Education

[ysabetwordsmith]

The Monty Hall Problem: Why Switching Doors Wins 2/3 of the Time

The host does not open a door uniformly at random. The host opens a door that he knows hides a goat, and he never opens the door you initially selected. These constraints are not incidental — they are the entire source of information in the problem. The host's action is not a random event that preserves symmetry between the remaining doors. It is a deliberate, knowledge-guided action that breaks that symmetry in a precise and quantifiable way.


I've heard the claim before, but this explanation of how it works is the best I've seen.

Comments

[erulisse]

well that's fascinating! Applied mathematics for the win.

[ionelv]

Your link is broken as that blog got suspended already. I like the wikipedia entry on this problem, and especially this explanation:

When the player first makes their choice, there is a ⁠2/3⁠ chance that the car is behind one of the doors not chosen. This probability does not change after the host reveals a goat behind one of the unchosen doors. When the host provides information about the two unchosen doors (revealing that one of them does not have the car behind it), the ⁠2/3⁠ chance of the car being behind one of the unchosen doors rests on the unchosen and unrevealed door, as opposed to the ⁠1/3⁠ chance of the car being behind the door the contestant chose initially.

Thoughts

[ysabetwordsmith]

Try it again, I linked to an archived version.