A Strange Game
Suppose that you go into an alien casino on the planet Zreebnorf, and you are offered to play a game. It works like this. The casino will match you with another player at random. The players don’t know who they are playing with, so there is no way for them to coordinate their actions or reciprocate after the game. Both players secretly pick a number between 1 and 100. The outcome of the game is then calculated as follows. If both players picked the same number, let X be the number they picked. Both players will receive X credits from the house and have to pay (100 − X) credits to the house. If the players picked different numbers, let X be the smaller number. The player who chose X will receive (X + 2) credits, and the other player will pay (100 − X) credits to the house. (Credits are standard Galactic currency worth approximately $1 USD each.) Some examples: Both players pick 50. They both pay 50 credits and receive 50 credits, for a net payout of 0. Both players pick 100. ...