The Monty Hall problem.

[Tiberius]

Another counter-intuitive example of mathematics.

Imagine you are on a game show, and you are presented with 3 doors. Behind two of the doors, there are goats (the booby prize). Behind the other door, there is a car. Your job is to win the car.

You select a door at random. The host of the show, Monty Hall, who knows the location of the car and goats, then opens one of the other doors, so that a goat is revealed. He then asks you whether you'd like to stick with your original choice, or to switch to the other closed door.

The question is, is there any advantage to switching? Or, is there any advantage to sticking with your original choice? Or, is there no advantage either way?

The answer may surprise you:

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Switching your choice wins you the car 2/3 of the time. Sticking with your original choice only wins you the car 1/3 of the time. Explain that

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[Darwinian]

That's because the chances of you winning if you stick are still 33% but if you change your mind they go up to 50% as you are only choosing between two doors.

It is certainly counter-intuitive but it does work in the real world..

[Tiberius]

Nope, if you change your mind the chances go up to 66.6...%

[Darwinian]

Aha!! That must be because your original door still has a chance of 33% as it was chosen out of 3 so the other door must now have a chance of 66%.

I think

[Tiberius]

Pretty much. Now to see if other people understand it

[Dotard]

Wait.... what?

Original choice 1 out of 3. 33%

After the first door is opened you are given another choice. Two doors. Your choice is out of two. Should it not now be 50/50? How can it be 66% if you only have two doors to choose from?

The first 1 out of 3 choice is now irrelevant is it not?

[Tiberius]

Technically it is the only relevant thing about the problem. Also, you do not get a second choice of door. You get a choice to stick or switch; this is very important (albeit confusing).

I'm not going to explain it yet. I like seeing people getting confused over statistics

[Rockthatpiano06]

That makes sense to me actually.

[Eilonnwy]

I'm not a big fan of statistics but visually in my head I get it.

The way I understand it is that the two doors you don't pick become a unit, so even if you know one of them has the goat, as a unit, there is still a 66% chance switching gives you the car because there was a 66% chance the goat was in one of the other two doors when you picked your door. And by revealing which of the two doors has the goat, there's still a 66% chance because there was always going to be a goat in one of those doors.

Am I understanding this correctly?

[theblindferrengi]

When you guess the first time, you have one guess (1:3 chance), you dont know of the three where the goat is; when the goat is revealed, if you change your awnser, that revealed goat is like your #2 guess, so u go from having one guess (1:3) to having two guesses (2:3).