General Discussion

Last edited Fri Jan 19, 2018, 06:58 PM - Edit history (2)

And the 'right answer' depends on Monty's motivation(s) (i.e. does he always want you to lose) and whether or not it's entirely his 'choice' to allow you to choose the other door, or if he must do so every time, no matter what.

EDITED to remove some confusing stuff and elaborate:
(As long as he must always conduct the game pursuant to these rules, then the correct answer is ... SWITCH. You're twice as likely to get the car.

If, however, he has the CHOICE of either exposing the first goat and/or letting you choose the other door after showing you the goat ... or NOT ... then his motivations come into play, and the odds (and correct answer) change entirely.

Note that the original problem does NOT state the critical assumption(s) that he MUST have no choice but to conduct the game in this way ... in order for the 33(stay)/66(switch) condition to be 'created'.
)

It is an interesting problem though (esp. for one so basic) and it literally has been debated TO DEATH over the years. Some folks can't wrap their head around the reason why the odds work out the way they do and argue til blue that the 'correct answer' cannot BE ... correct ... even though it is, which is also kinda interesting.