Looking for system crunchers

[BTRC]

Whew. Lots of questions.

Another thing that worries me about their interaction in the EABA approach:
Let's say that Class I gun does 1d damage (no idea if that's a 9mm in EABA or something else entirely). Now, there's a BFG that does 9d damage (that's 8 doublings (i.e. ×256) of firepower in EABA, right?). Now, a target wears armour that blocks 1d. Does this result in effectively halving the amount of firepower experienced by the target?

A .45 ACP would be about 2d+0. If this hits a 1d+0 armor, the target takes 1d+0 damage. The 9d+0 attack (probably about a 30mm) hits that armor. The target takes 8d+0 damage.

If the target had already taken hits to have a -1d damage effect, then from the .45 they would take 1 hit (2d attack, -1d armor, -1d from previous injury, but with a minimum of 1 hit because it is lethal damage). From the 9d+0 they would take 7d+0 (9d attack, -1d armor, -1d injury).

BTW, how many hits (hit points that is) a typical character can sustain before various stages of impairment? Before risking/guaranteeing death? What about the typical adventurer ('young adult fit for contract military service in a modern civilized state' or equivalent)?

A low average person has 12 hits, and would take a -1d effect each 3 hits. An average person would have 14 or so, and take a -1d effect each 4 hits. A 90th percentile human in Strength and Health would have 18 or so, and take a -1d each 5 hits. Absolute human maximum would be 26.

For a quick guide, a 9mm does 2d+1, head hits do +1d after armor, and any hit doing more hits than your Health is a crippling injury, which in the basic rules is immediately incapacitating on a head or torso hit. So a 2d roll of 7 or more (goes to 8 with the +1) will take down a normal person on head or torso hit, and a 3d roll of 7 or more will do so on a head hit (and of course the roughly 50% chance of doing all your hits and being instantly fatal rather than merely unconscious and bleeding to death). Even the maximum human falls to one 9mm head hit on a 3d roll of 13+. And with a 5.56mm being about 4d+1, the results for heavier weapons are uniformly bad without a fudge factor of some kind. And let's not even get into what your 9d BFG would do...

If you use the called shots doing extra damage rule, the "one shot kill" from the "pistol bullet to the head" execution model is almost certain, but for random combat effects it is merely very nasty on average.

For doing your own figuring, a knife wielded by an average person does about 1d lethal damage, a sword 2d, a .357 magnum 3d, a blast of buckshot three 1d+0, a medium caliber rifle 4d, a heavy rifle 5d. Head hits are +1d effect, extremities -1d effect (but not less than zero). These are all rounded, but sufficient to play with the system using the aforementioned hits and damage intervals. There are also rules for stunning and shock and such, but that depends on how much versimilitude you want.

[vicky_molokh]

Originally Posted by BTRC

On the Nd6 keep 3 subject:

The way this sort of system works out statisitically is that tends to keep a nice bell curve going across a broader range than an "Nd6+X vs target number". It would be easier to show than explain:

http://www.btrc.net/images/stories/siteimages/dicedist.gif

This shows the probabilities of Nd6+0 keep 3 rolls for a variety of target numbers. You can see the probability for an Nd6+1 or +2 just by shifting the appropriate curve over by 1 point. You can see that if you are only keeping "best three" that no matter how good you are your final result is capped at what you can do with 3 dice. The curves get squashed as you get more dice, showing diminishing returns for the investment in rarefied levels of skill.

So, I assume that the system is not meant to have results better than 18, and to make things such as the Mona Lisa an artist would take a large penalty to the roll, instead of hoping for a very good margin of success. I suppose it's a matter of preference.

The dice curve does make things clearer. BTW, you used the url tag backwards, which has hilarious effects on my browser.

[Tom B]

Actually, since the mechanic can include a +1 or +2, the range is actually 1-20.

[vicky_molokh]

Originally Posted by Tom B

Actually, since the mechanic can include a +1 or +2, the range is actually 1-20.

Wait, +1/+2 before or after the cap? Is the cap intended for three dice, or for a max of 18 even with bonuses?

[vicky_molokh]

Originally Posted by BTRC

Whew. Lots of questions.

If I'm wasting your precious time, just say so and I'll stop bothering you.

I do like to go through the crunch on a moderate level (i.e. I check for visually identifiable murphies, but do not make 3-dimensional probability spreadsheets), but I can't assemble a playtest group for various reasons (mostly of time, players, and time spent learning a new system). My familiarity with EABA mostly comes from Stuff!. I'm not sure if you find any of my posts any good.

Originally Posted by BTRC

A .45 ACP would be about 2d+0. If this hits a 1d+0 armor, the target takes 1d+0 damage. The 9d+0 attack (probably about a 30mm) hits that armor. The target takes 8d+0 damage.

Yeah, that's what I'm asking. More precisely:

Assuming 1d represents ability to barely penetrate 1mm of some armour, 2d means 2mm, 3d means 4mm and so on, up to 8d and 256mm. But the issue is, 1d armour (1mm) will reduce the injury from 8d to 7d. And 7d isn't the penetrative ability of 255mm, but rather 128mm. I'm not sure this is realistic.

[Mylon]

I guess I didn't look over the system enough to realize the keep 3d mechanic. That seems like it levels it out, except that extra dice can be sacrificed for a +2, which in turn means the maximum can exceed certain threshholds. The system seems to suggest there's a lot of gaming the system to do for those that really want to get analytical. I'm pretty sure that after a certain point it is more advantageous to turn extra dice into the flat bonus than to roll additional discarded dice. Just going from 3d6 to 4d6 (keep 3) the average changes from 10.5 to 11.5, so in general it's more advantageous to never accept the extra dice and always take the +2 bonus.

