Fabula Ultima math

[james_davis_nicoll]

Because the mathy parts of my brain are deader than other parts and I was never good at combinatorics.



The FabUlt RPG has four stats, Dex, Insight, Might, and Willpower. Each has an associated dice type, which can be as low as d6 and as high as D10. Tests are performed by rolling two dice to see if their sum equals or exceeds a target number. Usually this is a combination of two stats but sometimes it is the same stat twice.

Am I right in thinking there are ten possible pairs of stats, including self-pairing?

FabUlt has an elegant way of folding damage into to-hit: damage is equal to the higher value shown on the two dice, plus weapon modifiers. This means if you connect at all, you do serious damage. The smallest possible value on the higher of two d8 whose result equals or exceeds a target value of, oh, 9, is 5, so if your axe does High Roll + 10, if you hit, you will do at least 15 damage.

Huh, which means characters that are harder to hit won't take as many hits (dur) but the average damage per hit will be higher. Let me check that...

A Brigand waving an axe does HR + 10 that uses a d10 + d10 skill check hacks at someone whose Defence value is 6. The lowest possible values that hit are 3+3, so minimum damage is 13. Same brigand, same weapon, vs Def 12 plate. 6+6 hits, minimum damage is therefore 16. Only 3 more damage per hit and it is obs better not to get hit at all than to take less damage but I wonder what the numbers look like for an extended fight?

Oh, but I forgot criticals. If the dice come up double 6, double 7, double 8, double 9, double 10, double 11, or double 12, that's a critical. Crits do not do more damage, just create other advantageous outcomes for the attacker. Still, that easy to hit character has more results that hit them that are not criticals than the hard to hit character. I think.

Comments

[james_davis_nicoll]

Ok, so there's a 90% chance Mr d10 x d10 hits Def 6? And a 45% chance that they will hit Def 12?

So even if we assume minimum damage, ten swipes at Def six does at least 117 damage, and ten swipes at Def 12 does 72. So, yeah, armor good.

[james_davis_nicoll]

No, that's wrong.

[original_aj]

The chance of a hit is right, but you need to look at what each hit would do. A quick spreadsheet told me that on average an attacker rolling 2D10 does 15.88 damage against DEF 6 and 8.5 against 12.

A less maths intensive way to consider it is that for the same results on the roll they do the same damage, if it meets the DEF. A roll which meets DEF 12 exceeds DEF 6 so every hit which would damage DEF 12 would do the same damage to DEF 6. Rolls which meet DEF 6 but not 12 also damage DEF 6, so DEF 6 will over a long series of rolls take more damage than DEF 12. Though the actual numbers would be different for different dice combinations the principle would apply whatever dice the attacker is rolling - lower DEF take more damage on average.

The average damage per successful hit is higher for DEF 12 but only because of all the extra, lower value, hits DEF 6 takes which dilute the pool. It's more than offset by the lower number of successful hits meaning the average damage overall is lower. They can still get unlucky of course....

[rwpikul]

I did a quick bit of spreadsheeting, (your to-hit chances are correct):

With a d10xd10 +10 attack

Against Def 6, it does an average of 15.88 damage per attack and 17.64 per hit with 5.56% of hits being crits.

Against Def 12, it does an average of 8.50 damage per attack and 18.89 per hit with 11.11% of hits being crits.

So, depending on how nasty the crits are, good armour is very useful in the long run, (even better than your first blush estimate), and may only marginally make the hits which do happen worse.

[original_aj]

Do you mean D6 to D12 in range, rather than D6 or D8? You talk about D10s later...

I agree with ten possible pairs from four stats, allowing doubles.

[james_davis_nicoll]

Whoops, no. I meant d6 to d10. Specifically, they have to be one of three arrays:

Jack of All Trades: d8, d8, d8, d8
Average: d10, d8, d8, d6
Specialized: d10, d10, d6, d6

(In any order. Specialized could be d6, d10, d10, d6 or whatever)

[kgbooklog]

This is why we have spreadsheets.

d10 & d10, no bonus

DEF 6:
success 90%, avg dam if success 7.64, avg dam per attempt 6.88

DEF 12:
success 45%, avg dam if success 8.89, avg dam per attempt 4.00

[vatine]

Yep, you have (4 * 3)/2 (all possible order-ignored combinations of 2 items out of 4), plus the 4 self-pairings.

For the hits, I would probably need to write up a simulation. I will notice that "chance of being hit by a crit" will change in a strangely non-linear manner.

If you go from any 2*n to 2*n+1, your chance of a crit will drop. But, if you go from 2*n+1 to 2*n+2, it will stay the same (simply by the fact that a crit roll will always be even, and when going from an odd to odd+1, all even rolls that were hit before the increase will also be afterwards).

I don't think it has the incredibly weird "critical failure" mechanic of CthulhuTech, where half the time you get "one level better", your chance of crit-fail doubles, and half the time, it drops by a factor of "lots".

[vatine]

Oh, wait, since there's a smaller range of "can be a valid hit", a higher proportion of hits will of course be critical. Hm. That means that there may actually be a chance that "number of expected crits" change at every increased defence.