The Monty Hall Problem

This article has been imported from chorus.fm for discussion. All of the forum rules still apply.

Numberphile looks at one of the common game show tropes, The Monty Hall Problem, and explains optimal strategy.

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always switch

 

I'm not feeling the logic.

Doesn't the probability reset each time a door is opened? so start 100 doors. all have 1/100. Open a zonk. Now every door has 1/99 chance.

Fuck, just went ahead and did a visual trial using each combination of 3 and it was right

 

I found this to be the best explanation:

You start out with two goats and one car.
Monty always eliminates one of the goat doors.
Every time you choose a goat and switch you win the car.
Every time you choose the car and switch you win a goat.
There is a 66.6% chance of choosing a goat on the first pick.
Therefore switching would win you the car 66.6% of the time.

The 100-door example really clinched it for me (regarding why the probability doesn't "reset" after each eliminated door). What are the odds you happened to pick the 1 door out of 100 with the car? Far more likely is the 1 door Monty doesn't eliminate.

 

This was such a fun watch. I feel like I don't use youtube properly. I watch such trash anytime I'm on there.

 

Wow, super interesting. Never thought about this before.

 

I'm not sure how one would use YouTube properly but I'm sure a high percentage just goes on loops for videos about nothing.