## Odd man out

As usual, you’re a derainged jailer who is going to play an awful game with your prisoners.

You have 600 prisoners and you line them up in a row. Each prisoner has a position in the line, starting with 1. Here’s where the “fun” starts.

You pick a prisoner, at random, who is in an *odd* position, they’re out (you know what that means). Everyone behind them in line, shifts down. So, for example, if the prisoner is position 3 was picked, then the prisoner in position 4 will shift down into position 3, 5 -> 4, 6 -> 5, and so on.

You continue doing this until there is only 1 prisoner left. The last remaining prisoner gets to go free.

Here’s the question: *which starting position is best?* As in, if you wanted to maximize your chance of winning this game, what position would you like to start in when there are still 600 prisoners?