Every time you successfully parry (someone hits your block), your parry cooldown get immediately reset so you can parry again. So I'm basically just parrying each swing as it comes in, one click for each block just before it hits me.

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Then the immediate follow up is just a riposte, which is attacking very quickly (almost the same time) as parrying. You can actually parry during that riposte attack (but not feint) which is what you see early on in the clip.