I'm actually a bit surprised by it. In my mind, you should always switch doors after being shown one that doesn't contain the prize. The key is knowing that your original choice remains at a 1-in-3 chance of being right, whereas the odds just doubled the other door is the correct one.
It seems to me that the strategy of opening one of the two "not-prize" doors is basically to ensure you do something, preferably not calculate the odds. It's a psychological distraction. The player knows they didn't pick "that" wrong door, so they get a false sense of knowing the right answer. So they'll stick with their original guess, forgetting it actually is a guess. What they should be thinking is "I got that one right, so it's not that door. The chances of me being right on the original door remain at 1 in 3; I should switch my choice, the odds have just been improved to 2 in 3."
I know the logic of this -- I was one of those who wrote a program to simulate it, and was amazed. I just don't believe it. It feels like the joke about the guy who carries a bomb on board a board because while the odds against a single bomb are high, the odds against TWO are astronomical.
Its funny, I always tell my students that when picking a multiple choice answer, go with your original choice. The reasons are that in the real world, there are no truly random "door number one, door number two, door number three" scenarios. And I proved to my satisfaction over three years or so of monitoring pop quizzes that the "hunch" knows something. The "hunch" of course, might well be the subconscious mind (though not being a pscychologist I hesitate to use such fanciful phrases) You use the "hunch" a lot in day to day life. Driving for instance. When you have a Monty Hall problem, you handle it just like a "should I go right or left at this intersection" problem.
Knowing odds is what separates the professional poker player from the mere duffer...but poker is MUCH more complicated.
I ran across this problem several years ago...I really MUST sit down to try and duplicate the experiment. Should not be too hard...
Don't go broke doing it. And when you write it up for the Journal of Irreproducible Results, remember to use 'heuristic' rather than 'rule of thumb', and 'perceived likelihood' rather than 'hunch'. Sounds better.
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Don't feel bad - Paul Erdos got it wrong!
I'm actually a bit surprised by it. In my mind, you should always switch doors after being shown one that doesn't contain the prize. The key is knowing that your original choice remains at a 1-in-3 chance of being right, whereas the odds just doubled the other door is the correct one.
It seems to me that the strategy of opening one of the two "not-prize" doors is basically to ensure you do something, preferably not calculate the odds. It's a psychological distraction. The player knows they didn't pick "that" wrong door, so they get a false sense of knowing the right answer. So they'll stick with their original guess, forgetting it actually is a guess. What they should be thinking is "I got that one right, so it's not that door. The chances of me being right on the original door remain at 1 in 3; I should switch my choice, the odds have just been improved to 2 in 3."
Interesting. Very interesting. :-)
I know the logic of this -- I was one of those who wrote a program to simulate it, and was amazed. I just don't believe it. It feels like the joke about the guy who carries a bomb on board a board because while the odds against a single bomb are high, the odds against TWO are astronomical.
Its funny, I always tell my students that when picking a multiple choice answer, go with your original choice. The reasons are that in the real world, there are no truly random "door number one, door number two, door number three" scenarios. And I proved to my satisfaction over three years or so of monitoring pop quizzes that the "hunch" knows something. The "hunch" of course, might well be the subconscious mind (though not being a pscychologist I hesitate to use such fanciful phrases)
You use the "hunch" a lot in day to day life. Driving for instance. When you have a Monty Hall problem, you handle it just like a "should I go right or left at this intersection" problem.
Knowing odds is what separates the professional poker player from the mere duffer...but poker is MUCH more complicated.
I ran across this problem several years ago...I really MUST sit down to try and duplicate the experiment. Should not be too hard...
Don't go broke doing it. And when you write it up for the Journal of Irreproducible Results, remember to use 'heuristic' rather than 'rule of thumb', and 'perceived likelihood' rather than 'hunch'. Sounds better.
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