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Litany of Righteousness doubles damage.
Smite doubles damage vs evil undeads.
How would you calculate damage when an evil undead is under the effect of Litany of Righteousness and the paladin attacks with Smite Evil?
Is it:
Normal Smite: 10 dmg
Smite vs undead: 20 dmg
Smite + Litany vs undead: 40 dmg
or:
Normal Smite: 10 dmg
Smite vs undead: 20 dmg
Smite + Litany vs undead: 30 dmg (this uses the 3.5 method of doubling a double)

Wiggz |

Litany of Righteousness doubles damage.
Smite doubles damage vs evil undeads.How would you calculate damage when an evil undead is under the effect of Litany of Righteousness and the paladin attacks with Smite Evil?
Is it:
Normal Smite: 10 dmg
Smite vs undead: 20 dmg
Smite + Litany vs undead: 40 dmgor:
Normal Smite: 10 dmg
Smite vs undead: 20 dmg
Smite + Litany vs undead: 30 dmg (this uses the 3.5 method of doubling a double)
Common sense and basic math would suggest the first, but I'm pretty sure it would be the second, using the precedent set for things like critical hits (i.e. x2 doubled = x3).

Gauss |

Smite Evil does NOT double any damage.
If the target of smite evil is an outsider with the evil subtype, an evil-aligned dragon, or an undead creature, the bonus to damage on the first successful attack increases to 2 points of damage per level the paladin possesses.
Nothing about doubling, it uses a different calculation for the Smite Evil damage.
So if normal smite is 10 and smite vs Undead is 20 then Smite vs Undead +Litany of Righteousness is 40 damage.
- Gauss

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Note: When you multiply damage more than once, each multiplier works off the original, unmultiplied damage. So if you are asked to double the damage twice, the end result is three times the normal damage.
So in any ways whenever anything is doubled, trippled, or otherwise enhanced by a multiplier you add from the original.
x2 doubled = x3 etc
But Smite may or may not be a double effect. Ask your GM how he is going to rule it.

master_marshmallow |

Sunblade. $#!t happens.
The damage from smite itself is what changes for the purpose of calculating base damage.
For example, we have 1d10 + STR + smite.
Undeads and Evil Dragons take 1d10 + STR + 2smite.
Under LoR and going against undead we have that doubled for something like:
2(1d10 + STR + 2smite)
Distributive Property
2d10 + 2 STR + 4smite
Another effect that doubles this, such as a sunblade or spirited charge actually adds another of the base damages, rather than multiplying them for something like this:
3(1d10 + STR + 2smite)
Distribute
3d10 + 3 STR + 6smite
Having a sunblade-lance and charging, or performing a critical would make the damage add another multiplier:
4d10 + 4 STR + 8smite