Green’s Dictionary of Slang

(gambling) to double the stakes every time one loses; also as n., this gambling method.

[1781		Belle’s Stratagem 23: Fifty guineas! Call in the evening with them [i.e. a pair of matched ponies] and you shall have your money, old Martingale!].
1823		‘Jon Bee’ Dict. of the Turf, the Ring, the Chase, etc. 117: Martingale – at play, to double stakes constantly, until luck taking one turn only, repays the adventurer all.
1849		Sydney Emigrants’ Jrnl 29 Mar. 202/1: If you will only find the funds, there are people at Baden Baden always ready to try an infallible Martingale.
1854		Thackeray Newcomes I 266: You have not played as yet? Do not do so; above all avoid a martingale, if you do.
1864, 1867, 1870		Hotten Sl. Dict.
1874		M. Collins Frances ix: He’s got an infallible martingale – breaks the bank everywhere [F&H].
1886		F. du Boisgobey Day of Reckoning 28: She is an old card-player, and is always running after an infallible ‘martingale’.
1895		C. Crowe Aus. Sl. Dict. 48: Martingale, in gambling, means doubling the stakes till you win back your losses.
1988		S. Förster et al. Bismarck, Europe and Africa 244: Leopold II was not a gambler [...] [b]ut in political terms he clearly corresponded to the gambler who thinks he has found an infallible martingale.