Draw the extensive-form diagram of the Monty Hall three-door game. In this game, the host (player 1) privately selects an envelope in which to put the prize money (A, B or C). The contestant (player 2) does not observe the host's choice but then must select an envelope. The host must open one of the envelopes that the contestant did not select, but the host is not allowed to open the envelop containing the prize. Finally, the contestant chooses whether to stay with his/her originally selected envelope or switch to the other unopened one. If the contestant's envelope contains the prize then he/she wins the money. Otherwise, the money goes back to the host.