# One out of three? [duplicate]

You are coming to the climax of a very mischievous game show, the curtain opens and you are presented with three doors, behind each door there is a prize of varying qualities. Behind one door, there is a brand new sports car valued at over a million dollars, behind the second door, there stands a goat and behind the third door, there is another goat. The score stands at: one door has a sports car and the other two have goats. You randomly pick a door. The host then announces that he will now show you where ONE of the goats is.. he does so leaving the third door closed, he then gives you the option of switching your unopened door with the closed third one or just opening the door you chose first.

What is the best choice to make and why?

• Please explain the odds of winning for both decisions. – Xcoder555 Mar 7 '16 at 17:20
• Oops, I didn't realize that that was such a popular puzzle :( – Xcoder555 Mar 7 '16 at 17:25
• Yah. It's been in a handful of movies and also very famous statistics problem elsewhere. An identical wording can be found in the movie 21. ;) – Z. Dailey Mar 7 '16 at 17:28
• Most classes that cover game theory at all start with this problem. Partly because it is a fun problem. :) – Parthian Shot Mar 7 '16 at 17:52