The shooting-room paradox was introduced by John Leslie (e.g. , pp. 251ff), who says he developed the idea with help from David Lewis, who considers it "a good, hard paradox".
In the shooting room experiment we are to imagine a room of infinite capacity. First a batch of ten people are led into this room. A pair of dice is thrown in front of their eyes. If a double six comes up they are all shot. Otherwise they leave the room safely and a new batch, this one containing a hundred people, is thrust in. The process continues, with each consecutive batch ten times larger than the previous one, until there is a double six; whereupon the people in the room at that time are shot and the experiment ends.
Suppose you have been thrust into the room. You are asked to estimate the odds of leaving safely. One the one hand, since whether you will leave or not will be determined by the throw of a fair pair of dice, it seems that you have a 35/36 chance of exiting alive. On the other hand, 90% of all people who are in your situation will be shot, so it seems you have only a 10% chance of exiting alive. That is the paradox.