Even though mathematically, my odds have changed, in reality, they have not. because it is a two-step process with new information. If the two doors left were randomly swapped (or not), this would then give me a true 50/50 on the second choice, but as the doors have not swapped, the 50/50, though it may seem to be better odds, will not change what is behind the door I picked. The 50/50 will only apply if I change my mind, but because it is a 50/50 chance, I only have one choice, so it is not really 50/50. Basically, I have a 50/50 chance of being right after door #3 is opened, but I do not have a 50/50 choice.

I played 25 times (couldn't be bothered to do it more). Look at my results (edit, one of those time I accidentally clicked on the revealed door as well, so my wins would have been higher):

(March 13, 2016 at 11:10 am)IATIA Wrote: Even though mathematically, my odds have changed, in reality, they have not. because it is a two-step process with new information.  If the two doors left were randomly swapped (or not), this would then give me a true 50/50 on the second choice, but as the doors have not swapped, the 50/50, though it may seem to be better odds, will not change what is behind the door I picked.  The 50/50 will only apply if I change my mind, but because it is a 50/50 chance, I only have one choice, so it is not really 50/50.  Basically, I have a 50/50 chance of being right after door #3 is opened, but I do not have a 50/50 choice.

You have a greater chance of being correct if you swap. This is a fact that cannot be argued against. Or to put it another way, if you stick with your door, 100% of the time you will lose more often than you win.

Effectively applying the two envelope problem where the odds suggest that one should always pick the other envelope.

(March 13, 2016 at 10:16 am)pool the great Wrote:

(March 13, 2016 at 10:14 am)Excited Penguin Wrote: Can anyone answer a simple question?

Why do you think initially it's 1/3 to pick a car?

Because there is one car and 3 options to pick from

So what?

No random process guarantees that all three doors will be picked, let alone be picked just as much, throughout a certain number of iterations of the game. SO probability has got nothing to do with it.

(March 13, 2016 at 11:36 am)Excited Penguin Wrote: No random process guarantees that all three doors will be picked, let alone be picked just as much, throughout a certain number of iterations of the game. SO probability has got nothing to do with it.

What does how many times someone picks door 3 have to do with anything, the car is behind a random door every time. We are not calculating the probability of the car being behind specific doors we are calculating the probability of you selecting the door with the car behind it. Which is why your picking 1 door from 3 doors gives you a 33% probability that its behind the door you selected.

(March 13, 2016 at 10:37 am)Homeless Nutter Wrote:

(March 13, 2016 at 10:21 am)pool the great Wrote: [...]
Since you have a 50-50 chance of having chosen a goat initially, [...]

LOL... How do you figure that? Since initially you were choosing from 3 doors, behind which there are 2 goats and 1 car - therefore you have a 66-33 chance of having initially chosen the goat. It does not matter, that one of the goat-doors was opened afterwards - your chances of having picked a goat are the same.

Because we know that there is a goat behind one of the doors after the host shows it to us. Then we have a 50-50 chance of having chosen a goat initially.

People should actually just play the game and see how it works for themselves.

(March 13, 2016 at 10:21 am)pool the great Wrote: This is my final post for objecting why you guys are wrong. If you still don't get it, then idk wtf

If you pick a car in your first try then you will not get a car if you switch.

Therefore it is beneficial to switch only if you initially randomly choose a door with a goat behind it.

After the host opens a door behind which you will find a goat, you will have a 50-50 chance to have initially chosen a goat.

Since you have a 50-50 chance of having chosen a goat initially, you have a 50-50 chance of getting a car if you switch.

Therefore it is not beneficial to switch.

I simplified it into something so simple like this yet you guys refuse to accept it? I'm just going to have to give up then