# Re: Observation selection effects

`Addition to my last post:`

(1) The original game: envelope A and B, you know one has double the amount of the other, but you don't know which. You open A and find \$100. Should you switch to B, which may have either \$50 or \$200?

(2) A variation: everything is the same, up to the point where you are pondering whether to switch to envelope B, when the millionaire walks in, and hidden from view, flips a coin to decide whether to replace whatever was originally in envelope B with either double or half the sum in envelope A, i.e. either \$50 or \$200.

Say one envelope contains \$x and the other \$2x. If you keep the first envelope in game (2), and if you keep the first one OR switch in game (1), you should expect to win \$1.5x. If you switch in game (2), you should expect to win 0.25*(\$0.5x + \$2x + \$x +\$4x) = \$1.875x.

`Stathis Papaioannou`

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