Monty Hall With A Twist
On a game show, there is a popular game that is always carried out in the same way. A contestant is given the choice of three doors: Behind one door is a car; behind the others, goats. The contestant picks a door, say number 1, and the host, who knows what's behind the doors, always opens another door, say number 3, to reveal a goat. Then, the contestant is given the option to change his original door selection to the other unopened door, in this case door number 2.
A long term fan of the game show has noticed a hint or “tell” in the staging or presentation by the game show host in this game.This fan can consistently guess the door with the car behind 50% of the time, before any door selection is made.
This fan was selected as a contestant for the game. Using the best possible strategy what is the probability (as a percentage) that this fan will end up with the car prize?