Monty Hall's riddle

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Antithesys	Monty Hall's riddle	Lead	[-]
Posts: 22638 (08/10/08 9:22 AM) Gadabout Reply Quote More Recent Posts Message Connection Block Invite	Let's see if you dopes know this one. The game show host offers you a choice of three doors. Behind one is a prize, while the other two contain nothing. You pick a door. The host then opens one of the remaining doors to reveal that one was empty. He then offers you the chance to switch your choice to the third door. Should you do it?
bassoon291		#1	[-]
Posts: 6898 (08/10/08 9:23 AM) Registered user Reply Quote More Recent Posts Message Connection Block Invite	Yes, you increase your chances of winning the prize by 33.3333333...%. (Or something like that.)
NiceToAnimals		#2	[-]
Posts: 10587 (08/10/08 9:24 AM) Registered User Reply Quote More Recent Posts Message Connection Block Invite	Am I wearing a farmer costume or dressed like George Washington? This matters in my decision.
Antithesys		#3	[-]
Posts: 22639 (08/10/08 9:25 AM) Gadabout Reply Quote More Recent Posts Message Connection Block Invite	You're dressed like Yao Ming.
Bernard Wrangler		#4	[-]
Posts: 9392 (08/10/08 9:26 AM) this won't end well. Reply Quote More Recent Posts Message Connection Block Invite	nothing... the odds are the same. there is always another door with nothing.
NiceToAnimals		#5	[-]
Posts: 10588 (08/10/08 9:26 AM) Registered User Reply Quote More Recent Posts Message Connection Block Invite	Then I'd take the money in the container of Turtle Wax.
StarRider		#6	[-]
Posts: 18328 (08/10/08 9:27 AM) Reply Quote More Recent Posts Message Connection Block Invite	It seems as though you would still have a 50/50 chance either way, but if you switch choices, it would seem you would be risking guessing correctly twice instead of once. In short, i dunno.
Antithesys		#7	[-]
Posts: 22640 (08/10/08 9:27 AM) Gadabout Reply Quote More Recent Posts Message Connection Block Invite	Well bassoon is right...the chances it's behind your original door are 1 in 3, while the chances it's behind the remaining door are 2 in 3.
Bernard Wrangler		#8	[-]
Posts: 9394 (08/10/08 9:29 AM) this won't end well. Reply Quote More Recent Posts Message Connection Block Invite	's like saying you have diff odds on the heads tails thing after flipping tails 5 times in a row or summat.
bassoon291		#9	[-]
Posts: 6899 (08/10/08 9:31 AM) Registered user Reply Quote More Recent Posts Message Connection Block Invite	Yay, what do I win?
Antithesys		#10	[-]
Posts: 22641 (08/10/08 9:32 AM) Gadabout Reply Quote More Recent Posts Message Connection Block Invite	Actually it's not really like that at all. Each individual coin flip is a separate event, whereas the two choices of doors you make are not differentiated or separated by changes in knowledge of the situation.
merkyl		#11	[-]
Posts: 56752 (08/10/08 9:33 AM) Registered loser Reply Quote More Recent Posts Message Connection Block Invite	But it's still 50/50 on which of the two remaining doors has the prize.
TC		#12	[-]
Posts: 472 (08/10/08 9:33 AM) I Need A Clue Reply Quote More Recent Posts Message Connection Block Invite	Wow. Is this the next great fucking poindexter, pointy-headed geek MI thread??????
BJ		#13	[-]
Posts: 5832 (08/10/08 9:35 AM) MESS member Reply Quote More Recent Posts Message Connection Block Invite	anti just watched 21.
Antithesys		#14	[-]
Posts: 22642 (08/10/08 9:35 AM) Gadabout Reply Quote More Recent Posts Message Connection Block Invite	Indeed it's not. It would be 50/50 if you hadn't made a choice before. But you made a choice while there were three doors, so your first door was originally 1/3 while the other door was originally part of the 2/3 set. You knew that set would have at least one door that was empty, so revealing that door doesn't change anything. eta oh crap is this in 21? Oh well, no one's going to watch that anyway.
merkyl		#15	[-]
Posts: 56753 (08/10/08 9:37 AM) Registered loser Reply Quote More Recent Posts Message Connection Block Invite	But you haven't explained why changing your door increases your odds.
NiceToAnimals		#16	[-]
Posts: 10589 (08/10/08 9:41 AM) Registered User Reply Quote More Recent Posts Message Connection Block Invite	Initially, the chances were one out of three when the first choice was made. Once one door was shown, the chances became one out of two. To me this would be the same if you picked again or not.
Antithesys		#17	[-]
Posts: 22643 (08/10/08 9:44 AM) Gadabout Reply Quote More Recent Posts Message Connection Block Invite	Well try a different angle. Doors A B and C. You pick A. At this point, you know that A has a 1/3 chance of winning. B and C together have a 2/3 chance of winning, so if I asked you if you wanted to switch BEFORE opening a door, you'd probably do it, right? The odds are in your favor. Now, once you actually switched to a specific door B or C, your chances are still 1/3, just under a different door. But the chances of it being under the combined set of B and C were 2/3 before switching. You also know through logic that even with all the doors closed, that set of B and C must have at least one empty door. So if I open that empty door before you decide to switch, nothing changes. You already knew there would be an empty door. The set of B and C is still 2/3 in favor of winning, but now I've shown you which door among that set would have the prize.
BJ		#18	[-]
Posts: 5833 (08/10/08 9:46 AM) MESS member Reply Quote More Recent Posts Message Connection Block Invite	You pick door A. The chance that the prize is behind door A is 1/3. The chance that the prize is behind door B or C is 2/3. Monty now eliminates a door in the latter group: door C. This does not change the fact that your choice of door A has a 1/3 chance of being correct. It also does not alter the fact that the prize was in either door B or C with 2/3 probability. However, AFTER you made your initial choice, door C is removed. So now you have a set of doors that has a 1/3 chance of containing the winner, and a set of doors with a 2/3 chance of containing the winner. But wait, each set only has one door in it. Therefore, door A has a 1/3 chance of being correct, and door B has a 2/3 chance of being correct.
BJ		#19	[-]
Posts: 5834 (08/10/08 9:47 AM) MESS member Reply Quote More Recent Posts Message Connection Block Invite	Clearly I type too slowly.
UrbanRenewal		#20	[-]
Posts: 101 (08/10/08 9:47 AM) Reply Quote More Recent Posts Message Connection Block Invite	3 doors. 1/3 chance of prize being in each door. Pick door 1. 1/3 chance prize is behind door 1. Host opens either door 2 or 3. It's best to keep your original choice. 1/3 chance prize is behind door 2. Host opens door 3. It's best to change from original choice. 1/3 chance prize is behind door 3. Host opens door 2. It's best to change from original choice. So it's far better to change doors after one is opened. At the beginning of the game, door 1 has a 1/3 chance as well as the other doors; but, at the end of the game, door 1's chance remains at 1/3 while the other door has jumped to a 2/3's chance.

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