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I came across this interesting logic puzzle/problem/paradox thing in a book the other day and while I have actually read about it before I had forgotten it in the ten years or so since then so it impressed me all over again. I searched to see if it had been discussed on this forum before and indeed it has, but also not for ten years or so and not in a dedicated thread so I think this thread is warranted.

For the full details of it see here but I think it would be more fun if people took part on this thread first before reading up the solution and explanation.

I'd also be interested to see how important you think the wording of the problem is. I was very stumped by it at first but on reflection I think the version I read of it missed a crucial detail but perhaps I'm just still failing to fully understand the logic of it. So here goes the puzzle:

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You are on a gameshow and your objective is to win a prize. On this occasion, the prize is a brand new sports car! The host, Monty Hall, shows you three doors. The doors are numbered 1, 2, and 3. Behind one of these doors is the prize car. Behind the others there is nothing, or just some rubbishy token prize. You have to choose a door, the idea being that you win whatever is behind that door. You choose door 1. Monty then opens door 2, revealing that there is nothing behind it. He now offers you a choice: stick with your choice of door 1, or switch to door 3. This decision will be final. Once you make it, Monty will open the door you have chosen and you will win whatever is behind it.

So do you stick with door 1, or switch to door 3?

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Would be interested to hear your answers and reasoning behind it. For those that are already familiar with this problem, would be interesting to discuss it once a few answers have been posted.

Wow. A fresh Monty Hall problem thread in 2022.

Gavin Chipper wrote: ↑Thu Feb 17, 2022 6:25 pm Wow. A fresh Monty Hall problem thread in 2022.

Yeah I'm a bit late to the party but then again this is a phpBB forum about an old TV word game show so I'll forgive myself the unhipness.

Callum Todd wrote: ↑Thu Feb 17, 2022 5:46 pm I'd also be interested to see how important you think the wording of the problem is

It's critical. The way you have worded the puzzle, switching would not necessarily change your chances. You have to emphasise that Monty will always open an empty door.

For me the biggest puzzle about the Monty Hall problem is why so many otherwise very intelligent (ie way beyond my level) people seem to struggle with grasping it.

Fred Mumford wrote: ↑Thu Feb 17, 2022 8:31 pm

Callum Todd wrote: ↑Thu Feb 17, 2022 5:46 pm I'd also be interested to see how important you think the wording of the problem is

It's critical. The way you have worded the puzzle, switching would not necessarily change your chances. You have to emphasise that Monty will always open an empty door.

Yes, that's what got me. I worded it that way because that's how it has been worded in all the versions I have seen. When I first read it I refused to accept the answer and I'm still not convinced that the answer should be accepted if it isn't stated that Monty isn't opening any door at random. But most versions I see don't state that, so is it really necessary? Are we supposed to assume Monty knows where the prize is and won't reveal it? Is that part of the puzzle, or is it a bug?

Any representation of paradox that doesn't state that he reveals what he knows to be an empty door/goat is simply wrong.

Jon O'Neill wrote: ↑Fri Feb 18, 2022 7:14 am Any representation of paradox that doesn't state that he reveals what he knows to be an empty door/goat is simply wrong.

I thought that but then I couldn't understand why most representations I could find didn't state that. It seemed that maybe part of the puzzle was to infer that from the context of Monty being the game show host. Kind of spoils it for me if that inference isn't part of the puzzle, as otherwise it's either wrong (as you say) or too easy and not really that impressive.

There's similar issues with that question about someone who has 2 kids and at least 1 is a boy - what is the probability of them both being boys? Clearly the answer isn't particularly interesting if it's 1/2, so they want the correct answer to be 1/3 - but that entirely depends on how the question is worded and how you know that 1 is a boy.

For interest: viewtopic.php?t=47

Ian Volante wrote: ↑Fri Feb 18, 2022 1:11 pm For interest: viewtopic.php?t=47

I see Jon phrased it in a way that made clear Monty knows where the prize is. Best part of that thread is Dinos talking about the name Monty in 2008