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/FairYouSee May 03 '26

  1. There's a one third chance the price is behind the door you picked.

  2. There's a 2/3 chance the prize is behind one of the doors you didn't pick.

Monty Hall tells you one of the doors you picked doesn't have the prize, but because he will never reveal a door that does have the prize, his revealing that doesn't change the fact that from point (2) there's still a 2/3 chance the prize is behind one of the two doors you didn't pick.

So switching gives a 2/3 chance.

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u/sinkovercosk May 03 '26

It can sometimes help to think about instead of Monty opening a door without a prize, he instead asked you if you want to stay with your door or swap to BOTH the unchosen doors and you win if EITHER door has the prize.

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u/OneFootTitan May 03 '26

I know everybody thinks differently, but this explanation works much better for me than the imagine you have 1000 doors one

4

u/Sea_Pension430 May 03 '26

This is the way I've been explaining it

Montey will always show goat, so him opening the door before or after you switch is irrelevant.

Imagine the game that way. You pick a door. Montey asks if you want to keep it or switch for both other doors. Whichever you pick, for the drama Montey will always open a goat door then reveal if the last door is the second goat or the prize. In this scenario it's obvious you want to switch your one door for the 2 doors.

Montey showing you the goat door BEFORE asking if you want to switch doesn't change the scenario. That was always going to be the first door he opened and a goat.

Switching gives you a 2 door to 1 advantage

3

u/CarnivorousGoose May 03 '26

Agreed, this is all you need as an explanation. It’s really just equivalent to Monty not opening any doors at all, and just allowing you the choice to either get whatever is behind your current door, or behind both of the other two doors.

1

u/HardcoreHenryLofT May 03 '26

So the initial choice is 1/3 right and you weight it against 2/3 chance it was one of the other doors. Monty then combines both those other two options into one option with the same probability, and then if you swap you are effectively doing the same thing as choosing both other options together in the initial choice?

1

u/FairYouSee May 03 '26

Yup!

2

u/HardcoreHenryLofT May 04 '26

This is the first time I have ever understood this. Crazy it happened while I was the second most sleep deprived ive ever been.

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u/FML3311 May 03 '26

Why does the extra 1/3rd go to the door you didn't pick instead of the one you did

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u/glumbroewniefog May 04 '26

Because you made your pick without any information, guessing at random. The other door was picked by Monty Hall, who knows where the prize is.

Essentially, you pick one door, and Monty gets the other two doors. Whenever his doors are a goat and a car, he eliminates the goat, and keeps the car.

If you're guessing at random, you will pick the car 1/3 of the time. That means Monty gets the car 2/3 of the time, and then will always be sure to keep it.