Monty Hall problem - SP edition

With your other situation if you stay you have a 1% chance still if you switch then your chance will be .5%. A little different. Except if you knew where the first 100 doors were, one containing the , you could effectively make yourself still have a 1% chance of winning. Only if you knew which the new doors were, of course.

It's better if you think about the other 100 doors example: There are 100 doors, you pick one, and 98 doors are opened revealing pineapples. So there's the door you picked, and the door that's left. We can both agree that before the other doors were opened, you had a 1% chance of picking the right door. According to you, afterward, you have a 50% of getting the chinchilla if you stay. That means that your probability went up from 1% to 50% of picking the door with the chinchilla by doing nothing. This means that no matter door you picked at the beginning, you have a 50% chance of it having the chinchilla.

Now, minus a pineapple since he eliminated a door. So now you have two choices. Stay or switch. 2 choices, 2 doors. [...] The last door was eliminated, it doesn't count any longer since you can't choose it.

That last door DOES matter, even if you can't choose it, because you could have chosen it. Although you have 2 choices, there are still 3 doors to consider. You either stay with one of the 3 doors you picked, or switch after one of the bad doors was taken away.

Taking the 100 door example even further, let's you have an infinite amount of doors, 1 with a chinchilla, the rest with pineapples. The probability that the door you pick has a chinchilla is 1/infinity, or effectively 0. All doors except for the door you picked and the door with the chinchilla are opened, revealing pineapples. Knowing that the first door you picked has a pineapple, wouldn't it be smart to switch?

What I'm basically trying to say is having the contents behind another door revealed doesn't change the probability of what you picked before the contents were revealed. Otherwise, each of the 3 doors would have a 50% chance of being either pineapple or chinchilla, since a door that you will not pick will always be revealed to be a pineapple.