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With assassin's action and vorpal weapons that have xd4 damage dice, would the rolls of 1, 2 or 3 that become 4 damage get rerolled via the vorpal property?

Assassin's Action:

when you spend an action point to make an attack, and you roll a 1, 2 or 3 on any damage die associated with that attack (including extra damage from assassin's strike or critical hit dice), that die instead deals 4 damage.

Vorpal weapon:

Whenever you roll the maximum result on any damage die for this weapon, roll that die again and add the additional result to the damage total. If a reroll results in another maximum damage result, roll it again and keep adding.

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Assassin's Action does not trigger Vorpal.

Let's look at the wording in Assassin's Action (emphasis mine)...

When... you roll a 1, 2 or 3 on any damage die ... that die instead deals 4 damage.

...and in Vorpal weapon (emphasis again mine):

Whenever you roll the maximum result on any damage die for this weapon...

Assassin's Action doesn't treat the die as a 4, nor does it let your re-roll until you get a 4. It just says if you roll less than a 4 on a damage die you deal 4 damage instead of whatever you rolled. Vorpal weapon is explicitly triggered by getting the maximum value on the die; it doesn't care how much damage the die dealt, it cares about the actual number that was rolled, which Assassin's Action doesn't affect.

Assassin's Action gets you bonus damage when you roll less than a 4, and Vorpal weapon gets you another die when you roll a 4 (on a 1d4), but no single die can benefit from both effects.

After the first time people found a way to deal infinite damage with Vorpal weapon (Battle Engineers could originally give a weapon brutal 1, or increase its brutal rating by 1 if it was already brutal), that method was promptly errata-ed and WotC was pretty careful from then on about not adding any other ways to guarantee you always got a 4 on d4 damage dice.

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