Best Possible Stuffer Strategy for Game #2
Lorinda,
I believe that your solution is the best possible stuffer strategy! [img]/forums/images/icons/ooo.gif[/img] (i.e. That is the highest expectation that the stuffer can get if she tells the selector her strategy first.) Your solution has interesting properties:
1) If you open the randomly selected first envelope and it contains more than $2, then there is a 66.6664% chance that it is the larger envelope. (It seems very weird to me that when you open this "randomly" selected envelope, it is more likely to be the larger of the two envelopes! )
2) Even though there is a 66.6664% chance that it is the larger envelope, the guesser is forced to switch because he gets a 2 to 1 pay off on the amount risked.
It is neat that you force the switcher to switch even though is it more likely that he has the larger envelope.
Now, what is the best switching strategy?
(PS: I think you can get just a tiny tiny bit more expectation by going down to $1.)
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