The mechanics of the new Warhammer Fantasy Roleplaying edition (WFR 3rd) are very opaque. This results in many questions about how the mechanics really work. One common question revolves around the mechanics for stance. Characters can choose to be in reckless or conservative stance and this choice can change the dice that they roll and even the outcome of the same roll result. One analysis tried comparing reckless versus conservative stance for the classic test action Troll-Feller Strike. Unfortunately, errors in the probability generator they were using made the final result more difficult to interpret. This article is an attempt to answer the question of how the reckless and conservative stances effect attacks.

## Mechanics

For people that aren’t familiar with the mechanics.

Rolls in WFR 3rd use dice pools. These consist of dice of different sides, colors, and symbols. The basic roll uses a number of Blue dice equal to the controlling characteristic plus Yellow dice equal to the skill and possibly a number of White dice for a variety of reasons. The pool will also contain dice that represent the difficulty of the task, Purple and Black dice with negative results on them. Players can change this pool by choosing to go into what are called stances. These are either reckless, nominally representing risk taking, or conservative, nominally what it says on the tin. When they do so, they then replace a number of the basic Blue dice with either Red (reckless) or Green (conservative) dice.

As an added wrinkle, the results of the die rolls are determined by referencing a card. This card will often give different results depending on which stance the character is in. Also, even when someone isn’t in a stance, i.e. they are rolling all Blue dice, they still have to reference either the reckless or the conservative side of the card. Each character has a default side so that if they are in a neutral stance they will always use either the reckless or the conservative side depending on the character.

## Basic Dice Probabilities

Dice basics and the differences between the stance dice have been covered elsewhere, but for anyone that hasn’t read about it here is the general breakdown. Dice have five different types of results, success (can be positive or negative), boons (basically side effects, can also be positive or negative), comet (a positive wild card), chaos star (a sort of wild card negative result), and penalties (delay or exhaustion depending on the die being rolled). More than one result can appear on a die face.

The basic breakdown of results for the Blue, Green, and Red dice are

## Blue

Percent | Result |
---|---|

50% | 1 success |

25% | 1 boon |

25% | nothing |

Average 0.5 success, 0.25 boons

## Green

Percent | Result |
---|---|

70% | 1 success |

30% | 1 boon |

20% | delay penalty |

10% | nothing |

Average 0.7 success, 0.3 boons, 0.2 delay

Note that because of the multiple symbols on a side the total adds up to more than 100.

## Red

Percent | Result |
---|---|

20% | 2 successes |

30% | 1 success |

10% | 2 boons |

10% | 1 boon |

20% | -1 boons |

20% | exhaust penalty |

20% | nothing |

Average 0.7 successes, 0.1 boons, 0.2 exhaustion

As can be seen, both Red and Green dice average more successes than Blue dice. However, the Red die has a higher chance of rolling no successes (50%) than the Green (30%) but can roll 2 successes while a Green die can only roll 1. The result is that Red dice should have more variance in the successes rolled than Green dice. This can be seen graphically in Figure 1 which shows the distribution of success results for 3 Blue, 3 Red, and 3 Green dice.

## Figure 1. Successes on 3 Characteristic Dice

Interestingly, while Green dice yield more boons on average than Blue dice, the Red dice yield fewer. And because the Red dice can roll from -1 to 2 boons while the others can only roll 0 to 1 the variance for boons is very high for the Red dice, seen graphically for three of each in Figure 2.

## Figure 2. Boons on 3 Characteristic Dice

Three Red dice have only around a 40% chance of rolling positive boons and around a 30% chance of rolling negative boons. The Green dice have over a 75% chance of rolling positive boons.

## The Action Card: Troll-Feller Strike

Once the dice are rolled they need to be interpreted. This is done by referencing the card used for the action. In the case of an attack card it will list the damage and other effects available for the roll. Should the attack succeed the attacker will do their base damage, for their characteristic and weapon damage, with any modifiers from the results on the card. The target subtracts their soak, the sum of their toughness and armor value, and any damage that gets through is applied to wounds. If they exceed the number of wounds they can take then they are knocked out or killed. Some attacks will do critical hits. These hits result in special effects drawn from the critical hit deck and range from mild to severe. Because this comes from a deck draw and different games will have different decks depending on which supplements they are using the available criticals will vary from game to game.

For some reason the card that is generally used to discuss attacks in the game is Troll-Feller Strike. Because of this I used this action for this article. However, I would note that it is actually a pretty poor choice for these kinds of analyses. The action card is reasonably complicated and, as I will mention below, produces not one but two results with variable outcomes based on the situation. It also has some pretty complicated choices for the wild card result as will be mentioned later.

