History
Originally, martingale referred to a class of betting strategies that was popular in 18th century France. The simplest of these strategies was designed for a game in which the gambler wins his stake if a coin comes up heads and loses it if the coin comes up tails. The strategy had the gambler double his bet after every loss so that the first win would recover all previous losses plus win a profit equal to the original stake. As the gambler's wealth and available time jointly approach infinity, his probability of eventually flipping heads approaches 1, which makes the martingale betting strategy seem like a sure thing. However, the exponential growth of the bets eventually bankrupts its users, assuming the obvious and realistic i.e. finite bankrolls (one of the reasons casinos, though normatively enjoying a mathematical edge in the games offered to their patrons, impose betting limits). Stopped Brownian motion, which is a martingale process, can be used to model the trajectory of such games.
The concept of martingale in probability theory was introduced by Paul Pierre Lévy, and much of the original development of the theory was done by Joseph Leo Doob among others. Part of the motivation for that work was to show the impossibility of successful betting strategies.
Read more about this topic: Martingale (probability Theory)
Famous quotes containing the word history:
“You that would judge me do not judge alone
This book or that, come to this hallowed place
Where my friends’ portraits hang and look thereon;
Ireland’s history in their lineaments trace;
Think where man’s glory most begins and ends
And say my glory was I had such friends.”
—William Butler Yeats (1865–1939)
“The history of a soldier’s wound beguiles the pain of it.”
—Laurence Sterne (1713–1768)
“The history of all hitherto existing society is the history of class struggles.”
—Karl Marx (1818–1883)