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The Monty Hall problem continued to short circuit the “intuitive reasoning” part of my maths brain until I saw it explained as “Imagine there are a million goat
by archgrove 5y ago
The Monty Hall problem continued to short circuit the “intuitive reasoning” part of my maths brain until I saw it explained as “Imagine there are a million goats and one car. You pick a door, Monty opens 999,998 doors. Should you switch?”, to which the answer is clearly “Of course” (you had a one in a million chance the first time). Then reduce from there.
- klipt 5y agoThat's correct if Monty always opens the doors. But suppose Monty only opens the other doors if you picked the prize, then obviously you shouldn't switch.
- Deestan 5y agoThat would be a different problem. In Monty Hall, Monty always opens a door, and you're left to choose between your picked door and one other door.
- Jensson 5y agoThis isn't the Monty Hall problem though. The comic doesn't mention the show. It just has a similar setup so people just jump to the same solution even though it is wrong in this case. The correct answer is that it is impossible to know what the chances are if you switch since the problem lacks enough information to tell.
- Out_of_Characte 5y agoHow is it wrong in this case? your picked door had a 33% chance to have a price, since its one of three doors, now that a goblin is revealed the other door has a 66% chance of hiding the price. exactly like the monty hall problem
- Jensson 5y agoNo, you are wrong. The way the comic described it only describes a single instance of the host opening the door in this case. It could very well be that this host doesn't want you to win, and thus reveals another door and tries to goad you into switching only when you have picked the correct door. That is a very reasonable interpretation of a game like this, and in that case the correct answer is to not switch. If you think that this description means that the host always opens a dud after you open the first, then you are wrong. It doesn't say that anywhere, and there is no reason to believe that this game show works that way. The only reason you think it does is that you connect it to the original Monty Hall problem which worked that way, which causes you to make the mistake thinking the same rules apply here.
- Out_of_Characte 5y agoI thought about it some more, if the game is never played more than once then there's no strategy to develop for both the monty hall problem and the problem described in the comic, therefore that's a moot point. but if its played more than once then your evil host that sometimes opens a door doesn't make sense. If the host always opens a dud then its a monty hall problem. but if the host sometimes opens a door, the host still can't do it every time you land on the price because then you wouldn't switch. so the host would have to sometimes open the door when you're on the price and sometimes not. But then when he opens a door it would indeed become a 50/50 so an evil host's best option is to never open a door in the first place.
- mcguire 5y agoHow exactly does the comic's version differ?
- mcguire 5y agoMonty always opens a door concealing a goat.
- marcosdumay 5y agoThe problem with the Monty Hall is that there is a hidden rule that people never explain. If you put there rule there explicitly, it's reasonably easy to see that the presenter is messing with your up-front probabilities when he opens a door.
- tantalor 5y agoWhat rule is that
- mrob 5y agoMonty will always reveal a goat regardless of which door you picked (which also requires him to know where the goats are).
- jonplackett 5y agoBased on him knowing where the prize is, it’s hard to escape the idea that he’s only showing you a new door because you picked the right one, therefore intuitively you feel like you should stick with your guns. At least if you’re wrong the way you chose, you won’t feel like you’ve been manipulated.
- Biganon 5y agoPeople always explain that. Unless they have no idea what they're talking about. It's an essential part of the paradox.