CentralNotice From Wikipedia, the free encyclopedia Jump to: navigation , search This article's tone or style may not reflect the encyclopedic tone used on Wikipedia . See Wikipedia's guide to writing better articles for suggestions. (August 2013) 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: Of two indistinguishable envelopes , each containing money, one contains twice as much as the other. The subject may pick one envelope and keep the money it contains. Having chosen an envelope a...