The results available for Troll-Feller Strike are

Conservative | Reckless | |||
---|---|---|---|---|

1 success | base damage +1 | 1 success | base damage +1 | |

3 successes | D +3 | 3 successes | D +3 | |

1 boon | +1 dam, ignore armor | 1 boon | +1 dam, ignore armor | |

2 boons | +3 dam, +1 critical | |||

-1 boon | 1 fatigue | -1 boon | 1 fatigue | |

-2 boon* | 1 fatigue | -2 boon* | 1 fatigue | |

1 comet | +1 critical, special dam | |||

1 chaos | 1 wound | 1 chaos | 1 wound |

* all physical actions have this as a possible result so it isn’t listed on the card

As can be seen, the reckless side can produce more damage than the conservative side having two more damage increasing results.

## Assumptions

I started by assuming that base damage was 10, 5 strength plus hand weapon, as this is the fairly standard assumption.

More complicated assumptions were needed about boon choices and the use of the wild comet result. It should be noted that successes use the highest available result, so 3+ successes will use the 3 success result, but boons are used to purchase results separately. So on the reckless side 2 boons could be used to purchase either +1 dam, ignore armor for 1 boon or +3 dam, +1 critical for 2 boons. If the attack had rolled 3 boons both could be purchased for +4 dam, ignore armor, +1 critical. So the boon results require making choices. In addition, the comet is a wild die and can be used for several possible results, +1 success, +1 boon, +1 critical (mostly useless), or a special comet result on the card. In the case of Troll-Feller Strike the reckless side has a comet result, the conservative side does not.

Because of all the choices some valuation had to be placed on the different results. Two of the results have variable effects, ignoring armor and the bonus damage from the special comet critical on the reckless side. These make evaluating Troll-Feller more difficult and generally a poor choice for analyzing the system. But that is the card I used so I needed to know how much value to put on these results. In the article that started this, the author estimated the average armor value of the opponents in the rule book at 2, which would basically increase the wounds done by 2. He also looked through his critical deck at the damage that the comet critical was likely to inflict and settled on an average value of 2.25. These values seemed reasonable so I used them for this analysis. Given that the effect of critical hits on most NPC’s is pretty negligible critical hits were valued more than nothing but less than damage.

Putting this all together

+3 damage +1 critical > +1 damage ignore armor (+3 damage for this analysis) >

comet critical (+2.25 damage +1 critical) > +2 damage

This means that for 2 boons I chose the +3 dam, +1 critical over the +1dam, ignore armor. For 3 boons I chose both the +1 dam, ignore armor and the +3 dam, +1 critical.

The most difficult aspect is deciding the use of the comet wild card roll. Obviously, if the attack misses then bonus damage and critical hits mean nothing, the attack missed. Therefore, if a comet result can be used to increase the roll from 0 successes to 1 success that is the best use of the comet. However, increasing the results from 2 successes to 3 successes only increases the damage from D +1 to D +3, or +2 points, which is less useful than the comet result and so on the reckless side the comet was not used to increase successes above 1.

If the attack is going to miss no matter how the comet is spent then the only possible value is using it as a boon. It might cut down on negative effects. So that is how the comet was spent on all attacks of -1 success or lower.

In terms of boons, moving from 0 to 1 boon yields +3 damage (due to the armor assumption) and that is better than moving to 3 successes or the comet critical. Therefore, if the attack hit, but with 0 boons and a comet, the comet was spent increasing the boons to 1. For the reckless side there were more considerations. Moving from 1 to 2 boons only moved from +3 damage to +3 damage and +1 critical for a difference of +1 critical. In that case the comet was spent for the special damage. However, moving from 2 boons to 3 boons increased the damage from +3 damage, +1 critical to +6 damage, +1 critical. So for attacks that hit with 2 boons and a comet the comet was used to increase the boons to 3.

On the reckless side, once the attack had 1+ successes and 3+ boons the best use of a comet was the special critical so that was chosen. On the conservative side once the attack had 3+ successes and 1+ boons the only thing to add was +1 critical so the comet was used for that result.

For both sides a chaos star result was used to give the attacker 1 wound.

One complication that I left off is that all weapons have a critical rating. You can spend that many boons to gain +1 critical. As this varies from weapon to weapon and as criticals are mostly worthless I just left this out.

