The history of the martingale

The other day I found myself wondering “so what does the word martingale come from?” A short time on Google later, I came across this paper from Journal Electronique d’Histoire des Probabilités et de la Statistique, which had a special issue on The Splendors and Miseries of Martingales (Splendeurs et misères des martingales):

The Origins of the Word “Martingale”
Roger Mansuy
(earlier version : “Histoire de martingales” in Mathématiques & Sciences Humaines/Mathematical Social Sciences, 43th year, no. 169, 2005(1), pp. 105–113.)

It’s 10 pages and worth a read just for fun. Some of the fun facts:

• Doob is the one who really made the name popular (in addition to proving many fundamental results). He got the name from a thesis by Ville.
• A martingale is the name for a Y-shaped strap used in a harness — it runs along the horse’s chest and then splits up the middle to join the saddle.
• A martingale is a name for a betting strategy (usually we think of doubling bets) but it’s not clear which one from the historical record.
• “To play the martingale is to always bet all that was lost” (dictionary of the Acad ́emie Fran ̧caise, 4th ed.) — there are earlier dictionary definitions too, to 1750.
• “A very slim trail seems to indicate a derivation of the word from the Provençal expression jouga a la martegalo, which means ‘to play in an absurd and incomprehensible way’.” Apparently Provençal is also the origin of Baccarat.
• So what is martegalo? It might refer to a place called Martigues, whose residents are supposedly a bit naïve.
• “Martingale pants” are from Martigues, and have, according to Rabelais, “a drawbridge on the ass that makes excretion easier.”
• There’s a woman in the 17th century who called herself La Martingale and who made a number of prophetic predictions.
• There were sailors called martégaux who gave their name to a rope called a martegalo used on sailboats. Perhaps this is where the horse connection comes in?
• Apparently “martingale” is also vernacular for “prostitute,” but the etymology for that usage is not well-documented.

All in all, perhaps this essay ends up raising more questions than it answers, but I certainly had no idea that there was this much to be unearthed behind a simple word.