Monty Hall problem - SP edition

Since we're having probability fun...

Imagine you are on a game show. You are offered three doors. Behind two of these three doors are pineapples. Behind the third door is a chinchilla. You don't like pineapples. Pineapple pineapples. You want one of those damn cute chinchillas.

You are allowed to select one of the three doors. Upon selecting a door, your pimento host (me) opens a door that you did not select, revealing a pineapple. You now have a selection of two doors; the one you chose and the third one that's unchosen and unrevealed. You can either stay with your choice or you can switch doors.

What action will lead to a higher chance of getting the cute chincilla?

This is flawed logic which is the source of this famous problem.

Look at it from this perspective:

Let us say we had 100 doors. Only 1 door has a good prize. That means the chance is 1%.

Now, you are right in saying "Okay, lets eliminate 98 doors, if we were free to choose the two remaining doors at the beginning, the chance is 50% each"

But the fact is, we have stayed with our choice, which was, is, and will always be 1%.

Also look at it from this perspective, lets say we add 100 more doors. Does that mean the chance is now 0.5%? Of course not, and anyone will call you crazy for thinking that. But if we had to choose a door to start with from the 200 initial doors, then yes it would be 0.5%

Now, lets go back to 100 initial doors, picking one, and eliminating 98 incorrect doors. This leaves one door correct, and one door incorrect. Like above, if we started with 2 doors to start with, then the chance was 50%. But we had to make our initial guess from 100 doors, so that door still has a 1% chance of being correct. However, the other door has a very high increased probability of being correct because that door did undergo changing influences to affect its probability. While we kept with our original choice, the probability for that door kept increasing because technically, you can see it as "a free choice from an initial set of doors" as we have never chosen it.

I hope that is enough information to help you understand why it is better to switch and it is not a 50-50 chance to win. I'll be more than happy to explain anything you don't understand as long as it doesn't turn into trolling.

You are given the option to select again, thus changing the problem. Now you aren't allowed to choose the third door. This makes you have a 50-50 chance of selecting the . Or, as I see it. You chance from the beginning was 33%, or 1/3. Now, however, your odds have changed since you only have two options to choose from. That's how I see it. Even if you couldn't choose it you could say, in a way, that your chances are 50-50 of having the . This is since you know that 1/3 doors contains it and that 1/3 was already said to not contain it. This leaves 2 doors and NOW you have 50% chance of having it. I agree, initially, that you had a 1/3 chance.