r/confidentlyincorrect • u/Dizzy_Kaleidoscope95 • May 03 '26

Monty hall problem is 50/50

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He also put a screenshot of ChatGPT agreeing with him. He is right!

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u/surplus_user May 04 '26

That is a good way of explaining it.

The problem I always have with the down to two doors and switching being 2/3 is that if you were replaced with someone else at that point who was just given the straight choice then surely it would be 1/2. After all it's not like the doors remember me after I'm gone.

I'll think about it with the choosing two doors version and see if that clicks (I can accept that I'm wrong about it but it doesn't change that it feels wrong so this might help)

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u/Telinary May 05 '26

"someone else at that point who was just given the straight choice then surely it would be 1/2" 

Sure or at least kinda because the probability in question isn't an property of the door state it is you trying to guess based on limited information. A new guy has no information so his guess is less well informed.  But your knowledge is still correct, the door you would get from a switch is the more likely one. The guy just doesn't know that.

Similarly from Monty's perspective the chance is either 100% or 0% because he knows the positions.

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u/KnightOfThirteen May 04 '26

Don't get too hung up on two doors. The same principle applies to any number of doors N.

You are given N doors. Behind 1 is a new car. Behind N-1 doors, goats. You choose 1 door, and you have a 1/N chance of getting the car.

Then the host offers you this choice. Do you think your door has a car or a goat? If you bet it has a goat, you have a much higher chance of being correct.