The three door scenario understood and explained!
Title The three door scenario understood and explained!
Date 2024-11-30
Comment For a long time, but without really digging into the problem in detail, I was one of those who couldn't accept the fact that switching would make a difference. But now I'm lying flat down!

The situation briefly: You have three doors and behind one of them there is a prize you can win, if you pick the right one. All fine so far. Then your host offers you to remove one of the wrong doors, and asks if you want to stick with your choice or switch it to the other door. A simple and generous offer! And so, what do you do?

The lazy-minded, like me, will just look at what-is: By removing one door you all of a sudden got better odds, now 50 % chance of winning the prize. The right door could be either of them, so it is all the same if you stick to your first choice or switch it.

But this is where the trick is played. You are being manipulated by the magician waving you over here to catch your attention, while all the real action is happening elsewhere. [smart people always think twice].

Because, the situation is, removing a door doesn't change the fact that when you made your choice, you did it based on the poor rate of 33% of choosing the right door. The chances of you going to lose were much bigger than your winning chance. So yes, you get a better winning chance, when removing one door, and stick to your decision, but it is not as good as it can get.

Because by making a switch, you suddenly turn the odds upside-down, and that because you initially had two chances of getting it wrong, and when you switch these two choices, they inevitably will be changed to a winner-choice because the other wrong door is already taken out of the equation. Both wrongs will be changed to right, whereas the only right choice will be changed to wrong. 2 against 1 => 67%.

Any abilities to 'see through' the host, and perceive your way to the right choice by decoding his body language and all that, is beyond the scope of the strict math solution!