Prisoners’ Escape

Here’s an interesting puzzle for you.

One hundred prisoners are kept in a prison (obviously!). One day the prison warder comes by and tells them that they have a chance to escape. The downside is, that if they fail to escape, they will all be executed. In order to facilitate this escape, they are given a number from 1 to 100. In a sealed and windowless room there are 100 numbered lockers, each with a number inside it on a piece of paper (not corresponding to the number on the locker, necessarily). The prisoners are to enter the room, one at a time, and open up to 50 lockers (in any order). If they find their own numbered piece of paper, they take it and stop opening lockers. Every time they don’t find their piece of paper, they replace the one they found and close the locker door again, leaving it exactly as it was. If all 100 prisoners find their own, numbered piece of paper, then they can all go free. If just one of them fails to find it, however, they will all be executed. Once the process starts, they aren’t allowed to communicate in any way, but beforehand they can decide on a strategy.

What should their strategy be?

Surprisingly, if they pick the right strategy, their collective chance of survival is around 30%.

Hint in a few weeks.