4 ms·
One thing that bothers me about the problem as it's stated in the article is that it isn't explicit about whether the game show host is required to open one of
by elihu 12y ago
One thing that bothers me about the problem as it's stated in the article is that it isn't explicit about whether the game show host is required to open one of the goat doors regardless of which door the contestant picks, or whether the host is allowed to choose whether to open a door or not. If the host were to only open a goat door if the contestant initially picks the correct door, then the contestant would lose every single time if he/she always switched doors.
- sukilot 12y agoYes, this was the source of the controversy and why vos Savant's self-congratulatory tempest was so annoying.
- hudibras 12y agoThe original column and response is online and is unambiguous for fluent English readers.
- hudibras 12y agoI think you're splitting hairs here. It goes both ways: if the host were to only open a goat door if the contestant initially picks the correct door, then the contestants would quickly learn to stop switching doors.
- deleted 12y ago[deleted]
- xom 12y agoIf the host can choose between doing nothing and revealing a goat, and the host wants the contestant to lose, then the contestant's best strategy is to never switch, in order to avoid being exploited by a host who only reveals a goat when switching would lose. Any reader who wrote in to say the probabilities were 50-50 after a goat was revealed was probably not thinking the host wanted the contestant to lose (or to win).
- mcphage 12y ago> whether the host is allowed to choose whether to open a door or not The problem as stated is: "you select door #1. Then, the host, who is well-aware of what’s going on behind the scenes, opens door #3". Why would you think the host has the option of not opening a door? And if you think they could do that, why couldn't the host also do other things, like offer the contestant cash to walk away, or swap what's behind the doors, or add more doors, or open all three doors, or sucker-punch them in the gut?
- T-hawk 12y ago> Why would you think the host has the option of not opening a door? Because the actual TV show of Let's Make A Deal worked that way. Here is Monty's own take on it (click to page 2.) http://www.nytimes.com/1991/07/21/us/behind-monty-hall-s-doors-puzzle-debate-and-answer.html http://www.nytimes.com/1991/07/21/us/behind-monty-hall-s-doo... This is the source of all the confusion from vos Savant's original column. vos Savant got the math right for her version of the problem where the host always opens a door, but that isn't how the show worked. She presented a simplified "spherical frictionless cows" version of the problem. The actual show did not compel Monty with any rules on opening doors. He had free rein to do whatever he wanted. He could reveal an incorrect guess right away with no opportunity to switch. He could and would offer the contestant cash to switch or not switch. Monty could try anything to trick or bluff or deceive the contestant, all for the sake of producing entertaining television. Of course, there is no correct mathematical answer at all to a game of bluffing and outwitting. At best you might find a Nash equilibrium in game theory, but even that is hard to pin down. You need to know Monty's tendencies precisely, but even that is hard when his goal isn't to maximize expected value but to produce entertainment.
- mcphage 12y ago> This is the source of all the confusion from vos Savant's original column. vos Savant got the math right for her version of the problem where the host always opens a door, but that isn't how the show worked. She presented a simplified "spherical frictionless cows" version of the problem. A bunch of PhDs aren't going to have a problem with a precisely specified version of the problem, which is what was asked of her in the original column. (which, incidentally, didn't use the name "Let's Make a Deal" at all).