Bell Curve on 1D6 [math]

[martinl]

One of the things that bugs me about GURPS is that the damage probability distributions vary so much with how many dice you roll.

The worst offender is the 1d6 - if it was just a bit more bell-shaped, it would make me happier. So here's my idea:

When rolling 1d6 damage, actually roll 3d6 and take the middle value. I don't think this is too hard.

1	16	7.4%
2	40	18.5%
3	52	24.1%
4	52	24.1%
5	40	18.5%
6	16	7.4%

Thoughts?
It's not as sharply belled as 3d6, but it is belled.

[sir_pudding]

That the damage probability distributions, what?

Have you tried Armor as Dice? Penetration is fixed but injury is randomized.

[martinl]

Originally Posted by sir_pudding

That the damage probability distributions, what?

Hit a button that I thought would select a tag that posted instead.

[martinl]

Originally Posted by sir_pudding

Have you tried Armor as Dice? Penetration is fixed but injury is randomized.

That makes sense for guns, but few guns do 1d+x damage, so the non-belled nature doesn't bother me often.

[Landwalker]

Another way to approach it would just be to roll 3d6, divide the result by 3, and round to the nearest integer. That yields the following distribution:

1   1.85%
2  14.35%
3  33.80%
4  33.80%
5  14.35%
6   1.85%

Clearly more weighted towards the center, and it might be too mathy for table-top play, but there it is.

2d6 also has a bit of odd behavior, namely that it's a linearly-changing distribution (each level of probability is the same roughly-2.78% change from those on either side of it). Unfortunately, taking the "multiply by 2, divide by 3" approach yields weird results because of how the rounding works (for example, you are less likely to get a result of 4 than you are a result of 3 or a result of 5... the whole "curve" is a bit spiky).

If you're bothered by 2d distributions, you can take a similar approach to your original suggestion: Roll 3d6, and instead of taking only the middle result, omit only the middle result. That yields:

 2     0.46%
 3     2.78%
 4     6.02%
 5    11.11%
 6    17.13%
 7    25.00%
 8    17.13%
 9    11.11%
10     6.02%
11     2.78%
12     0.46%

Which is a significantly more "curvy" distribution curve.

[ericthered]

I'm enough of a math nerd that the changing of the curve shape even from 3d to 5d bugs me. I've tried a variant where damage is read as an "average" amount (1d becomes 4) and everything is multiplied by (2d-2)*.2. It requires a bit of math, but most of my play is by post, so it yields really nice results, if you don't mind worrying about tenths of points of damage (I don't, but your milage may vary).

[Anthony]

I've pondered going to a single log-based roll system -- say, make a skill check and look up the margin of success on a table, or roll 3d6+n and look up the results. This allows you to have granularity between 1d6 and 1d6+1, which is nice, but the table tends to be ugly, because you need fairly large numbers unless you want damage to be really really random. For example, this MoS system works out to variability comparable to 3d6:

MoS  F  0  5  8 11 14 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 +30
Dam  1  2  3  4  5  6  7  7  8  9 10 11 12 13 14 15 16 17 18 20 21 23 25 27 29 31 34 37 40 43 46 50 54 58 63 68 74 80 86 93 x10

[Not]

Say more about log rolling. Interest piqued.

[Anthony]

Originally Posted by Not

Say more about log rolling. Interest piqued.

My actual preference is to just have wound levels based on MoS, but that introduces its own complexities.

[JCurwen3]

Originally Posted by ericthered

I'm enough of a math nerd that the changing of the curve shape even from 3d to 5d bugs me. I've tried a variant where damage is read as an "average" amount (1d becomes 4) and everything is multiplied by (2d-2)*.2. It requires a bit of math, but most of my play is by post, so it yields really nice results, if you don't mind worrying about tenths of points of damage (I don't, but your milage may vary).

Wouldn't 1d become 3.5?