Three Curtains

[posthuman]

You are a contestant on a game show. There are three curtains. Behind one of the curtains is a new car. You are asked to choose one of the curtains. Lets say that you choose curtain #1. The host of the show - who knows where the car is so as not to end the game prematurely - opens curtain #3 and there is no car behind it. The host now gives you a choice. You can stay with curtain #1 or you can change your choice to curtain #2. The question now is: would it be to your advantage to stay with curtain #1, or would it be to your advantage to change to curtain #2 or would there be no advantage either way?

You have a mathematically greater probability of success if you change your guess to curtain #2 after curtain 3 is revealed to not have the prize.

 

[posthuman]

Those odds go somewhere though. They don't just disappear. Specifically, half the odds go to each of the remaining doors.

Essentially, the odds don't change.
You picked one door with 1/3 chance of success - the doors you didn't pick have 2/3 chance of success.

When one of the other 2 is revealed as not-success, there's still 2/3 chance your first guess was wrong but the alternative has been collapsed to only one other door. That other door has the whole other 2/3 chance now.

 

[posthuman]

Not at all. When the host opens #3, it changes the probability of the remaining curtains. Your area B now has a 50/50 chance, not a two thirds chance.

Learning something about door #3 later doesn't change the odds you originally chose with

 

[posthuman]

What would you do if after your pick of curtain #1, and before any curtains were opened, the host told you that you could change your pick to both curtains #2 and #3?

That's a really smart question to ask

 

[christian74]

Essentially, the odds don't change.
You picked one door with 1/3 chance of success - the doors you didn't pick have 2/3 chance of success.

When one of the other 2 is revealed as not-success, there's still 2/3 chance your first guess was wrong but the alternative has been collapsed to only one other door. That other door has the whole other 2/3 chance now.

I knew the answer only because this same question was asked in a movie called '21' (it's about counting cards, Kevin Spacey) but never really understood why until having read your explanation.

 

[rstrats]

Essentially, the odds don't change.
.

Actually, they do. The odds of the car being behind curtain #2 go from 1/3rd to 2/3rds and the odds of the car being behind curtain #3 go from 1/3rd to zero. But try telling Lynx that.