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Standing and Irish martingales are not allowed.
The Irish martingale is not a true martingale in the sense of a device that affects the rider's control over the horse.
The Irish martingale
The Irish martingale's purpose is not to control the head, but to prevent the reins from coming over the horse's head, risking entanglement, should a rider fall.
Irish martingale: Unlike the previous designs, this very simple "martingale" does not control the height of the horse's head, but merely keeps the reins from going over the horse's head in the result of a fall.