Parlour Games

Baston and Bostock [11] considered the following zero-sum game. There are two players, say 1 and 2. Two numbers are chosen from [0, 1] independently by means of uniform distributions. Player 1 looks at the numbers privately, chooses one of the two and opens it to his opponent. Player 2 then accepts either the opened number or the covered (unopened) one, and receives from player 1 his accepted number. Baston and Bostock showed that the optimal strategy of player 1 is to choose the nearest to 1/2 number and open it, the optimal strategy of player 2 is to accept the opened number if and only if it is at least 1/2. The value of the game is 7/12 which is greater than 1/2.