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Not one for puzzles or brain-teasers but this one I like ...

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I'm not generally one for puzzles or brain teasers, but I just ran into one that is elegant in its simplicity, yet profound in its implications. I like it so much that I have posted it on a handful of other Internet forums. I guess I've had about ten responses - about five on target and five misses. Count me as a "miss" - I didn't figure it out until I did some online research about it.


Consider a deck of only three playing cards. One of the cards is a Joker. The other two cards could be anything - even duplicates of each other - anything but another Joker. Three cards, one Joker.


You play this game with a computer. The computer can only play fairly and exactly by the rules. The computer deals the cards face down in front of you, Left, Center and Right. The computer is perfectly randomized so that before the deal, the probability that the Joker will be dealt in any particular order (Left, Center or Right) is always one chance in three. After the deal, the computer always knows which card is the Joker.





The cards have been dealt. This is what the computer "sees" ...



Your objective is to select the Joker. You are perfectly versed in the rules of the game and about how the computer is programmed. But you cannot predict the outcome of the computer's randomizing calculations. At this point you can't do any better than a random selection of your own, so you point to one of the cards - Left, Center or Right. It doesn't make the slightest difference which one. Let's say you select the card on the Left.





This is what you see. You select the card on the Left ...



There is only one Joker, so whichever card you selected, at least one and possibly both of the other cards are losers. Whichever card you selected, the computer responds by facing one of the other cards and showing you a loser. If, on the strength of one chance in three, you selected the card that the computer knows is the Joker, then the computer has one additional computation to perform. It must decide which one of the two cards that you didn't select - both cards, losers - to reveal to you. It does so in a perfectly random way. It performs the software equivalent of flipping a coin to determine which one of the two losers to face.


After the computer shows you a loser, and only two cards remain face down, you have an option: You can play the card that you selected - or you can switch (renege) and play the last remaining card.





The computer has faced a loser from the cards that you didn't select (Center; Right). Should you play your selection - the card on the Left - or should you switch and play the last remaining card - the card in the Center ..?



You want to win. So what decision do you make? Or does it even make any difference to your odds of winning, whether you play your selection, or renege and play the other card?


Instead of posting, why not just send me a PM? I will respond with a link to a small essay that you can read online - and that way, you won't be "letting the cat out of the bag" for anyone else who wants to think about this. I will post only a statistical breakdown of the responses - no user names.



Images: Iraq Playing Cards. Courtesy of WNBC, New York City, New York.

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