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Topic: **Military history/Early Muslim military history**

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# Two Envelopes Problem

The **two envelopes problem**, also known as the **exchange paradox**, is a brain teaser, puzzle, or paradox in logic, probability, and recreational mathematics. It is of special interest in decision theory, and for the Bayesian interpretation of probability theory. Historically, it arose as a variant of the necktie paradox.
The problem typically is introduced by formulating a hypothetical challenge of the following type:

It seems obvious that there is no point in switching envelopes as the situation is symmetric. However, because you stand to gain twice as much money if you switch while risking only a loss of half of what you currently have, it is possible to argue that it is more beneficial to switch. The problem is to show what is wrong with this argument.

### Discussed on

- "Two Envelopes Problem" | 2022-05-30 | 249 Upvotes 300 Comments
- "Two envelopes problem" | 2013-11-11 | 11 Upvotes 1 Comments
- "Two envelopes problem" | 2013-09-14 | 42 Upvotes 88 Comments
- "Two Envelopes Problem" | 2010-08-06 | 112 Upvotes 88 Comments