Clearing the Whole Probability Session

OK I did not think the so-called "Information-paradox" through... and I'm a bit ashamed.. :)

What I proposed as the information (not-really) paradox was nothing more than the rephrasing of the Monty Hall problem. I must clear this up a bit before posting anything else.

So we're playing the Monty Hall game, and I get to chose between three doors, and I chose one at random.

Monty Hall gives shows me one of the two remaining doors that has a goat behind it. I now have a 2/3 chance of winning if I switch doors.

What I said was that someone new should now come in; someone who has no idea what we were playing up to here. He is told that there are two doors, one has a goat behind it, the other a brand new car.

What confused me was that this person now has a 50% chance of hitting the jackpot.

What happens if now, we both choose one of the two doors at random? He will win 50% of the time, and so will I! Because 1/2 * 1/3 + 1/2 * 2/3 = 1/2 (because I chose the door with 1/3 chance half of the time and I choose the door with 2/3 chance the other half of the time).

If we both chose the same door all the time, say the left door, then we will win according to the 2/3 : 1/3 odds.

So simply put, that is just the Monty Hall problem rephrased... I sort of confused myself ... heh. Sorry about any unnecessary cluttering in your mind.

A cool little plus:
As mentioned before, we can play the Monty Hall game with 50 doors - in which case I will have a 49/50 chance of winning if I change to the other door. Now the cool part is that we can continue adding more and more doors. As we have more and more doors, my chances of winning because of changing grow!

While adding more and more doors, I can eventually get to an infinite amount of doors - I can even keep going until I get a continuously infinite amount of doors (or points), like on an axis.

Imagine trying to guess a number on a line - on an infinite amount of points. It's impossible to think of my number if I chose randomly. But after you choose, I reveal that the number I thought of is either the point you chose or one other point! Well it's basically for sure now that you have to switch. :)