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.