# Dice Size: Calculating Average Damage

### Pathfinder First Edition General Discussion

Hi friends,

I've been a DM and player since 3.0 in 2004 or so, and I'm only just now really trying to get into the granularity of the much-maligned challenge rating system. In particular, I am looking at guidelines for custom monsters and custom traps, and a thing I keep coming across when I look at officially published things for examples is the unhealthy prevalence of the d6. Why?

Perhaps we should back up a bit. I'm looking at the rules for making custom traps in line with the CR system, and the GMG advises that the CR should increase by 1 for every 10 average damage. Simple enough, I suppose; though, since none of our default polyhedrons has an average result of 10, we must compromise. The most obvious would be to have every trap do damage measured in Xd20, and just tack on a -1 for every 2d20; i.e., a CR 2 trap could roll 2d20-1 for damage and average 20 damage. But for what is probably good reason we don't do that: 1d20 is a lot of variance, even if the average is close to what we want. So what do we use instead? For some bizarre reason, usually Xd6. Why?

3d6 gives us the same average result (10.5) as 1d20 with less variance. But why stop there? 4d4 gives us an average result of 10, which is actually our target number, with even less variance.

For a CR2 trap then, getting our desired 20 average damage we could do any of these:
• 2d20–1 yields the average result 5.00% of the time, with a range of 1–39.
• 4d10–2 yields the average result 6.70% of the time, with a range of 2–38.
• 6d6–1 yields the average result 9.28% of the time, with a range of 5–35.
• 8d4 yields the average result 12.35% of the time, with a range of 8-32.

Most folks would for simplicity's sake just say the average of 21 produced by 6d6 is "good enough" and call it a day. But why? And why, especially for traps where you can abstract everything as much as you like without invoking the 3rd-edition convention of D6=arcane and D8=divine, do so many effects that are not even spells go for a bunch of d6 instead of say d8 or d10?

I'm sure something like this has been discussed exhaustively, but a google query of "why d6" didn't really get me far. Thoughts? Links?

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Because rolling a pile of d6s is more fun than a few d20s.

Or because most gamers already have a pile of d6s (since lots of other games use them), but far fewer dice of the other sizes.

The most obvious would be to have every trap do damage measured in Xd20, and just tack on a -1 for every 2d20; i.e., a CR 2 trap could roll 2d20-1 for damage and average 20 damage. But for what is probably good reason we don't do that: 1d20 is a lot of variance, even if the average is close to what we want. So what do we use instead? For some bizarre reason, usually Xd6. Why?

History.

Pathfinder is derived from D&D which was originally created in order to put heroes into a wargame (specifically, Chainmail). Chainmail exclusively used d6s (which was very common for wargames at the time and even today) because people tended to have quite a few around (I mean, everyone had a box of Risk or Monopoly they could raid a few dice from).

When D&D was created, Gygax and co. had a bunch of D6s floating around from their wargaming so when there were multiple dice to be rolled they tended to just use multiple D6s. Then because of that, dice packs started coming with 1 each of d4, d8, d12, d20, two d10s (for percentile), and four d6s. Now everyone always had a bunch of extra d6s so the trend continued.

To address your designed trap - when you want to be more random, use more dice. When you want to trend towards the middle, use fewer dice.

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MeanMutton wrote:

To address your designed trap - when you want to be more random, use more dice. When you want to trend towards the middle, use fewer dice.

Isn't that backwards? The less dice, the flatter the curve, the more steeper the bell?

The swing on larger dice is too great, failing to disarm a trap and taking 3D6 damage is going to result in fewer dead PCs than failing and taking 2D20-1, in that a level 2 PC can drop into the negatives with 18 damage but is extremely unlikely to be outright dead. Not many level 2 PCs can take 39 damage and be saved. Although i do like the idea of a rogue failing to disarm a simple spring loaded dart trap and being immediately exploded into a pink mist in front of the completely dumb founded remainder of the party.