[vicky_molokh]

Originally Posted by Mylon

I guess I didn't look over the system enough to realize the keep 3d mechanic. That seems like it levels it out, except that extra dice can be sacrificed for a +2, which in turn means the maximum can exceed certain threshholds. The system seems to suggest there's a lot of gaming the system to do for those that really want to get analytical. I'm pretty sure that after a certain point it is more advantageous to turn extra dice into the flat bonus than to roll additional discarded dice. Just going from 3d6 to 4d6 (keep 3) the average changes from 10.5 to 11.5, so in general it's more advantageous to never accept the extra dice and always take the +2 bonus.

Importantly, if the +2 applies after the cap, then it increases both the minimum and the maximum possible result, in addition to boosting the average. So yeah.

[Tom B]

Dice rolls will be, progressively:

0d+1
0d+2
1d+0
1d+1
1d+2
2d+0
...
Any time modifiers total +3 they convert to another die. So if you had 2d+1 with a total of +4 in modifiers it would convert to 3d+2.

So, you can end up rolling something like 5d+1, keep the highest three, which will have results from 4-19. If you're rolling 6d+0 you could choose to instead roll 5d+2...but that's really about the extent there is for "gaming the system".

Damage doesn't do this. You sum all of the damage dice, after subtracting armor dice. So a 6d+1 shell vs. 2d+2 armor would be 4d of lethal damage that get through (the +2 component of the armor would stop the +1 component of the damage but no more than that.)

[BTRC]

If I'm wasting your precious time, just say so and I'll stop bothering you.

Far from it. I had originally just wanted to get some eyeballs on the EABA v2 system over at the BTRC site, but a long discussion constantly getting bumped to the top of the "roleplaying in general" page here works just fine for that.

Assuming 1d represents ability to barely penetrate 1mm of some armour, 2d means 2mm, 3d means 4mm and so on, up to 8d and 256mm. But the issue is, 1d armour (1mm) will reduce the injury from 8d to 7d. And 7d isn't the penetrative ability of 255mm, but rather 128mm. I'm not sure this is realistic.

That is perhaps true, but in a game mechanic sense there is not really any other option. There is not really a way in game terms to generate an armor thickness that will reduce an 8d penetration to a 7d, that will not by itself stop far more than 1d. Games have to compress the energy levels, otherwise a .22 would have a damage of 1 and a tank cannon would have a damage of 100,000 (a linear scaling). Most of the time it does not matter, because even if an 8d attack hitting a 1d armor actually does 7.999d instead of 7d, to the person who has just taken 24 out of their 12 hits (7d) instead of 28 out of their 12 hits (8d), the difference is between "dead" and "more dead". I imagine the same is true in GURPS. Once a certain amount of damage gets through, most other considerations pale in importance.

Using real-world penetration vs. homogeneous armor, it takes approximately 4x energy to penetrate 2x armor thickness. So the actual progression would be 4x energy = +2d and 2x armor thickness = +2d (i.e. 2x armor thickness blocks 4x energy which is +2d). So in terms of armor thickness and damage (energy,damage,armor thickness):

1x/1d/1x
4x/3d/2x
16x/5d/4x
64x/7d/8x

Or in real-world terms, if a 1d attack exactly penetrates X thickness of your armor, then a 7d attack represents something with 64x the energy and will penetrate an 8X thickness of that armor.

It is not a perfect progression (energy, damage and armor) because of all kinds of vagaries in penetration mechanics, but it holds up pretty well over a wide range of energies. I believe the notion of energy and penetration also comes up here:

forums.sjgames.com/showthread.php?t=62684

A thread which also references my 3G3 product, interestingly enough. The EABA penetration and damage scale is derived from the 3G3 model, just scaled differently.

On "best three" rolls:
Yes, the +1 or +2 is after the roll, so rolls are capped at 20 (you can only take the +2 once). Quite often, it would be in your best interest to roll an even number of dice like 6d+0 as 5d+2, which you can see if you play with the table I linked in a previous message. The game reason you would not do this all the time is that skills are linked to attributes. So if you have a 3d+1 Agility and a +2d skill, you are rolling 5d+1, and 5d+1 "keep 3" is better than 4d+2 "keep three".

On the low end, in EABA v2 (in testing), there is a "take 2's" optional rule, where you can simply count all your dice instead of "best three", but they all count as 2's. This is the "automatic success" rule. If I have a roll of 4d+1, my "take 2's" result is 9 (4 times 2, plus 1), so I can claim autosuccess on tasks with a difficulty of 9 or less. The odds that a 4d+1 "best three" roll will get at least a 9 is close enough to autosuccess for most purposes, and lets players avoid statistically unlikely fumbles. For instance, if all of us had to actually roll our driving skill every time we got behind the wheel, the roads would be strewn with wreckage. But if you say that "a driver's license represents a skill roll of Nd6", and "the difficulty of casual driving is 2N", then casual driving is an autosuccess.

In EABA, a difficulty of 20 pretty much defines the limit of human ability. So, if the difficulty is harder than 20, it simply cannot be done unless you can find a way to reduce the difficulty. An example of this would be the Accuracy stat for a weapon, which if you aim, will reduce the raw difficulty for range. If you aim, you can hit something at a distance that would not be possible without aiming. So, if the difficulty for range was 21 you could not hit. Aim, and it would become possible.