A prison has 100 prisoners, and the sadistic warden has decided that tonight, all the prisoners will be set free or die. In order to toy with them, the warden decides that they will determine their own fate. In a separate room, he will write down each prisoner's name and put it in a box at random. One by one, the prisoners will enter the room and open 50 boxes each. If every prisoner opens the box with his own name, the prisoners all live. If any prisoner fails to find his name, all the prisoners will die. The prisoners can decide on a strategy beforehand, but they cannot confer once the first prisoner has begun opening boxes. What should the prisoners' strategy be to maximize their chance of seeing another dawn?
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