Do you or don't you?
I found this on the 'net. Agree?
Curb chains or straps have no effect on a true snaffle because there is no leverage to act upon. English riders do not add any type of curb strap or curb chain to a snaffle bit. While some riders in western disciplines do add a curb strap to the rings, it is merely a "hobble" for the rings, has no leverage effect and is there only as a safety feature to prevent the rings from being pulled through the mouth of the horse, should the animal gape open its mouth in an attempt to avoid the bit.