Forum: Probability
10-03-2002, 04:37 PM
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Replies: 36
Views: 635
Best Possible Stuffer Strategy for Game #2
Lorinda,
I believe that your solution is the best possible stuffer strategy! /forums/images/icons/ooo.gif (i.e. That is the highest expectation that the stuffer can get if she tells the...
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Forum: Probability
10-03-2002, 04:02 PM
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Replies: 36
Views: 635
Re: Envelopes! (Problem #1) Long
Heihojin,
Great observations. Any monotonically increasing switching function beats random. (i.e. 0 <= f(L) < f(H) < 1 when L < H).
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Forum: Probability
10-03-2002, 08:38 AM
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Replies: 36
Views: 635
Re: Envelopes! (Problem #1) Long
Heihojin,
The value of Pseudo's Y solution is easy to explain. Assume that the stuffer has a probability distribution for stuffing envelopes. For example, suppose his distribution is
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Forum: Probability
10-02-2002, 11:03 PM
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Replies: 36
Views: 635
Re: Envelopes! (Problem #1)
Picking any number Y before opening the first envelope and switching whenever the envelope contains less than Y has a higher expectation than random as long as there is any chance that the stuffer...
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Forum: Probability
10-02-2002, 10:48 PM
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Replies: 36
Views: 635
Re: Commentary on Solution to game #2
Often the game theory will answer the following question:
In a particular game, what is the best strategy I can have if my opponent knows or guesses my strategy?
For example in rock, paper,...
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Forum: Probability
10-02-2002, 04:33 PM
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Replies: 36
Views: 635
Commentary on Solution to game #2
>pick a random number from the set {1, 2, 4, 8, 16, 32, 64, 128, 256} and put it in the low envelope.
Many people had very interesting stuffer and guesser strategies. I don't have time right now...
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Forum: Probability
10-01-2002, 03:12 PM
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Replies: 36
Views: 635
Re: Envelopes!
Pseudo,
If the two players in game #2 (stuffer and guesser) are permitted to collaborate, then their combined expectation is $666 as in your solution.
If no communication is permitted...
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Forum: Probability
09-30-2002, 09:59 AM
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Replies: 36
Views: 635
Worst Strategy for game 2
Carl wins the ribbon for finding the worst envelope stuffer strategy for game #2. If the stuffer puts $333 in one envelope and $666 in the other, then you always win $666. The stuffer wins nothing.
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Forum: Probability
09-29-2002, 09:19 PM
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Replies: 36
Views: 635
Clairification of question #2
Carl,
For game 2, the $1000 is just the maximum amount that can be put into the envelopes. You want to do your best to guess which envelope has the most money because you get to keep the money...
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Forum: Probability
09-29-2002, 12:32 PM
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Replies: 36
Views: 635
Envelopes!
Two envelope questions to think about:
1) A kind man tells you that he has two envelopes each with money in them. He says that you can choose either envelope, open it, and keep the money in that...
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