
Originally Posted by anoetic
I won't get into the math of it and all but actually the Monty Door Problem is actually one of those test case to show that common sense is not always right. It isn't a brand new problem your odds are actually better if you switch doors. Here is a site to explain it better. If you just do the problem yourself and play it out, there are plenty of sites on the internet that do it, you will see that switching improves your odds.
http://www.uvm.edu/~dhowell/StatPage...ThreeDoor.html
The problem with all of the math "proofs" of the threedoor problem is that they do not recognize that the decision NOT to switch doors is, in fact, a new, seperate, affirmative, decision to choose the that door (that you had already picked).
As in my example, say that, after one door is tossed out of the mix, Monty Hall then said: "We were just kidding you, you don't have to choose one of three doors, just one of two. Your first pick doesnt count. One of the two doors has a prize. You need to start over and pick one of them, which one do you want?" In that case, there is a 50% chance of being right whichever door you pick. In the classic threedoor problem, the person is given the choice of remaining with their first pick or switching to the other door. The boolean math proofs (and the computer programs that have fun with this) dont recognize that if the person keeps their original door choice that, then, is really a brand new independant choice of the door just llike in my example where Monty was kidding.
To really do a computer program to test it you would first need to decide which door had the prize (truely randomly, not with a pc random number generator). Save that decision separatly. Then make a choice of doors. Then, turn off/on the computer and start over. Input the "correct" door choice, then show the results of a computer run that either stayed with the original choice or made the switch, showing the results between staying with your first door and switching. That is what is actually going on on "Lets Make a Deal"
The second computer program can be as simple as this
Input A (the correct door choice from previous true random generation)
Input B (the original contestant door choice)
"Do you want to change doors?" (y/n)
If y then input C (new door choice)
if n then B=C
If A=C then "win"
Then just keep track of wins and losses in relation to if a change was made. Will come out to be close to 5050 if you do a long enough run. Of course, the "contestant" cannot know what the original door choice was (input A).
FWIW, however, I have seen pretty good explinations that, on the quatum level, the threedoor choice actually does work as described in the threedoor problem, so if Monty has you choosing between three different spinning bosons, then, by all means, change your pick!