## Comparing the Card Sides

The reckless side is obviously better in terms of damage. But how to quantify the difference? The easiest way was to compare rolls using only Blue, no Red or Green dice. Due to the default for each character, some will use the reckless side when in neutral stance and some will use the conservative side. Because the rolls were the same the only difference in performance was from the card sides.

The original article used a pool of 3 Blue dice, 2 Red or Green dice, 1 Yellow die, and 1 Purple die. So I used a basic pool of 5 characteristic dice (Blue plus maybe Red or Green), 1 Yellow die, and 1 Purple die. Aficionados will note that this dice pool is technically impossible as Troll-Feller Strike has a penalty of 1 Black so the pool would have to have at least 1 Black. However, on average White dice basically cancel out Black dice. They do increase the variance of the roll, but it isn’t enough to worry about, and the pool would likely have one or more White dice so I’m sticking with the original pool.

So, after all of that a Monte Carlo analysis was run generating 1 million rolls of the pool 5 Blue, 1 Yellow, 1 Purple. The results were interpreted using the conservative side and the reckless side of the action card. The results are listed in Table 1.

## Table 1. Troll-Feller No Stance Dice

Conservative | Reckless | |
---|---|---|

Percentage Hit | 88% | 88% |

Average Damage | 11.2 | 12.0 |

Adjusted Average* | 12.6 | 13.2 |

Average Criticals | 0.08 | 0.42 |

Average Fatigue | 0.07 | 0.07 |

Percentage wound attacker | 12.5% | 12.5% |

Percentage ignore armor | 67% | 48% |

Percentage comet critical | NA | 8.8% |

*Adding in 2 damage for ignore armor and 2.25 damage for the comet critical

The reckless side does do more damage on average, though not by tremendous amounts (0.6 damage).

## Is Average Any Good?

But that brings up the question, is average damage a good way to look at attacks in WFR 3rd? It is the traditional method for comparing attacks. That is probably because it works well for D&D. In that system damage is a smooth, continuous function, at least in terms of whole numbers. An attack that does 1d8 +3 damage has equal chances of doing 4 damage, or 11, or any number in between. 3d6 has a much better chance of yielding a 10 or 11 than 3 or 18 but can roll 3 or 18 or anything in between. Targets can also take damage ranging from 1 to several hundred depending on the target. The result is that average damage is a pretty good indication of how effective an attack is in D&D.

WFR 3rd does not have smooth, continuous damage functions. This should be evident from the discussion of the Troll-Feller Strike card but is really stark in the case of Thunderous Blow. For the typical user that attack will do either 12 damage or 19. It can’t roll 14 or 15. In addition the amount of damage opponents can take is fairly restricted. Unless they are a henchman, the weakest human requires 12 wounds to drop. I haven’t read the monster stats in the main game but in looking through published adventures I haven’t seen anything that required more than 19. That is a small range.

These two elements can combine to give some odd effects. Imagine attack A that always does 14 damage. Its average damage is thus 14. A second attack, B, has an 80% chance of doing 12 damage and a 20% chance of doing 17. The average damage is 13. Attack A has higher average damage, but is it a better attack? It depends on the target.

Imagine a target with 2 soak that needs 12 wounds to defeat. 14 damage will drop the target in one hit, 14 -2= 12. On the other hand, 12 damage will leave the target standing, 12 -2= 10. Obviously 17 damage will drop them as well. So of the two hypothetical attack cards attack A will always defeat that target in 1 hit but there is an 80% chance that attack B will require 2 hits. In this case attack A, with the better average damage, is superior.

Increase the target’s toughness. Give them 3 soak and require 14 wounds to defeat. Attack A will do 14 -3= 11. The target is still standing and it will require 1 more hit to drop them. Attack B has an 80% chance of doing 12 damage for 12 -3= 9 wounds. That would leave the target with 5 and another hit will finish them, just like the first attack. However, attack B has a 20% chance of doing 17 damage for 17 -3= 14 wounds. The target goes down in 1 hit. Against this opponent the attack B is better with a 20% chance of defeating them in one hit.

Increase the target’s toughness again. Give them 5 soak and require 18 wounds. Again, the attack A defeats them in two hits, 14 -5= 9 x 2 =18. Attack B has a 20% chance of doing 17 damage for 17 -5= 12 wounds. If the next hit does 12, the minimum, then the target takes 12 -5= 7 for a total of 19 and goes down. Obviously the same result occurs if the first hit does 12 and the second 17. However, there is a 64% chance that the first two hits will both do 12 damage. This would cause 12 -5= 7 x 2= 14 wounds. A third hit would be necessary. So for this opponent attack A is back on top.

