Fontaine plays a rather minor role in the development of probability. In the Mémoires donnés à l'Académie royale des sciences, non imprimés dans leur temps published in 1764, we find a short work on the Petersburg Problem entitled "Solution d'un Problème sur les Jeux de Hasard." The date of composition is unknown. To accompany this piece there is a commentary and a Maple worksheet generating his solution.
Of course, for the Petersburg problem see Montmort, Nicolaus Bernoulli and Daniel Bernoulli.