Ok, So I’m a little behind the times, but I just finished reading through the Cecil Archive on the Monty Hall Paradox (Search to refresh your memory). There was a long debate whether or not Cecil was right, and at the end alot of readers weren’t satisfied with the explanation. I love Cecil (in that way) but his explanation for this was pretty lame. I got the feeling even he didn’t “get it” even though he was right. Anyway, I got to thinking about it and drew a diagram below that makes it absolutely clear to anyone (I think). Tell me if you agree.
Ok, In the following example, I start with the prize behind door number three (marked by a ! following the X). It doesnt matter which door it starts behind so I just picked any. Then, on the y axis, I listed the three possible situations after you have made your inital choose (since you have the option of three doors). Now, knowing that Monty will not open the door with the prize, and will not open the door you have chosen, watch how this new info changes the odds.
Door1 Door2 Door3
Poss1 X* O X!
Poss2 O X* X!
Poss3 O O X!*
In Poss1 you choose door number 1 as marked by the * after the X. Monty only has the option of opening door 2 (because you have chosen door1 and the prize is behind door3. In this situation, switching will DEFINATELY win you the prize.
In Poss2, you choose door2, Monty MUST open door1, and once again switching DEFINATELY wins you the prize.
In Poss3, switching will always make you lose.
If, after the new information, you switch, you will win 2 in the 3 situations. Hence the odds of winning = 2/3.
Tada! Ok someone give me kudos for this cause I crave validation.
Having said that, I haven’t figured out something about the two children question (refer to same article). While the odds statiscally do say there is a 2/3 chance of the next child being male, clearly, (as far as I know), betting on this in real life will be a losing bet. In the Monty Hall bet you will actually win money (Yes play the game with friends and play the contestant). Can anyone explain how the children works statistically but doesnt seem to work in real real life?