He is famous for having inspired the two envelopes problem in 1953, with the following puzzle in La mathématique des jeux:
- Two people, equally rich, meet to compare the contents of their wallets. Each is ignorant of the contents of the two wallets. The game is as follows: whoever has the least money receives the contents of the wallet of the other (in the case where the amounts are equal, nothing happens). One of the two men can reason: "Suppose that I have the amount A in my wallet. That's the maximum that I could lose. If I win (probability 0.5), the amount that I'll have in my possession at the end of the game will be more than 2A. Therefore the game is favourable to me." The other man can reason in exactly the same way. In fact, by symmetry, the game is fair. Where is the mistake in the reasoning of each man?
Kraïtchik was « agrégé » of the Free University of Brussels, engineer at the “Société Financière de Transports et d'Entreprises Industrielles (Sofina)”, and director of the “Institut des Hautes Etudes de Belgique”.
Among his publications were the following:
- Théorie des Nombres, Paris: Gauthier-Villars, 1922
- Recherches sur la théorie des nombres, Paris: Gauthier-Villars, 1924
- La mathématique des jeux ou Récréations mathématiques, Paris: Vuibert, 1930, 566 pages
- Mathematical Recreations, New York: W. W. Norton, 1942 and London: George Allen & Unwin Ltd, 1943, 328 pages (revised edition New York: Dover, 1953)
- Alignment Charts, New York: Van Nostrand, 1944