martingale

1. The strap of a horse's harness that connects the girth to the noseband and is designed to prevent the horse from throwing back its head.
2. Nautical. Any of several parts of standing rigging strengthening the bowsprit and jib boom against the force of the head stays.
3. Games. A method of gambling in which one doubles the stakes after each loss.
4. A loose half belt or strap placed on the back of a garment, such as a coat or jacket.

[French, perhaps alteration of Spanish almártaga, almártiga, rein, harness, perhaps of Arabic origin.]

The sequence of random variables X₁, X₂,...(with finite expectations) is a martingale if the of X_n+1, given the values of X₁, X₂,..., X_n, is given by E(X_n+1|X₁=x₁, X₂=x₂,..., X_n=x_n)=x_n.An example is provided by letting X_n be the amount of a gambler's winnings after the nth of a sequence of fair games.

A leather strap running from the girth to the reins or the noseband for the purpose of restricting the movements of the horse's head. There are many designs. The common ones are the standing martingale, which is attached to the noseband, and the running martingale, which is divided in two, each of which has a ring through which one of the reins passes.

Martingale can refer to:

• Martingale (probability theory), a stochastic process in which the conditional expectation of the next value, given the current and preceding values, is the current value
• Martingale (tack) for horses
• Martingale (collar) for dogs and other animals
• Martingale (betting system)
• Martingale (rigging)
• In the sport of fencing, a martingale is a strap attached to the sword handle to prevent a sword from being dropped if disarmed.
• In the theatrical lighting industry, martingale is an obsolete term for a twofer, or occasionally a threefer.

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