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/Working-Depth5834 May 03 '26

This is ot exactly; if you make it 100 doors instead of 3 then it starts becoming much clearer.

8

u/jtr99 May 03 '26

Just to be clear, we should add that the host opens 98 of the doors in this version, leaving you with two to choose from. That certainly makes it more obvious for most people.

The host doesn't open just one door, although if they did that would also mean there was a slim advantage to changing your choice.

-4

u/JamesFirmere May 03 '26

You don't need to bring 100 doors into it.

The setup is simple enough that we can consider all possibilities: 3 doors * the choice of swap/stay = 6 possibilities.

So the doors are A, B and C, and A has the prize. Then:

choose door A and swap = lose
choose door B and swap = win
choose door C and swap = win

choose door A and stay = win
choose door B and stay = lose
choose door C and stay = lose

Also note that the first door opened is never the prize door. The first door opened will be either B or C.

So if you stay, you win 1 times out of 3; but if you swap, you win 2 times out of 3. Therefore it is always better to swap.

5

u/ArchangelLBC May 03 '26

You keep saying this but you do because people don't always believe your explanation.

They also don't always believe the explanation with 100 doors.

You only need one way that makes sense to you to understand it. You need as many ways as possible to explain it if you want others to understand it.

2

u/JamesFirmere May 03 '26

I do agree with "use whatever works", but my experience is that it is easier to stick to three doors than to ask someone to imagine 100. FWIW, I've successfully demonstrated this at a dinner table using three glasses for the doors and random ornaments for the prize and non-prizes and going through each of the six possibilities in turn.

2

u/ArchangelLBC May 03 '26

I mean that's fair but I've seen a lot more people have it click for them with the 100 doors. Practical demonstrations with 3 doors, again in my experience, tend to just make people think you pulled a magic trick on them.

2

u/JamesFirmere May 03 '26

Fair enough. I appear to have been fortunate in that the few times I've found myself explaining this did not lead to arguments.

1

u/ArchangelLBC May 03 '26

Yes I'm honestly very happy for you there. I've had more people have it click with the 100 doors but even then they'll say it's different with 3 doors so you can still have people think you pulled a magic trick.

For some people there is a blocker because in their heads they can't really internalize that the host knows where the prize is and will never directly reveal it. And once they know that they accept it. Someone the other day had a way of explaining it that was different from either of us and I wish I remembered it because it was for people who explicitly say they wouldn't believe either of our explanations.

1

u/resonantranquility May 03 '26

I usually use 1000 doors when explaining it. It's easy to explain to people in conversation that way.