In addition to the print version which will of course be available at the door that weekend (August 911, 2013), you can download it as an ebook in three different formats: .PDF (good for viewing onscreen on PC, iPad, etc.), .ePub (for Nook, Kobo, Sony Reader, etc.) and .mobi (for Kindle, etc.)
The files should be posted shortly to the official convention site, but you can also get them from:
In order to make it complete I needed a comparable result for Troll Feller. That meant calculating results including the 1 Black die penalty on the attack. So I calculated results for 5 characteristic dice, 1 Yellow, 1 Purple, and 1 Black. I also changed the base damage from 10 to the 12 I have been using for the other actions.
As an interesting aside I plotted the results for 2 Red and 2 Green dice with and without the Black die. For rolls in the middle of the distribution the Black die decrease likelihoods by a little less than 10%. The effects became less pronounced at either end of the distribution.
Attack  3 Green  2 Green  1 Green  0 Green (Blue)  0 Red (Blue)  1 Red  2 Red  3 Red  

Melee Strike  12.6  12.3  11.9  11.5  11.5  11.7  11.9  12.1  
Thunderous Blow  11.4  11.2  10.9  10.6  11.9  11.9  12.0  12.1  
Mighty Swing  13.4  12.8  12.1  11.4  11.3  11.7  12.1  12.4  
versus 3+ Armor  12.9  13.3  13.7  14.1  
Troll Feller  14.9  14.4  13.8  13.2  13.6  13.8  14.1  14.3  
Reckless Cleave  15.7  15.3  14.9  14.3  15.7  15.7  15.7  15.7 
Putting all 43 damage curves together would have been an unreadable mess so I plotted damage curves for 2 Green dice and 2 Red dice.
Looking at the overall comparisons the higher damage attacks generally seem to come in two styles. The highest average damage comes from having large damage for minimal success. If the attack roll is 1 success and 1 boon on the reckless side the attacks do
Reckless Cleave  18 

Troll Feller Strike  16 
Mighty Swing (3+ armor)  15 
Mighty Swing  13 
Thunderous Blow and Melee Strike  12 
Reckless Cleave is the big winner gaining +5 damage from the single boon, though Troll Feller gained +3 (versus armor 2). Thunderous Blow is an odd version of this. Instead of 1 boon, it needs the rarer 1 comet to get its huge damage boost making it a sort of pale shadow of Reckless Cleave.
The other style is to have a large number of available damage additions yielding the possibility of very high damage on a good roll. For 3 success, 6 boons, and 1 comet the results look like
Mighty Swing (3+ armor)  26 

