An exploding damage die for GURPS?

Some of the recent threads and comments about armor as dice have led me to think about alternate ways to get what I want out of Armor as Dice – less variable penetration so that if you armor rated for X (and GURPS defines X as 3.5 points per die for both penetration and resistance), and a bullet hits you with basically less energy than X, it won’t go through.

Some of these distinctions don’t seem like much, or important. And to a certain extent, they’re very much not. If you have (say) a DR 8 bullet resistant vest, in theory it should be proof against a .45 ACP (2d pi+) but not a 9mm (2d+2 pi).

Turning to AnyDice (and we’ll be doing that a lot this post) we see that the .45ACP will punch through DR 8 with 1 point or more of damage potential remaining just over 27% of the time in round numbers. The 9mm, which should always go through, will go through 58% of the time.

This is very easy to rationalize. Poor angles, uncertain coverage, and other variables make armor less certain. The tendency to treat an armored vest as if it fully covers the entire torso (a legit simplification) makes the push to make every thing just work out neatly less mandatory.

Still, players buy armor to buy protection, and some armors really are that good. The “solution” tends to be “if you want full protection in a gamist manner, buy DR6 per die of protection you want.” Thus, if you want to be fully protected vs. that 2d or 2d+2 bullet, buy DR 12 and DR 14 respectively, which will increase the weight of that armor piece by about 70%.

OK, fine, but I am going to press forward and solve the non-problem anyway, because though there are many instances where you can rationalize the roll, there are others where you can’t.


Armor as Points, Penetration as Points


Armor as Dice has gotten plenty of love elsewhere. But there’s another method discussed in Armor Revisited (Pyr #3/34), which inverts the method: instead of listing Armor as dice and keeping the damage as dice, express the penetration as a fixed number, and go with variable injury.

So instead of 2d, a .45ACP handgun would have a pentration rating of 7, a 9mm would be 9, a 5.56x45mm might have a 17, and a .50 BMG would be something like 40-46 depending on the barrel.

So the effect is the same. Compare Penetration to DR, and if Pen is higher, it goes through. This also allows either using HP or “Mass-based” HP as a blow-through threshold as a number read right off a character sheet, precalculated before play starts for the mass-based number.

So, for a straight-up, GURPS standard application, subtract DR from PEN, and then roll injury dice. Roll 1d for every 3.5 points of penetration that get through would be the most straight-forward conversion, though “divide by 3 or 4” would be easier in play. Remainders might just be adds. Actually, rolling 2d per 7 PEN, and converting so you always roll two dice might not be that bad.

So a notional M4 carbine might do 16 penetration, and impacting DR 10 would have 6 remaining penetration points. Injury results, and you roll 1d+2 (average 5.5) or 2d-1 (average 6).

A tank cannon that usually does 6dx20(2) would convert to 420(2), and faced with DR500 would be 420 PEN – 250 DR (thanks to the armor divisor), leaving 170 PEN left. Against machines, maybe you don’t roll, maybe you convert to 2dx24 or even 3dx17 if you want some randomness.

Explode it!


But what if you want even more random injury – because injury is far, far more variable than penetration?

I’ve recently been exploring the Savage Worlds system, which features exploding dice. Called an Ace in the game, if you roll the highest value on your die, you get to roll it again, and add it to the prior roll. Leading to the unusual circumstance that you can’t roll a 6 on an exploding d6. But nevermind that.

An exploding die is basically a geometric progression. It’s the average value of the die (3.5 for d6), multiplied by 1 + the probability that you get to roll again (1/6) + the probability you get to roll a third time, fourth time, etc.

In short:

and in this case, a = 3.5 and r is 1/6. If we were rolling a d8, a would be 4.5 and r is 1/8.
So our average values for exploding dice would be 
Of course, GURPS only uses d6, so a more useful table would be 
And one of the very interesting things here is that the first four values are of great interest to GURPS players, since they represent typical wound multipliers for crushing (Never), just under +1 per die (6), pi+ or cut (5-6), and imp or pi++ (4-6).
So you could replace damage multipliers with exploding dice, and each die explodes separately. So your .45 ACP that does 2d pi+ could legitimately roll a 2.
They All Explode!

