Recently I have been examining dice pool mechanisms in Shadowrun, to compare two methods for resolving opposed skill checks. In those posts I have found that for opponents with equally matched skill the probability of success tends to nearly 50% as skill increases, and that skill checks based on target numbers lead to sudden changes in success probability due to rounding error. In this post I thought I would examine the same problem in Warhammer Third Edition (WFRP3).
WFRP3 also uses a dice pool system, but it is much richer than other dice pools, being composed of seven different kinds of dice. It also doesn’t use the same dice for attacker and defender: the attacker adds some purple “challenge” dice to his or her dice pool, with the number dependent on the target attribute of the defender. The standard rule for determining this number in WFRP3 is:
- Defender’s attribute is less than half the attacker’s: 0 dice
- Defender’s attribute is less than the attacker’s: 1 dice
- Defender’s attribute equals the attacker’s: 2 dice
- Defender’s attribute less than twice the attacker’s: 3 dice
- Defender’s attribute more than twice the attacker’s: 4 dice
This leads to some obvious problems: if you have an ability score of 8 and your target has an ability score of 8, the difficulty of your attack is 2 challenge dice; but this is the same difficulty if both of you have attribute scores of 4. So as your skill increases, your chance of success against someone with your own skill level increases markedly. Also, if you have an attribute score of 2 you will face the same difficulty on your check for all opponents with a score of 4 or more. You have the same chance of success whether your opponent is just slightly above average (4) or of god-like power (10).
I have considered two alternative ways of setting the difficulty based on the defender’s attribute: a number of challenge dice equal to half the attribute rounded down; and a similar method, but with the half value converted into black dice (so that someone with an attribute of 4 gives 2 challenge dice; while someone with an attribute of 5 gives 2 challenge and one misfortune dice). I have simulated the results of 10000 challenged skill checks – using only attribute dice – for skills from 2 to 6, against various defender attributes, using all three methods.
Figure 1 shows the probability of success using the standard rules described above, i.e. with difficulty set by comparing attacker and defender attributes. The high probability of success regardless of defender attribute is obvious for large attribute values, and the plateau effect at higher defender attributes is also visible.
Figure 1: Probability of success for various combinations of attributes, standard rules
For an attacker with an attribute score of 6, success is highly likely (about 80% chance!) even against targets with the very high attribute score of 8. Conversely, a wimpy attacker with an attribute score of 2 can be expected to be successful against anyone with attribute of 4 or more about 10% of the time – even if their attribute is 8. Remember, in WFRP3 a score of 8 in an attribute is almost impossible for a human, and mostly the province of giants and dragons. This means a party of 1st level mages could attack a giant and actually do physical damage against it! And this is before including stance dice, training, etc. A human with an attribute score of 6, a fortune die on that attribute, and two ranks of training could reasonably expect to hit a much more powerful opponent pretty much every time, unless that opponent burns through defense cards, cunning, etc.
Figure 2 shows the probability of success for various combinations of attacker and defender attributes using a system in which difficulties are set at one challenge die per 2 points of attribute.
Figure 2: Success probability for difficulty set at half target attribute
This chart shows that probability of success declines with increasing target attribute score for all levels of the attacker’s attribute. It also doesn’t show the jagged pattern arising from rounding error that we saw for target numbers in Shadowrun or Exalted; rather, it plateaus for odd attributes. Note the generally high probability of success; a person with attribute of 6 can expect to beat someone with attribute of 8 about 80% of the time. This could be easily adjusted by making the base difficulty of all checks 1 challenge die; then all success probabilities in this chart would shift two steps to the right.
Figure 3 shows the probability of success when we eliminate the rounding effect by turning half points of attribute into misfortune dice. Under this system, the remainder from dividing the target attribute by 2 is turned into a misfortune die. The overall pattern is similar to that of Figure 2 but we see a smoother trend with rising ability.
Figure 3: Success probabilities without loss due to rounding
This is a very smooth success curve, with somewhat high overall success probabilities and no unexpected values due to rounding error. Furthermore, the probability of success against someone of equal attribute score decreases as attributes decrease, which I guess is what one might expect as one watches increasingly amateurish people trying to thump each other; in contrast, in Shadowrun and Exalted this probability tends to 0.5 as skills increase.
I think then that my final recommendation is to set difficulty for skill checks at 1+(defender attribute)/2, with the remainder from the division converted to misfortune dice. This will reduce the success probabilities compared to Figure 3 but retain the smoothness and other properties shown in that chart. For games where you want the PCs to have lots of success, make the base difficulty 0; for really challenging, gritty games make it 2.
By setting difficulty in this way and using challenge dice that are different to the attack dice, the WFRP3 system is able to generate a sophisticated and realistic set of probability results. Unfortunately, the method for setting difficulty provided in the original rules doesn’t take advantage of these properties at all, and should be revised.
