Let Xt+1 = Xt bt where +bt and -bt occur with equal probability bt is measurable !1t, and the outcome bt is measurable !1t+1 (in other words, my "bet" bt can only depend on what has happened so far and not on the future, but my knowledge !1t includes the outcome of all past bets). Then {Xt|!1t} is a martingale.
The Martingale System is commonly compared to betting in a casino with the hopes of breaking even. When a gambler who uses this method experiences a loss, they immediately double the size of the next bet. By repeatedly doubling the bet when they lose, the gambler, in theory, will eventually even out with a win.
