If a creature has DR 3, and is hit by a weapon that does 1d8 damage, then the damage it will take is between 0 and 5. I think I understand that part.
What I really want help with is understanding how to apply Damage Reduction in various situations, what are the edge cases for it?
If a creature has DR 3, but only protects against slashing, and is hit with something that does 2d6 damage (1d6 slashing and 1d6 fire), what steps should I be going through to calculate the final damage?
Finally, for something like Flurry of blows, if a Monk can attack something multiple times, I am under the assumption that each attack applies DR separately. Does that also apply to individual die rolls? So if each attack in flurry of blows does 2d6 damage, is a DR of 3 going to cap each attack's damage at 6? (After all, it's supposed to be a flurry of blows, so is each attack itself composed of multiple punches?)
Any additional clarification as to how Damage Reduction works, even if not explicitly stated in this question, would still be appreciated. I get the feeling that I have a lot to learn, and may even have to un-learn some things.
Best Answer
DR is deducted per hit, not per die.
Flurry of Blows suffers a deduction to each successful hit. Each attack's damage roll is totaled up separately from each other, and DR is applied to each separately. If a Monk hits with 3 attacks out of 7, then the DR applies three times, once to each individual damage roll total.
DR from multiple sources do not stack.
On a per attack level, you simply apply the strongest source of DR.
If you make multiple attacks of different damage types per round (deciding to slash instead of pierce with a weapon at the end of a full attack), then the best DR source may be different for each attack.
Certain damages bypasses DR
Energy damage (such as Fire), Damage from Spells, and Damage from Supernatural Abilities will generally not be reduced by DR unless otherwise stated.
Generally, the sources of damage reduced by damage reduction are Slashing, Piercing, Blunt, and untyped physical damage (such as that from from falling).
DR/X or DR/-
This format may be confusing. Instead of this DR applying to the damage type X, it applies to everything else. This was not directly asked by the asker, but it's important to address to someone who's not familiar with the DR system.
DR vs. Slashing/Piercing/Blunt/etc.
Each type of damage dealt by an attack is separated into totals for each type/element. The defender's best DR is chosen and deducted from the relevant totals.
If any damage type is reduced to 0 damage, DR has no further effect on that damage type. For example, if only part of your damage is piercing, but the piercing DR would reduce that piercing damage to below 0, it instead reduces it to 0. If this would reduce all damage dealt by an attack to 0 total damage, the damage is ignored altogether as well as most special effects that accompany the attack, such as injury poison, a monk's stunning, and injury-based disease.
Putting it all together
Dealing +1d6 Piercing +1d6 Fire with a +4 STR bonus flurrying for 4 times against a DR 1/Slashing, 3 DR vs. Piercing, 1 DR vs. Slashing:
The best DR source the defender has for each attack is 3 DR vs. Piercing, so it is applied.
1d6+1 P +1d6 Fire
1d6+1 P +1d6 Fire
1d6+1 P +1d6 Fire
1d6+1 P +1d6 Fire