Damage Dice Multiplied

[WhiteLily]

I'm looking through damage tables and see that some have multipliers. For instance, P.277 Table for Hand Grenades shows these damage stats for Concussion Grenades:

TL. Damage
6 6d cr ex
7 5dx2 cr ex

Is there any particular reason the TL 7 Concussion grenade is multiplied instead of just written as 10d?

[AlexanderHowl]

It is easier to roll 5d rather than 10d.

[Anthony]

Yeah, attacks over about 15d are almost always written as multipliers, attacks in the 10-15d range are often multipliers, attacks under that are rarely as multipliers though you do see 4d*2 in places I think.

[Anaraxes]

The usual threshold in the rules is 6d. Numbers higher than that are broken into multiples -- for convenience, as already noted.

Also, smaller numbers of dice preserve the chance of seeing the more extreme results and having more interesting variation around the average. If 60% of the time you're going to be within 5% of the average with those 60d6, and 90% of the time you'll be within 20% of the average (190-230), you have to ask why you're bothering to roll and add up 60 dice instead of just going with the average of 210.

[Kale]

6d averages nicely to 20 points, so optimally you want your damage to be some version of 6d x X to avoid rolling giant buckets of dice. On the other hand, if your players enjoy rolling buckets of dice feel free to let them go ahead and roll those ten dice. It's really just written with the multiplier to let new players realize that they don't need an absurd amount of dice to roll damage for the game. The reality of course is that most experienced gamers will already have enough dice to fill several buckets.

[Anaraxes]

Originally Posted by Kale

6d averages nicely to 20 points

21, to be precise. 3.5 points per die.

[johndallman]

Originally Posted by WhiteLily

Is there any particular reason the TL 7 Concussion grenade is multiplied instead of just written as 10d?

As well as the convenience reasons, described already, rolling large numbers of dice tends to give results without much variation. This is counter-intuitive, but true.

For example, we know from experience that when we roll 3d, 9, 10 and 11 are the most common results. If you roll 30d, 105 is quite common and 104 and 106 not far behind, to the point where it's hardly worth all the rolling and adding, you might as well assume the total is 105.

Rolling 4d to 7d gives a degree of variation that seems about right for explosions, so rolling and multiplying works well for larger ones.

[whswhs]

Originally Posted by johndallman

For example, we know from experience that when we roll 3d, 9, 10 and 11 are the most common results.

The chances of 9 and 12 are both 25/216. For example, 9 can be rolled as 126, 162, 216, 261, 612, 621, 135, 153, 315, 351, 513, 531, 144, 414, 441, 225, 252, 522, 234, 243, 324, 342, 423, 432, or 333.

Not to detract from the general principle! Though the actual point is slightly subtler. One standard deviation for 3d is approximately 3; about two-thirds of rolls fall within ± one standard deviation of the mean—by actual count, the fraction of rolls that fall between 7.5 and 13.5 is 146/216. But if you roll 3N dice, you multiple the standard deviation by sqrt(N). For 3x10 = 30 dice, sqrt(10) is about 3.1, so the standard deviation is about 3x3.1, or 9.3, and two-thirds of rolls fall between 95.7 and 104.3, which is a wider range. But it's a smaller proportion of the range from lowest to highest possible roll: 18-3 = 15, and 6/15 = 0.4; 180-30 = 150, and 19/150 = 0.127. If you draw the two curves, the one for 30d is wider, but it will look sharper-peaked.

[Plane]

The more dice the more average the results, less likely to get really low or really high min/max amounts. If you really wanted to save on rolling/summing you could prob do 1d * anything, but then you'd never get intermediate amounts, it would always be a multiple of whatever.