(probability:) Named after a gambling system. Any sequence of random variables X_1, X_2, ... satisfying E(X_n | X_{n-1},...,X_1) = E(X_{n-1}).

Martingales have important convergence properties. For example, monotone and l2 martingales converge almost always (pointwise).

Mar"tin*gale (?), Mar"tin*gal (?), n. [F. martingale; cf. It. martingala a sort of hose, martingale, Sp. martingala a greave, cuish, martingale, Sp. almartaga a kind of bridle.]

1.

A strap fastened to a horse's girth, passing between his fore legs, and fastened to the bit, or now more commonly ending in two rings, through which the reins pass. It is intended to hold down the head of the horse, and prevent him from rearing.

2. Naut.

A lower stay of rope or chain for the jib boom or flying jib boom, fastened to, or reeved through, the dolphin striker. Also, the dolphin striker itself.

3. Gambling

The act of doubling, at each stake, that which has been lost on the preceding stake; also, the sum so risked; -- metaphorically derived from the bifurcation of the martingale of a harness.

[Cant]

Thackeray.

 

© Webster 1913.

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