Two envelopes problem: Difference between revisions

Revision as of 08:11, 12 May 2024

Revision as of 08:41, 13 May 2024

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{{Cquote|Imagine you are given two identical [[envelope]]s, each containing money. One contains twice as much as the other. You may pick one envelope and keep the money it contains. Having chosen an envelope at will, but before inspecting it, you are given the chance to switch envelopes. Should you switch?

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Since the situation is symmetric, it seems obvious that there is no point in switching envelopes. On the other hand, a simple calculation using expected values suggests the opposite conclusion, that it is always beneficial to swap envelopes, since the person stands to gain twice as much money if they switch, while the only risk is halving what they currently have.<ref name=":5" /> While this may appear paradoxical, in fact one stands to double only the ''smaller'' amount, but risks losing half the ''larger'' amount, so in fact the gains and losses even out.

==Introduction==