The armless guy has a higher chance of winning. Your legs are much stronger than your arm, and you can also kick much faster than you can punch. Even grappling, the guy with no arms can use his legs pretty well. If the guy with arms grabs one of his legs, the armless dude could still kick him. The worst the legless guy could do is probably a choke hold. Even then, the armless guy could probably bridge out of it. But if the armless guy has the legless guy in a figure four, then it's all over.
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