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In probability theory, a martingale is a sequence of random variables (i.e., a stochastic process) for which, at a particular time, the conditional expectation of the next value in the sequence is equal to the present value, regardless of all prior values. Stopped Brownian motion is an example of a martingale.

How does the martingale work? Martingale puts pressure on the reins and horse's mouth when the animal wants to raise its head too high. This mechanism forces the horse to put its head down. In comparison to other similar equipment, martingale has a mild effect on the horse.