Shortly after you open the 3e Dungeon Master’s Guide
(DMG) you’ll find a little section titled General Guidelines. It’s here that
the mathematics that you’ve grown up with are going to begin abandoning you and
it’s here that our exploration of 3e really beings.
Rounding Fractions
In 3e you’re going to encounter fractions and like when
you were in elementary school these fractions are always to be rounded to the
nearest whole number. Only unlike the math you learned alongside your letters
and what it means when a pretty girl slides you a note asking if you want to be
her boyfriend in Third Edition there is no artificial demarcation line drawn at
1/2. Everything rounds down to the lowest number – except for when it doesn’t. Certain
types of damage, hit points, and on a few other occasions it isn’t possible for
the math to give you a result lower than one.
Congratulations, we’ve just run into our first exception
of the game and we’re only on page six of the 3e DMG. Get ready because there
are going to be a lot more.
Multiplying
So let’s talk about how you multiply in 3e because this
is going to come up eventually in any game you play. Now normally multiplication
works as it always has when you have a single multiplier. For example, if you
make a critical hit (the best result in combat) then your weapon damage is
multiplied by its critical modifier as always (the numbers here for new players
are going to look a bit crazy but don’t worry about them right now as this is
just putting a little bug in your ear so that you will remember it later). Let’s
say that your fighter is swinging a war-hammer which has a X3 critical modifier.
When you roll that critical you multiply your normal damage as follows:
3(1d8+6) = 3(1d8)
+ 3(6) = 3d8 + 18
Pretty standard stuff, right?
Now where things get weird is when you have an additional
multiplier to factor into the equation for combat. Let’s say that you have a
special magical effect that happens when you fight a particular enemy that
multiplies your damage by two every time you attack that creature with your war-hammer,
and on this particular occasion you score a critical. How would you imagine
that you would combine those two multipliers? For some of you it would be
obvious that you should follow the order of operations. First you would resolve
the doubling of the damage, since it happens every time you attack that enemy,
and then applying the triple for the critical to arrive at a result similar to
this:
3[2(1d8+6)] =
3[2(1d8) + 2(6)] = 3[2d8 + 12] = 3(2d8) + 3(12) = 6d8 + 36
Not so fast my friend. In 3e you combine the multipliers
through an addition of a subtraction. Sound odd?
It is.
When you have two multipliers in combat you’re supposed
to take one away from the lesser of the two multipliers and add the results.
Let’s again consider our magical war-hammer and the critical strike. 3e would
like us to combine the 3 multiplier and the 2 multiplier, minus one. This
results in a multiplier of 4. To put it in a mathematical formula:
((3 + 2) – 1)(1d8
+ 6) = (5 – 1)(1d8 + 6) = 4(1d8 + 6) = 4(1d8) + 4(6) = 4d8 + 24
In the revision of 3e, lovingly referred to as three-five,
this would be explained as follows:
“. . . Another way to think of it
is to convert the multiplication into additions. Tordek’s critical hit
increases his damage by 2d8 + 12, and the dwarven thrower’s doubling of
damage increases his damage by 1d8 + 6, so both of them together increase his
damage by 3d8 + 18 for a grand total of 4d8 + 24 . . .” (Tweet, 304)
Over the years I’ve played Third Edition using both
systems of math, that found in the real world and that found in 3e, and
honestly, the game plays better when you use the 3e method. Oh, it’s a strange
math all right, but the game is more challenging and exciting when you use it.
Before we close up this section of the Guidebook I should
note that at the time 3e was first published the multiple multiplier rule was
confusingly written and implied that this sort of math should be applied to all
situations where multiple multipliers were in play. This would be cleared up in
the revision of the game to show that only combat modifiers as described above
should be handled in this way. All other similar situations should be handled
like the rest of the world deals with all math: in a standard order of
operations, with a calculator, and avoided whenever possible.
Works Cited:
Tweet, Johnathan. Dungeons & Dragons Player’s
Handbook, Core Rulebook I v.3.5. USA: Wizards of the Coast, Inc., 2003.
Print. 304
