paradox · traps · decisions
Two envelopes paradox
An average win can be a bad reason to switch, or to play.
One envelope has more than the other. Do you switch?
One envelope holds twice the other. Yours is open.
You
Lock a side, then deal.
Lock a fee, then flip.
—This deal, stay · switch
—Average if you stay
—Average if you switch
One envelope holds twice the other. You may keep yours or take the other one.
The 5/4 story treats “twice as much” and “half as much” as equally likely after you look. The deals are not built that way.
Stay and switch pay the same average. The 5/4 story sits higher than either. In St. Petersburg the average prize grows when the coin may flip longer, and the prize you see most often stays 2.