crumbcake
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May 20, 2013, 07:06:44 PM

If you are offered to swap as often as you want, with your new envelope randomly holding double or half the money of the one before, then you should swap endlessly often (lets say: as often as feasable).
After all of your swaps, the chance that you get more than 100$ from your envelope is almost 50%, the chance that you get less than 100$ is also almost 50% (and a small chance that you hold exactly 100$).
However, if you get more than 100$ in your envelope, you get at LEAST 200$, but possibly much more. If you get less than 100$, you will still never get less than 0$.
Every swap will increase your expected return (too lazy to research the exact equation though).

 Wink

see electricmucus's link: http://en.wikipedia.org/wiki/Two_envelopes_problem ?