You’re about to play a game. A single person enters a room and two dice are rolled. If the result is double sixes, he is shot. Otherwise he leaves the room and nine new players enter. Again the dice are rolled, and if the result is double sixes, all nine are shot. If not, they leave and 90 new players enter.
And so on, the number of players increasing tenfold with each round. The game continues until double sixes are rolled and a group is executed, which is certain to happen eventually. The room is infinitely large, and there’s an infinite supply of players.
If you’re selected to enter the room, how worried should you be? Not particularly: Your chance of dying is only 1 in 36.
Later your mother learns that you entered the room. How worried should she be? Extremely: About 90 percent of the people who played this game were shot.
What does your mother know that you don’t? Or vice versa?
(Paul Bartha and Christopher Hitchcock, “The Shooting Room Paradox and Conditionalizing on Measurably Challenged Sets,” Synthese, March 1999)