A curb strap is typically used to apply pressure under a horse's jaw when the reins are pulled. When using a snaffle bit, there is no leverage to create that pressure. Yet people still use curb straps with the ring bits. You can see one in this Classic Equine photo attached behind the reins. While the curb doesn't function in the traditional 'curb' manner on a snaffle, this is a good safety feature. When you use a curb strap, you ensure that the rings of the snaffle bit will stay perpendicular, and on the horse's cheek, even if you have his head pulled around quite a ways.