…subtracting twelve maintains the same odds with ties ‘succeeding’ for the rolling adversary; some instead subtract eleven and flip ties for the rolling adversary to lose which is mathematically identical, but then you have to keep track of flipping tie-resolution back-and-forth depending upon who’s rolling…
Perception +6, Trap DC 14 = Passive Perception 16, Trap +2
(both have 65% chance of detection)
Hm. That could work. But it would be quite tedious.
Also: why 12 and not 8? Doesn’t a DC calculate 8+prof+ability?
…subtracting twelve maintains the same odds with ties ‘succeeding’ for the rolling adversary; some instead subtract eleven and flip ties for the rolling adversary to lose which is mathematically identical, but then you have to keep track of flipping tie-resolution back-and-forth depending upon who’s rolling…
Perception +6, Trap DC 14 = Passive Perception 16, Trap +2 (both have 65% chance of detection)