with the first person saying the number "1", the second person saying the number "2", etc. all the way around the circle, and we just keep going around the circle again and again counting higher and higher. There isn't any activity in the game other than people saying numbers. The game continues for a total of M moves, where M is a number that none of the players know in advance, and then it ends (it's like musical chairs, where people keep moving around until the music abruptly stops). Finally, at the end the winners and losers are determined at follows: if you ever said a number that was higher than your magic number, you lose. Otherwise, you win. So to sum up, you know your magic number K and the number of people playing N. The only thing you have control over is where to sit, i.e. do you want to be the first player, the second player, etc. Also, although you don't know in advance exactly what the total number of moves M is going to be, you do know some rough information about it, perhaps a probability distribution, or the likely confidence interval that M/N is within. So given this, how do you choose where to sit in order to maximize your probability of being a winner? I apologize if this question is vague or convoluted. As I said, I don't really know what subject of mathematics this falls under, but although it's fairly abstract, it's a problem that's inspired by various real-life situations I've encountered. I'm happy to clarify anything that's confusing in my description. Any help would be greatly appreciated. Thank You in Advance.