Quote:
Originally Posted by balint-glm
BUT, the question here is: Do you have more chance to win if you switch or if you stay with your first choice? In this case switching means 66.6 and staying 33.3.
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O'rly? Now please give me the mathematical explanation for this phenomena of teleportation. How exactly the other door got 2x times more chances when you have changed your mind? Some magic happened? Gandalf has moved the diamond to another cup? A quantum teleportation maybe?
You know what? You will never give it to me, because there is no mathematical formula for that. Even a senile Monty Hall was unable to prove it with formulas, because of Alzheimer. Wanna prove that I'm wrong? Just show me the formulas! That's so easy, ah?
It doesn't matter if you have changed your mind or not, both doors will sill have a 50% chance. And it doesn't matter that the 3rd door is opened and empty. The probability was simply
redistributed. That's all that have changed, because one variable was taken out from the formula. With 3 rooms it was 100/3=33.3(3) (the formula is a+b+c=100), now it's 100/2=50 (the formula is a+b=100). Your decision does not affect the
expected value. Mathematically. And this is the very basics of math.
P.S. The picture you have posted above it stupid as fuck. The diamond is always in the 1st cup there. Now re-draw it like it's in the 2nd or 3rd cup. And add to it a variant where the opened empty cup was #1, #2 and #3 for each case. You will see that in all cases, the probability to find a diamond under one of 2 remaining cups is 50% and it does not matter if you have changed your mind or not. If you want, I can redraw this picture to "prove" that changing your mind loses 2 times of 3. And you will see that probability of success is not 2/3 but only 1/3 (in fact it's
50%, because
(2/3+1/3)/2=0.5). That's in case if you are used to learn math by comics, not by formulas...