The Monty Hall Puzzle

[MilDoc]

Yep, made no sense to me either first time I heard it years ago. But switching is right every time.

[LCHIEN]

The key is the way the problem is stated.
I originally assumed that if you picked the right door the first time you won right away. The wikipedia explanation is that the rules must be explained right - even if you pick the winning door the first time Monty is required to show you a door with a goat/lump of coal.

This wiki diagram showed me why:
1.
Host reveals
either goat
Player picks carSwitching loses.


2.
Host must
reveal Goat B
Player picks Goat ASwitching wins.

3.
Host must
reveal Goat A
Player picks Goat BSwitching wins.



The player has an equal chance of initially selecting the car, Goat A, or Goat B. Switching results in a win 2/3 of the time.