If I give a monster a powerful magic item, should I
increase its CR?
Yes, but only if the item has a dramatic effect on the monster’s statistics. Remember that increasing a monster’s CR by even a single point can increase the XP award by 50%, so it shouldn’t happen very often.
There’s no hard-and-fast rule for adjudicating this, but a general rule of thumb might be this: To increase a monster’s CR by +1, the added equipment should make it function as if it were at least a level or two tougher than normal (including hp, attack modifier, damage, saves, and so on). Changes smaller than that aren’t enough to merit a CR change but might still merit an ad hoc XP adjustment (such as +10% or so). In the long run, it’s probably not worth the DM’s time to adjust XP awards too much, though.
Giving a CR 3 ogre a masterwork greatclub makes it marginally tougher, but certainly not as tough as a CR 4 monster. Giving it full plate armor, an amulet of health +2, and a +1 flaming greatclub increases its AC by 4 points, its hp by 4, its Fortitude save by +1, its attack by +1, and its damage by 4
or 5 points per swing, which might well merit an increased CR. (Of course, it still has poor Reflex and will saves, making it just as vulnerable to many effects, so it’s arguable that this ogre isn’t truly a CR 4 monster.) The right two or three extra potions might well change a 1st-level warrior from CR 1/2 to CR 1 if the potions had a great effect on his AC, attack modifier, hp,
and damage rolls, but the same potions probably wouldn’t alter the CR of a frost giant (since they reflect a smaller change, relative to the giant’s original statistics).
Remember also that many monsters, including all NPCs, are assumed to have equipment already. Don’t adjust the ogre barbarian’s CR for the gear he gets from his class levels, or the dragon’s CR for the magic items it’s using out of its hoard. A dragon wielding a staff of the magi or sphere of annihilation might merit a CR adjustment, but one wearing a ring of protection and carrying a few potions certainly wouldn’t.
