Well heck though, a saddle would be a gadget too though, as would a bit - the most amazing training ever seen is done without any gear on the horse at all

But really on a personal preference though, I do like the running better than standing martingales. The Standing martingales can tend to lead a horse to "lean" onto them (sometimes, not as much with hotbloods) weras with a running martingale, you can be in more control of the pressure yourself and still be able to reward the horse with your hands.