Not sure what a roller mouth gag is but maybe this will help? I have added pics of the two types that I have mentioned.
True gag bits offer a "head raising" effect by working on the corners of the lips, accentuating the action of a normal snaffle. They can assist the rider with a horse that tends to travel with his nose to ground, but should only be used by a competent rider with independent seat and hands.
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The Dutch Gag is a leverage bit, it's strength depending on the number of rings. Contrary to belief it's main effectiveness comes from pressure across the jaw rather than the poll.
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How is a Dutch gag not a leverage bit? You attach the bit to the bridle on the top ring and the reins attach to any of the rings below applying varying amounts of leverage the lower you go. Just because it does not have a lip strap or curb chain on it does not make it any less of a leverage bit.A Dutch gag is NOT a leverage bit. It could only apply leverage if you used a curb chain/strap on it, which it is not designed to be used with. It adds poll pressure, not leverage.