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I would allow a +1 DC for the Death Attack for 5 ranks in Knowledge (anatomy) or Heal. But I would only allow skill ranks gained from levels of assassin or after the PrC is completed to count towards this total.
I would allow this because both Heal and Knowledge (anatomy) are cross-class skills for the Assassin, and 10 ranks (5 in either skill) represents a 20 skill point investment; a heafty sacrifice.
I would not allow ranks in those skills gained from other classes to count on the flavor basis that while a cleric may learn anatomy to heal, the assassin will study a specific curriculum for harming. There will be similarities, but enough of a difference for me to enforce it.
That hefty skill-point sacrifice will mechanically balance the assassin's synergy bonuses to the DC.
The DC is: DC 10 + the assassin’s class level + the assassin’s Int modifier
The only other ways of increasing the DC I know of are Ability Focus, which will add 2 to the DC, increasing the assassin's Int, and a magic item or two that might do the same. I don't think a total +2 synergy bonus from two skills is out of line.
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Shadow Assassin,
You weren't wrong for posting in the General Discussion forum, but there are forums for specific topics; The
House Rules forum is good for discussion on how to change the game the way you like it; the
Rules forum is good for sounding out the mechanics of the game as they are written; the
Off Topic forum is good for hanging out with other posters and talking about things other than D&D; and the
Meta forum is a great place to learn more about how ENWorld works.
Happy posting!