multiplication or addition?

[Khazan]

This question came up in this evening's session (homebrew 3.5): when spells or other attacks deal multiple die worth of damage (i.e., Fireball does xd6 of damage, a Warlock's Eldritch Blast does xd6 damage, etc), how does your DM allow the damage to be rolled?

For example, for a 7d6 damage effect, do you roll 7 actual 6-sided dice and add them up, or do you allow a roll of just 1 6-sided die and multiply by 7?

Two new players to our group were surprised to see that our DM allows us to roll a single die and multiply if we want. Of course, the DM does the same thing when opponents are damaging us, so it's an equitable way of rolling damage, and, for all the times we manage to roll a 5 and multiply by x (hooray!), there are the times when we unfortunately roll a 1 and multiply by x (ouch...).

I'm not well-versed in the mathematics of which method results in the higher damage, but since it came up in tonight's session, I'd thought I'd solicit some opinions. Thanks!

 

[Fifth Element]

The average damage is precisely the same - however the variation using the multiplication method is much, much higher.

For instance, rolling 7 dice and adding them up, the chance of you getting minimum damage (or maximum damage) is about 1 in 280,000 if I've done my maths right. When multiplying, the chance of getting a minimum result of 7 is 1 in 6, over 46,000 times more likely.

Rolling all dice and adding them up tends to give results close to the average (a bell curve). Rolling one die and multiplying just gives a straight line - each of the 6 possible results is equally likely.

 

[G-Man]

"I firstly need to say that my English is not that well but i hope everyone can understand what i'm trying to tell. Because of this, please forgive me if i use "wrong" words."


Multiplying damage rolls with x, just restricts damage unbalanced imo.
For example, level 6 wizard can cast fireball that deals 6-36 damage but this includes every single numbers between 6 and 36.
With that method you can only hit 6 - 12 - 18- ... - 36. It has same base damage as rolling 6 times (21) but still not the "same"

look at this: 2d6 = average dice is 7
1/6 chance you'll have 7 as a result
5/12 chance you'll have better than 7
and 5/12 worse than 7.

With your method, all results have same chance instead of REGULAR

Eventually, its up to DM and players but i'm not sure i might want to use this way for determining damages.

"A DM only rolls the dice because of the noise they make." result is not that important

 

[HoboGod]

Aye, letting a fireball deal 1d6 * 12 makes things very silly. The maximum and minimum ends of the spectrum should be reserved for the unlikely events that sway the tide of a destructive explosion (i.e. a strong wind out of nowhere). If somebody has more damage than they do dice, I use electronic dice. If electronic dice is not an option, I let them roll a certain number of dice, usually 6, and add the average of their remaining dice. For example, if they deal 28d4, they must roll 6d4+55 (the average of 1d4 being 2.5).

The averages of common dice are as follows:
1d2:1.5
1d3:2
1d4:2.5
1d6:3.5
1d8:4.5
1d10:5.5
1d12:6.5
1d20:10.5

 

[Jhaelen]

I let them roll a certain number of dice, usually 6, and add the average of their remaining dice.

I'm doing the same thing, though I'm using either three (for odd total numbers of dice) or four dice (for even total numbers of dice).

 

[Persiflage]

Rolling one die and multiplying by the number of dice is a very, very different proposition from rolling multiple dice, no two ways about it.

Without boring you to death, I'll just illustrate that the chances of getting maximum damage on a 10d6 fireball by rolling "perfectly fair" dice is one-in-sixty-million-four-hundred-and-sixty-six-thousand-one-hundred-and-seventy-six, whereas with your DM's method it's... one-in-six.

I'd hate the multiplying-up method: it makes damage from lots of things too "swingy". It's not just spellcasters: characters like rogues and sniping builds would also suffer greatly from swingy damage. The whole idea is that as the number of dice gets greater, the deviation from the average gets smaller and less likely. Doing it the way you described not only breaks the random number generator, but makes other meta-mechanical abilities (such as re-rolls for minimum damage, or additional rolls for maximum damage) either a lot more or a lot less powerful depending on circumstances.

Using average damage for large numbers of dice is fine - I do it all the time when running characters that are generating dice explosions - but this multiplying-up thing has far-reaching implications throughout the game that I for one wouldn't be comfortable with.

 

[IronWolf]

The math folks have already weighed in, but on another front - I would just miss rolling a bunch of d6's for my damage. Nothing like having a handful of dice go skittering across the table and hoping for lots of high rolls!

 

[irdeggman]

Well the rules as written say it is supposed to be a number of dice and not a multiplier.

From the SRD (or PHB pg 5)

DICE
Dice rolls are described with expressions such as “3d4+3,” which means “roll three four-sided dice and add 3” (resulting in a number between 6 and 15). The first number tells you how many dice to roll (adding the results together). The number immediately after the “d” tells you the type of die to use. Any number after that indicates a quantity that is added or subtracted from the result

 

[radmod]

Just to throw something a little similar but a little different:
Coming from 1e, we always doubled the damage on crits - it made it easier to multiply by 2 (or maximum single damage, whichever was higher). On a crit followed by a crit followed by a confirm we would triple the damage (or double max), and so on. This allowed the EXTREMELY rare case of the 1st level killing the way overpowered monster in a single shot.

It wasn't until a few months back that I discovered that 3.5 has you roll extra dice instead of simply doubling!

 

[Khazan]

The math folks have already weighed in, but on another front - I would just miss rolling a bunch of d6's for my damage. Nothing like having a handful of dice go skittering across the table and hoping for lots of high rolls!

lol Yes there is the audible delight of rolling lots of dice, that is true.

Thanks to all for showing the math and explaining the reasoning behind rolling multiple dice rather than rolling one and multiplying.

I guess the DM and our group thought that as long as the rolls are done in the same way on 'both sides of the screen' that is was a way to speed up play (our group is 7 or 8 players).