Wednesday, August 12, 2015

The D&D Guidebook, 3rd Edition Part 2: Let’s Talk About All That Funny Math

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.
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


  1. Funny this is where you would start.
    I don't think I ever, used or was even aware of the 3ED "new math."

    1. I like the funky math so I thought it would be a great place to start.

  2. Stupid blogger has messed up my formatting and I can't get it to look right. Stupid blogger.

  3. I wouldn’t call it funny math. No doubt this could be better explained in actual math terms. Call it a coefficient rather than a multiplier or somesuch? But the game needs to start with just basic arithmetic and explain the concept the hard way.

    1. I can see what you're saying Robert, but it still seems like funny math to me since it only applies under certain circumstances and is called multiplication but should be treated like addition. It's weird.


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