Torbyne wrote:
The swing on larger dice is too great, failing to disarm a trap and taking 3D6 damage is going to result in fewer dead PCs than failing and taking 2D20-1, in that a level 2 PC can drop into the negatives with 18 damage but is extremely unlikely to be outright dead. Not many level 2 PCs can take 39 damage and be saved. Although i do like the idea of a rogue failing to disarm a simple spring loaded dart trap and being immediately exploded into a pink mist in front of the completely dumb founded remainder of the party.

You made an error in your typing here which was pretty crucial for your point. 3D6 is an average of 10.5 damage, appropriate for a CR 1 trap. You are comparing it with 2D20–1 which produces an average of 20 damage, appropriate for a CR2 trap. The top-end of 6D6–1, which yields an average of 20 damage appropriate for CR 2 trap, is 35—only 4 lower than the top-end of 2D20–1. I would hazard to guess that a similar number of Level 2 characters would be dusted by taking 35 damage as would by taking 39.

If anything, the issue with the variance in large dice is more concerned with the low-end of damage than the high.

D6D–1 yields an average of 20 damage, yields exactly 20 damage 9.28% of the time, and yields at least 20 damage 56.64% of the time. 2D20–1 yields an average of 20 damage, yields exactly 20 damage only 5.00% of the time, and yields at least 20 damage only 52.5% of the time. These small changes may not seem like much, but when you extend the bell curves out from the center the changes become pretty drastic as shown in the image.

http://i.imgur.com/MzdRpks.png

Consider the chances of a "20 average damage" CR 2 trap dealing at least 15 damage: with 2d20–1, the probability is 73.75%; with 4d10–2, the probability is 82.39%; with 6d6–1, the probability is 90.35%; with 8d4, the probability is 95.97%. Looking at it from the reverse, consider the chances of a "20 average damage" CR 2 trap dealing 10 damage or less: those probabilities are 13.75%, 4.95%, 1.00%, and 0.07%.

More, smaller dice results in less variance; i.e., consistency.

Ah, thank you for the correction.

Pathfinder Lost Omens, Rulebook Subscriber

Flashblade, the point isn't how often the average comes up, nor how often above average comes up (that will always be very close to 50%). It's how often the extremes come up.

6d6-1 only gets 35 0.002% of the time (1 in 6^6).
2d20-1 gets 39 0.25% of the time.

6d6-1 deals at least 30 damage (enough to kill outright most 2nd level character), 0.99% of the time.
2d20-1 gets at least 30 damage 13.75% of the time. 14 times as likely to kill.

On the flip side, 8d4 only gets 30 damage 0.07% of the time. In fact, 8d4 is between 16 and 24 fully 84.8% of the time. Very predictable. A little boring. So d6's.

Anydice stats

Large numbers of d6's are pretty much equally predictable. Enough so that for my epic game I created a stat sheet to have players just roll a single die to cover the (statistically averaged) range of possibilities. You can see how likely close to average results are on that.

For example, 20d6 average 70, and are 70 +/-5 50% of the time. It's tedious to roll out 20 dice, count them all up, and get "dead average" *so* often. The chart keeps most of the possible range, while reducing it to a single roll. I suppose using a d100 would keep more of the extreme possibilities, but then 26-75 would still be +/-5 from the average.

Mind you, there *are* highly random traps. Mostly swinging blade types, that could crit, which keeps the odds fairly low. But throwing in a trap that makes sense to be more random (maybe a hall of axes) can use different dice - 3d12 would be scary, and traps should be, when appropriate.

Brew Bird wrote:
Or because most gamers already have a pile of d6s (since lots of other games use them), but far fewer dice of the other sizes.

That. I have dozens of d6 at home (from Yahtzee etc.) but apart from the set of dice I got for PF, I have one single d8 (from a specific board game) and a few extra d20.

Our resident blaster lover has to scavenge the whole table for d4s every time he casts magic missiles.

thejeff wrote:
MeanMutton wrote:

To address your designed trap - when you want to be more random, use more dice. When you want to trend towards the middle, use fewer dice.
Isn't that backwards? The less dice, the flatter the curve, the more steeper the bell?

You're right. Brain didn't engage.