While average damage provides a nice simple number it is a poor indicator in WFR 3rd. What would be better? The number of attacks needed to defeat an opponent can’t be calculated. It depends on the opponent and because attacks in WFR 3rd generally can’t be used again and again since they have a cool down it would also depend on what other attack actions the character had. While more complicated than a simple number a damage curve is probably more informative. This would be a graph showing the chance of doing that much damage or more on an attack roll. Such a graph for the 5 Blue die Troll-Feller Strike example is shown in Figure 3.

## Figure 3. Comparing Conservative/Reckless with No Stance Dice

The reckless side produced higher damage with the same roll almost 70% of the time and some 20% of the time scored higher damage than the conservative maximum.

## Adding in the Dice

While the reckless side of the card was clearly better, the Red dice seemed worse than the Green dice. So I ran a Monte Carlo analysis of dice pools containing 1 Yellow and 1 Purple dice and 5 characteristic dice ranging from 1 to 3 Red dice and 1 to 3 Green dice, with enough Blue dice to total 5. The results are shown in Table 2.

## Table 2. Troll-Feller at Different Degrees of Stance

3 Green | 2 Green | 1 Green | 1 Red | 2 Red | 3 Red | ||
---|---|---|---|---|---|---|---|

Percent Hit | 95% | 93% | 91% | 89% | 90% | 91% | |

Average Damage | 12.4 | 12.1 | 11.7 | 12.1 | 12.2 | 12.4 | |

Adjusted Average | 13.9 | 13.5 | 13.1 | 13.3 | 13.4 | 13.4 | |

Average Criticals | 0.10 | 0.09 | 0.09 | 0.41 | 0.40 | 0.40 | |

Average Fatigue | 0.07 | 0.07 | 0.07 | 0.32 | 0.55 | 0.74 | |

Percent Delay | 49% | 36% | 20% | NA | NA | NA | |

Percent Wound | 12.5% | 12.5% | 12.5% | 12.5% | 12.5% | 12.5% | |

Percent ignore armor | 76% | 73% | 71% | 46% | 44% | 41% | |

Percent comet critical | NA | NA | NA | 9.4% | 10.0% | 10.7% |

Quite surprisingly, 2 or 3 Green dice on average did **more** damage than 2 or 3 Red dice, despite the fact that the reckless side of the card is significantly better. This is presumably driven by the higher chance of rolling positive boons and the higher chance of hitting at all. Look back at the results table for the attack. In the absence of boons and comets, comets are only found on the Yellow dice and so have nothing to do with stance, both sides of the card are identical. Indeed, without those the damage done by Troll-Feller Strike, considered one of the best attacks in the game, is only 1 point higher than melee strike, the default attack that everyone gets. The key to doing serious damage is to roll boons. But Red dice roll fewer boons on average than even Blue dice. The Green dice also result in fewer misses as they more consistently roll successes, 70% chance versus 50% chance.

Of course, the same caveat applies about average damage as mentioned above. As the original example looked at 3 Blue, 2 Red or Green, 1 Yellow, and 1 Purple Figure 4 shows a damage curve for those two results.

## Figure 4. Troll-Feller 2 Green Versus 2 Red

As expected, the Green dice are more likely to hit and give decent damage than the Red dice. However, at the high end the Red dice have around a 20% chance of scoring more damage than the Green dice possibly can and are more likely to score above 14 damage as well.

## Thoughts

In the end it looks like the mechanics actually worked. The Green conservative dice gave more consistent results. The Red reckless dice and the reckless side of the card combined to give worse average performance but a higher chance of significant results.

Of course, despite this article being way too long this doesn’t really answer the question. The utility of Red versus Green dice will vary depending on the action card used. Possibly more importantly they will likely vary depending on the difficulty of the roll. Most action cards top out at 3+ successes. At low difficulty levels like 1 Purple, maximum -2 successes, the ability of the Red dice to roll large numbers of successes is likely wasted. Higher difficulty levels could swing things in favor of Red dice. Though that is a topic for another article.

Filed under: community, Game Design | Tagged: dice, Probability, RPGs, rules, statistics |

House of Cards: Reckless Cleave in Warhammer 3rd | Emerald City Gamefest, on July 12, 2013 at 9:39 am said:[…] already generated the dice pools to analyze Troll-Feller Strike I figured I might as well see what would happen if I applied those results to a different action […]