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May 1st, 2013, 06:21 PM   #1
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Face down paper strategy

Three pieces of paper each have one random number written on them. They are
placed upside down on a table. The objective is to choose the slip with the
highest number on it.
The rules are: You may turn over any one of the three papers and look at its
number. If you think it is the highest, then keep that paper and stop. Otherwise,
discard that paper and choose a second one. You may then either keep the second
one or discard it and take the last paper, in which case you must keep that one.
1. Is there any strategy you may use to increase your chances of winning, or will
it make no difference how you play the game?
2. If there is a superior strategy, describe it. If there is none, then explain why.
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May 1st, 2013, 06:54 PM   #2
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Re: Face down paper strategy

If you turn over a sheet and discard it in favor of another, what do you know about the two numbers? From that, what is the probability that the third sheet, or the second sheet (given it is higher than the first) is the highest number? If you keep the first sheet, what is the probability it is the highest?
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May 1st, 2013, 08:09 PM   #3
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Re: Face down paper strategy

All numbers > 0 ?
All numbers different?
Is there a limit? Or is 100000000000000000000000000.........00000000000000 000000000000000 possible?
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