It boils down to being super patient on stage and getting good reads on a Villager off stage. Zard actually has pretty good tools to edgeguard Villager with imo. When Villager is trying to get back from above or even with the stage level, fair is big/somewhat fast/quite strong, you have an extra jump to bait and position with, and you have armor. Not to mention a pretty good spike to threaten a low Villager recovery. I recommend staying slightly below and in front of Villager so his fair can't threaten you and you can respond to a Lloid or dair. Fair is fast enough to be unreactable so you put them in a position where they have to try and hit you or guess when you try to fair them. It's kind of how M2K recommends gimping Cloud and although Villager up b has huge distance, forcing him to use it should still be your goal (if you can't outright kill) because it's completely non-threatening and allows you to try and hit him with your big, strong moves. Neutral is not easy and the reason why Villager has an advantage but it's not terrible. Jab is incredible in this matchup if you can get in range of it.
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