The envelope paradox dates back at least to 1953, when [[Belgians|Belgian]] mathematician [[Maurice Kraitchik]] proposed a puzzle in his book ''Recreational Mathematics'' concerning two equally rich men who meet and compare their beautiful neckties, presents from their wives, wondering which tie actually cost more money. He also introduces a variant in which the two men compare the contents of their purses. He assumes that each purse is equally likely to contain 1 up to some large number ''x'' of pennies, the total number of pennies minted to date. The men do not look in their purses but each reason that they should switch. He does not explain what is the error in their reasoning. It is not clear whether the puzzle already appeared in an earlier 1942 edition of his book. It is also mentioned in a 1953 book on elementary mathematics and mathematical puzzles by the mathematician [[John Edensor Littlewood]], who credited it to the physicist [[Erwin Schrödinger]], where it concerns a pack of cards, each card has two numbers written on it, the player gets to see a random side of a random card, and the question is whether one should turn over the card. Littlewood's pack of cards is infinitely large and his paradox is a paradox of improper prior distributions.
[[Martin Gardner]] popularized Kraitchik's puzzle in his 1982 book ''Aha! Gotcha'', in the form of a wallet game:
