Choose a positive integer.

The winner will be the person who chooses the least positive integer not chosen by anyone else.

Note that all entries will be divided into groups of 100 players. This may (in fact, it should) affect your strategy.

For example, if ten people chose the numbers {2, 2, 2, 3, 3, 4, 5, 5, 7, 9}, then the person who chose 4 would win -- it was the least positive integer chosen by only one person. Although 2 was the least positive integer chosen, it was chosen by three people. Likewise, the number 3 was chosen by two people, so they wouldn't win, either.

[Update] This game was originally run for one week, Nov 28 - Dec 5, 2011. The results of that initial trial (based on 1,042 entries) are available at the link given below. That said, I see no reason to prevent others from participating and, from time to time, I will update the results page to reflect new data.

http://mathjokes4mathyfolks.wordpress.com/2011/12/05/results-for-my-favorite-game/