I was asked by someone to clarify / improve the Goat hall problem questions: * If the contestant always switches, what is the probability of them winning the car and what is the average number of goat bleats? * If the contestant never switches, what is the probability of them winning the car and what is the average number of goat bleats? chongo (Landon Curt Noll) /\oo/\ =-= On 2009-Nov-11, at 17:42, Landon Curt Noll wrote:
The contestant finds themselves in a Goat Hall game containing:
host: a goat
3 doors hiding: 2 cardboard cutouts of Monty Hall and a car
The contestant selects a door at random, the goat bleats once and another door showing a cardboard cutout of Monty Hall is revealed. The contestant either keeps their original door or switches to the other unopened door. When their final choice door is opened:
* If the door reveals the car: the contestant wins the car and the game stops
* If the door reveals a cardboard cutout of Monty Hall: then one of 3 things happen with equal probability:
1) The contestant wins the zonk prize, a cardboard cutout of Monty Hall, and the game stops
2) The contestant begins playing a classic Monty Hall game containing:
host: Monty Hall
3 doors hiding: 2 goats and a car prize
NOTE: This game works in the standard way: The contestant picks a door and Monty opens a different door showing a goat. They may keep their original door or switch to the other unopened door. If their final choice door reveals the car, then they win the car and the game stops. If their final choice reveals a goat, then the goat bleats once, they win the goat and the game stops.
3) The contestant is teleported to another Goat Hall game containing:
host: a goat
3 doors hiding: 2 cardboard cutouts of Monty Hall and a car
NOTE: This game runs under the same Goat Hall rules as previously indicated.