Quote:
Originally posted by ModelPerfect
If the host randomly chooses which of the 2 boxes to open, then you get tons more information. Here's the possible outcomes, presuming for this example the cash is in C and you always select a different box (if the host selects C that doesn't eliminate it):
(1) You select A, host shows B, you choose C = WIN
(2) You select A, host shows C, you obviously choose C = WIN
(3) You select B, host shows A, you choose C = WIN
(4) You select B, host shows C, you obviously choose C = WIN
(5) You select C, host shows A, you choose B = LOSE
(6) You select C, host shows B, you choose A = LOSE
Your odds of winning by always switching, even though the host RANDOMLY chooses between the 2 remaining boxes = 66.7%
It's because you get the additional information when the host randomly chooses C that alters your odds.
Maybe you just didn't understand my original statement: You aren't randomly selecting the boxes...only the host is randomly selecting which of the 2 remaining boxes to show you in round 2. Sometimes, he will show you exactly which box to choose. Now if the host revealing a box eliminates it, then your odds of winning drop to 33.3% no matter what you do (because instances #2 and 4 will then be loses). So the end result is your odds are never 50% if the host randomly reveals one of the 2 remaining boxes.
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I see what the problem is.
You are assuming that when the host reveals a random box, after that you get to switch no matter if the box that was revealed was the right one or not, and the revealed box is not eliminated.
I am assuming that when the host reveals a random box, if it's the right box you just lose the game, and if it isn't you can choose whether to switch or not, with the revealed box being eliminated.
I am obviously counting your chance on switching only if the box revealed turns out to be the wrong one, because if it's the right one, the game is over and you don't get to switch anymore.
Switching, in this case, does not improve your chances.
Guess the problem here was just some differences in opinion on which definition of the rules of the alternative game to use
