Two envelopes conceal different amounts. Opening one seems to leave you entirely at the mercy of chance, yet that partial information can be used in an unexpected way.
After Opening the Envelope
Riddle statement
Two sealed envelopes contain different positive amounts of money.
You do not know the amounts, how they were chosen, or any range containing them.
Choose one envelope at random and open it. After seeing its contents, you must either:
- keep the opened envelope;
- switch to the other envelope, which remains sealed.
You may prepare a randomized strategy in advance, but you may obtain no additional information about the amounts.
Is there a strategy that, for every possible pair of distinct amounts, gives you a probability strictly greater than \(1/2\) of ending with the larger amount?