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In D&D3e, if you successfully hit a target you always did at least 1 point of damage (before applying Damage Resistance), even if you had a Strength penalty. I can't find any mention of that rule in the 5e PHB. Does the rule no longer apply, or did I just overlook it?

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It is correct to say the 3.5e rule no longer appears in 5e. Another tweet (god I wish we had that back in the 90s) clarifies that the minimum is indeed 0.

JeremyCrawford
@JeremyECrawford
There is not a damage minimum of 1, so it is possible to deal 0 damage with an attack.

Jack Abrasion
@jackAbrasion
@JeremyECrawford Do attacks do a minimum 1 point of damage, or would an unarmed strike from a goblin (STR -1) do 0 damage?

8:56 AM - 11 Jun 2015

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There is no such rule in 5e.

An unarmed strike by someone (other than a monk or tavern brawler) with less than 10 strength will never do any damage, (even on a crit), for example.

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