The envelope paradox dates back at least to 19531943, when Belgian mathematician [[Maurice Kraitchik]] proposed a puzzle in his book ''Recreational Mathematics'' concerning two equally rich men who meet and compare their beautifulfine neckties, presents from their wives, wondering which tie actually cost more money.<ref Hename=brown>{{Cite alsojournal introduces|last=Brown a|first=Aaron variant in which the two men compare the contents of their pursesC. He|year=1995 assumes|title=Neckties, thatWallets, eachand purseMoney isfor equallyNothing likely to contain 1 up to some large number ''x''|journal=[[Journal of pennies,Recreational theMathematics]] total|volume=27 number|issue=2 of|pages=116–122 pennies}}</ref><ref mintedname=kraitchik>{{cite tobook date.|first=Maurice The|last=Kraitchik men|authorlink=Maurice doKraitchik not|title="Mathematical lookRecreations" in|publisher=George theirAllen purses& butUnwin each reason that they should|___location=London switch|year=1943|url=https://archive.org/details/mathematicalrecr0000maur}}</ref> HeEach doesof notthem explainknows what ishis theown errornecktie inis theirworth reasoning.and Itagrees is not clear whetherfor the puzzlewinner alreadyto appearedgive inhis annecktie earlierto 1942the editionloser ofas his bookconsolation. It isKraitchik also mentioned indiscusses a 1953variant bookin on elementary mathematics and mathematical puzzles bywhich the mathematiciantwo [[Johnmen Edensor Littlewood]], who credited it tocompare the physicistcontents [[Erwinof Schrödinger]],their wherepurses. itHe concernsassumes a pack of cards,that each cardpurse hasis twoequally numberslikely writtento oncontain it,1 the player getsup to seesome alarge randomnumber side''x'' of a random cardpennies, and the questiontotal is whether one should turn over the card. Littlewood's packnumber of cardspennies isminted infinitelyto large and his paradox is a paradox of improper prior distributionsdate.
The puzzle 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:
