There is a well-known brainteaser based on the Lets Make a Deal show, wherein the contestant picks one of three doors -- one of which has a nifty prize, two of which do not. The contestant having picked one, but not seen if the prize is nifty or not, the host opens one of the other two doors, always opening a door that has a bogus prize, and then asks if you want to switch doors of the two remaining ones. (A nice description of this brainteaser can be found here.)
Having read that site, you know that the person tried a simulation, doing the exercise one hundred times, and found that the originally chosen door was the one with the nifty prize 35 times, while the second door (the remaining one - remember, the host has already opened one door) had the nifty prize 65 times. I read this to my wife, and we both thought Oh, that must be bogus. So we decided to try it ourselves.
Being impatient, we tried the same stunt ten times. One card was the prize card; two were the bogus cards. I picked one, she removed another, and I then switched to the third.
Three of ten times, the first card would have won.
Seven of ten times, the second card won.
What the heck is going on here?
2 comments:
Thats a fairly classic "Lady and the Tiger" problem. I have seen it explained. I have had it explained to me. Your results are perfectly statistically valid.
I have no idea why. they just are.
Now Texas Hold'em has 52 variables instead of just three. No wonder there are so few winners.
Come by my blog for a coffee....and sort this out.
Lady and the Tiger...interesting. I hadn't heard it put that way before.
When I was (briefly) thinking about it, I kept going back to the idea that the odds for each door were 1/3, no matter if they were open or not. Once you opened one, you knew whether that 1/3 had panned out, but the odds were still that. Further, if you took any two doors, the odds were 2/3, if you opened them or not.
The part that nails me is the switching. I keep thinking of phrases like 'collapsing the wavefunction', but that way lies insanity. At least for me.
Thanks for the invitation. I might just do that.
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