If one really got enamored of exploding dice due to the variability, I’d simply apply a -1 per die to all damage, and let all d6 explode on a 6. That doesn’t quite balance out. It’s a 1.2 multiplier for the explosion, but -1 per die is x0.71, for a net of a 15% loss in damage.
In any case, you’ll wind up converting any penetration that gets through DR to dice. Exploding dice. So the injury can be pretty variable.I’d convert at 4 points per die.
Blowthrough

Though injury might be variable, it would be easy to make blowthrough not be that way. So if you were shooting with a firearm with PEN 25 at a person with DR 8 and a blowthrough threshold of 11 (maybe he weighs about 180 lbs), you’d have 17 penetrating damage, or about 4d+1 injury.
But what happens downstream? The bullet loses a flat 11 going through the guy, and stops in the DR 8 armor in his back. 
Let’s say it was an AP bullet at 25 PEN. So DR drops to 4, and so does blowthrough, dropping to 6. So the bullet punches through the DR on both sides and the guy, with 11 remaining to threaten others.
You then make a choice – do you apply the full amount (PEN 25 less DR 4) which is PEN 21, or 5d+1 to your foe, or limit it to blowthrough, either 11 or 6. 
This might call for revisiting the pi ratings of some rifle rounds – the 7.62x51mm bullet that we’re more or less simulating here can have a pretty impressive temporary cavity, which can cause some odd effects. But if it doesn’t hit anything vital, the AP bullet might just zip on through, with something like a 2d+3 wound. 8.4 damage on the average, about a pistol-sized wound.
Bullets that (say) tumble and fragment might expend a lot of energy blowing through, etc. But that’s a detail best left to other rules.
Parting Shot

We’re borrowing a mechanic from another game here (Savage Worlds, but other games have had exploding dice before SW), so one has to be careful. 

Still, it’s a better fit – isolated to effect rolls, and applied to something that’s highly variable, an injury roll – than the D&D Advantaged mechanic is to the GURPS space. 

The impact on actual damage rolled isn’t that high – a 20% boost in damage if you let the dice explode infinitely, but honestly if you let the die explode 3 times (providing a potential 4x damage multiplier at the high end) you’re already averaging the 4.2 that is the asymptote. Since that’s the same as a brain hit (x4), you might as well cap it at 3 extra rolls per die. 

I think this might be fun at the table. The fixed (or partly variable; I’d suggested something like a varability of about 1/5 before) DR and PEN values would make some sense. If you made a PEN of 18 into (say) 14+1d, and/or DR the same kind of treatment (though it might depend on the armor), you could account for “no way in hell” penetration values as well as some degree of random for both injury and penetration. Exploding dice are icing, since it takes fixed penetration, and gives back randomness to it without changing the number or distribution of dice you roll. 
Seems like with a good code base, such as the free-form stuff you can write in MapTool, this would be invisible to the user, even including variable penetration, armor, and exploding dice. 
The big issue I have in play with Armor as Dice is I like to let the players roll their damage, and by letting them do that, I must give them intel on the armor rating in dice of the enemy. That’s less fun, because it kills tension.
Fixed PEN values would pose the same problem, though. It would add a little high-end variability on the injury side, which is good. 
Ultimately, what we’re doing though is converting a fixed PEN-DR to injury. If you’re really doing it with a computer, the GM might as well double the penetrating energy (so in our example above, 24 PEN – 8 DR is 16 Penetrating Damage) and just roll 1d(2xPEN) or 1d(1.5xPEN) if you’re in (say) Roll20. That allows for grazes and lucky vitals hits, and the right kind of arbitrary where you can get a .50 that just wings you, or makes your head assplode. With rolling many dice, you get a mean effect that may or may not be swingy enough.
But I will say this in passing; while armor as dice does have some nice effects, it also has some drawbacks, so YMMV. For every case where you say “My vest should stop a .45 ACP cold!” you can find a case where your angle to the shot wasn’t right and it misses the primary protection. That might be best modeled as a clean ‘no DR!’ case, though. In that sense, the Rules-as-Written are no loss. The player gets to roll his damage (and players like effect rolls), and the GM can keep DR and injury hidden, if she wants.

4 thoughts on “An exploding damage die for GURPS?

  1. "you can't roll a 6 on an exploding d6"
    Instead of adding any sixes you roll, just count +5 for every reroll, and add only the final die. It computes quicker (most people have an easier time counting 5+5+5+3 than 6+6+6+3) and lets you roll any number. It also normalizes damage back down towards RAW. The downside is that rolling (6, 1) is a bit disappointing.

  2. Here's a lever that I wish GURPS had: "how catastrophically does a given armor fail when it fails." This system, which is very interesting and I particularly like the focus on penetration and damage as distinct, assumes that all armor provides its full protection when it's penetrated, but I'm not sure that's the case. I know this is focused on firearms vs. modern ballistic armor, and I don't know much about how modern ballistic armor fails, but I get the impression that pre-ballistic armor being attacked by impaling weapons (for example) either failed catastrophically or not at all. That is to say, if you're trying to put a spear in me, I think I'll either get a nasty bruise if my armor holds, or much worse if it doesn't: I'm not going to walk away with a nick.

    What's your take on that? Is it worthwhile to model, perhaps by putting a multiplier on a category of armor such that, if penetration is higher than a vest's DR, only 80% of the DR is applied to damage?

    1. There's a rule I have used where if the penetration is larger than the DR (in dice) the armor only provides one point per die of DR. So DR 14 (4d) armor when penetrated would only proivide DR4. If you want to stick with DR as points, only provide 1/4 DR or something like that.

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