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Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?
Do any of you have any noteworthy experiences where knowledge of math helped you in an unusual way?
https://en.wikipedia.org/wiki/Monty_Hall_problem
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Get Those Brain Cells Working: The Monty Hall Problem
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(Score: 2) by Flyingmoose on Friday July 29 2016, @10:33AM
In the actual game, the host opens one of the wrong doors to create drama, but the contestant is never allowed to switch doors. Monte Hall himself confirmed that the problem is inaccurate.
(Score: 1) by Demena on Friday July 29 2016, @10:39AM
Just change the name to "The Pick A Box" problem (Australian TV show) and it becomes valid again
(Score: 2, Informative) by Anonymous Coward on Friday July 29 2016, @01:12PM
In the actual game, the contestant is sometimes allowed to switch doors. Monte Hall confirmed that the show manipulated this rule because they knew it increased the odds. (Sometimes they wanted to give away the car.)
For the purposes of the math exercise, the problem must be stated that you are always allowed to switch if you choose.
If you recreate the game with physical objects, the person who plays the host understands the issue within a couple of rounds, even if the contestant person doesn't see it. I find the best way to explain the math exercise here is, instead of showing one empty door and then offering the switch, the host can open no doors, but offer to switch to both remaining doors from the single chosen door. This isn't a change of rules in effect, but it makes the logic clear. The contestant can understand that one of the two doors other doors must be empty, but having two doors is still better than just one.
(Score: 3, Informative) by tangomargarine on Friday July 29 2016, @02:25PM
If he doesn't offer the choice to switch every time, on the "you can have both other doors" offer I would be extremely suspicious I had already selected the winning one. Assuming they wanted to save money and *not* give away the car.
"Is that really true?" "I just spent the last hour telling you to think for yourself! Didn't you hear anything I said?"
(Score: 3, Informative) by WalksOnDirt on Friday July 29 2016, @04:41PM
Sure, that makes it a simple exercise in game theory. You should never switch. The problem has to be stated very carefully to avoid that, and it usually isn't.
(Score: 1, Insightful) by Anonymous Coward on Friday July 29 2016, @06:56PM
That makes sense given your assumptions, but as noted before, sometimes they wanted to give away the car. The sponsor gets better publicity when the contestant wins the car. They have to strike a balance between giving away the car and ending up with a goat to keep the audience interested.
(Score: 3, Interesting) by sjames on Friday July 29 2016, @07:19PM
But the assumption is wrong. They want to give away the car often enough to keep the excitement high. Besides that, the car was given to them by a sponsor and it only holds value for the game as long as it is the current year model. They make a lot more producing the show than they will selling the car off.