Compromise and Conceit 
October 5, 2013 at 8:39 pm
When i was thinking up a combat system, I thought of the famous warriors Pyrrhus (he of the Pyrrhic victory) – brained by a roof tile; Styrbjorn the terror of the north – copped a chance spear; Richard the Lionheart – ditto crossbow bolt. Combat should be chancy – that encourages the players to stack the odds beforehand and puts a premium on knowing when to run away. Mind you, my game has very few long-lived characters.
October 6, 2013 at 4:22 pm
So are we gonna do this in the next game?
October 6, 2013 at 7:28 pm
Yes we will, I think. The next problem is how to handle the difficulty settings in combat – I suspect they are borked as well…
October 7, 2013 at 12:39 am
Interesting. You have to wonder how much thought goes into this stuff on the part of the game designers.
I think the curve of success for folk of equal skill would probably vary based on the nature of the opposed test though that’s probably too fiddly to actually model.
In combat, it might be the other way around – decreasing with skill level? One can imagine that two expert fencers would both find it hard to land telling blows so the chance of success should be lower for them in comparison to two novices, both of whom know the basic principle – stab the other guy with the pointy end – but for whom basic parries might well be beyond them – so they both hit each other very easily in a MAD fashion.
In contrast, for the thief sneaking past the guard, if both are of equal low skill should that be more or less likely than if they are both of equal great skill? I think here there’s no reason for the two to vary. Similarly with the thief picking a lock.
I thought it was interesting how WHFRP distinguished between intrinsic task difficulty which sets the number of challenge dice (are you picking an easy, routine or difficult lock), and circumstance which sets the number of boon dice (correct tools, good light, and no hurry) vs bane dice (rusty nails, pitch black and rushing to escape before rains flood your dungeon cell), with the potential for both bane and boon dice in the same check of course. Most systems would boil all these modifiers down to a single difficulty check. Is WHFRP’s more complex approach adding any value beyond this? It’s cool rolling all the dice, but is it easier for a GM or player to judge their chance of success (probably not). Is there some other gain? Or is this one of the candidates for the streamlining you were considering?
The other thing you could look at would be the actual impact of all those dice results on power card outcomes. As we discussed, most seem just to add token damage, and often, seemingly good results (comets, multiple success or multiple boons), can have no value at all if the power card doesn’t specifically list a consequence for that particular result – leaving players a bit underwhelmed when they role 3 spare successes only to discover that their particular power doesn’t reward extra success, only extra boons (I may be using the terminology slightly incorrectly here but you get the idea).
April 24, 2020 at 12:59 pm
Great article and break down. I’m about to pick up a campaign with some friends. One of them has a barber surgeon with a 5 fellowship and charm trained. Most of the time he’s rolling one challenge die on his charm and guile checks. I’ve been looking for a way to make these more challenging for him and I love what you’ve done here! Cheers
April 24, 2020 at 1:36 pm
Great! Another way to make that dude a little less effective is to do something horrible to his face – I dunno, have an orc bite it off or something. Then he can have multiple extra challenge dice whenever you want!
April 25, 2020 at 3:35 am
It’s been a very investigative campaign in Bogenhafen with only one combat so far (about session 20). I did incorporate some disposition rules to add challenge/fortune/misfortune dice to increase the challenge rating but I really like what you’ve laid out here.
There’s only two of them, a Barber-Surgeon and an Agent, both with two Strengths. I’ve made the streets in the bad areas scary enough they are pretty fearful going about after dark. The problem, as you clearly laid out was that unless I have an equal opposing characteristic the tests are “Easy”. And having a five willpower opponent feels like they should be rare and the more than the two purple dice the rules provide.
January 28, 2022 at 4:11 am
I know this was done ages ago, but thought I’d follow up. I’ve using this tweak to the opposed rolls since my last post.
I love it.
Most challenges are one purple and one black, though occasionally two purples for a slightly significant opponent. Using the target’s ACE budget, when appropriate let’s me tweak the challenge appropriately.
Just thought I’d say thanks and great work.
PS. We started a parallel campaign that was supposed to be a few sessions, but has now gone on for the last year and a half. The above player has a Smuggler with a two Willpower and needed his crippled leg looked at. He went to his Barber Surgeon as a laugh and during that exchange we used his two Willpower to resist the five Fellowship using your above rules. Worked as expected 😉
February 3, 2022 at 3:28 pm
I’m really glad my rules suggestions have helped! I’m running Genesys now and the system has updated the skill checks to work kind of similar to my suggestions, so it seems the people in charge also realized that their difficulty system needed improvement.
February 10, 2022 at 8:05 am
Yeah, it’s a bit of a thorn in side of the folks still playing. Your solution was intuitive and elegant. Your understanding of the math proved it out. Just thought I’d let you know how it was working in game.
Do you have a post on you thoughts on playing Genesys?
February 19, 2023 at 3:18 am
Quick update. We’ve been playing weekly, for the most part and have used the figure 3 style. I think you nailed it with your suggested one purple + half defender attribute with the remainder converted into a black. I’ll be trying that going forward. Thanks again!