Mighty Swing  24 
Troll Feller Strike  23.25 
Reckless Cleave  20 
Thunderous Blow  19 
Melee Strike  14 
Notice how the order of Mighty Swing, Troll Feller, and Reckless Cleave invert as the attack becomes more successful.
One attack, however, sort of has both, Troll Feller Strike. The 1 boon line is +1 damage and ignore armor. For all of these calculations I have been assuming an armor of 2. The result was a good but not great 1 boon line of effectively +3 damage. This was not as good as Reckless Cleave with +Str, generally 5 for a combat character. But as the target’s armor increases Troll Feller Strike becomes a better attack. At armor 4 its 1 boon line is as good as Reckless Cleave but Troll Feller also has 2 boons for +3 damage +1 critical and 1 comet for +1 critical and a random amount of damage. If the target’s armor is one lower than the character’s strength Troll Feller Strike becomes possibly the best melee attack in the game. The flavor text for Troll Feller is that it is used by fanatic dwarfs to kill huge monsters like trolls, the kind of opponents that would have a high armor. In addition the attack can only be used if outnumbered or against large opponents. So it is not unreasonable that it would excel at fighting huge, heavily armored foes.
The graphs only cover damage. There is more to an attack in WFR3 than damage. They have recharge rates so that they can’t be used all the time, some come with penalties to use, and some have particularly horrible things happen on a poor roll.
Melee Strike is free and can pretty much be used all the time being the only attack with a recharge of 0.
Thunderous Blow doesn’t really have penalties other than needing to recharge.
Mighty Swing has a 2 Black die penalty making it more difficult and increasing the chance of simply failing.
Reckless Cleave penalizes the character’s active defense and on a poor roll increases the damage they take from attacks.
Troll Feller Strike can only be used if outnumbered or against large foes, has a 1 Black die penalty, and on a chaos star, which no amount of good dice can counteract, damages the character, though at recharge 2 it can be used fairly often.
These articles highlight the opaque nature of the WFR3 rules. Just looking at the action it is not obvious that the conservative side of Mighty Swing would generally do more damage than the reckless side. That increasing the number of reckless dice can decrease the effectiveness of Reckless Cleave was also unexpected.
I must admit, however, that the actions basically work. The only garbage action, conservative Thunderous Blow, is obviously garbage. The rest are fine for conservative or reckless characters. The two attacks considered to be really good by the WFR3 community, Troll Feller and Reckless Cleave, actually are good attacks. The better attacks have more restrictions, penalties, and bad things happen on poor rolls. At least for this group of cards a player with a reasonable knowledge of the game could make good choices without having to run through all the statistics.
]]>To remain consistent with the other posts I modeled Melee Strike using a great weapon.
Conservative/ Reckless  

1 success  base damage 
3 successes  D +2 dam 
2 boons  free maneuver 
2 boons#  +1 critical 
2 boons  foe can disengage 
2 boons*  1 fatigue 
# from the Critical Rating of the weapon
* all physical actions have this as a possible result so it isn’t listed on the card
Comet use
The comet was given the following priority: increase 0 success to 1 > increase 2 successes to 3 > +1 critical
When using boons in order to maximize damage the +1 critical was given priority over the maneuver. Foe escape was given priority over fatigue.
From a pool of 1 Yellow and 1 Purple plus 5 characteristic dice from 3 Green to 3 Red
3 Green  2 Green  1 Green  0 Green (Blue)  0 Red (Blue)  1 Red  2 Red  3 Red  

Percent Hit  95%  93%  91%  88%  88%  89%  90%  91%  
Average Damage  12.6  12.3  11.9  11.5  11.5  11.7  11.9  12.1  
Average Criticals  0.52  0.49  0.45  0.41  0.41  0.41  0.40  0.40  
Average Fatigue  0  0  0  0  0  0.20  0.36  0.49  
Percent Delay  49%  36%  20%  0%  
Percent Foe Escape  4.7%  4.2%  3.9%  3.6%  3.6%  5.0%  5.9%  6.5% 
The attack is the same on both sides of the card and Green dice are better. Not surprisingly, characters rolling Green dice get better results. That seems pretty stilted for a basic action, though give the differences in the dice the two sides can never give exactly the same results. Given that conservative actions often take longer to recharge and that the conservative penalty is to delay the recharge of actions conservative fighters probably need Melee Strike more often than reckless fights. On the other hand, fights tend to be short so someone with a decent number of attacks probably never needs to roll Melee Strike.
]]>The card has some special effects.
On the conservative side the weapon Critical Rating is reduced by 1 to 1.
On the reckless side, if the target has 3 or more points of armor then the attack ignores 2 points of armor, effectively increasing damage by 2 points.
Conservative  Reckless  

1 success  base damage +1  1 success  base damage  
2 successes  D +1 dam  
3 successes  D +3 dam  3 successes  D +3 dam  
4 successes  D +5 dam  
1 boon  +1 dam  
2 boons  +3 dam  2 boons  +3 dam  
3 boons  +5 dam  
2 boons#  +1 critical  2 boons#  +1 critical  
2 boons  1 fatigue, delay this attack  2 boon  1 fatigue, 2 if target has 3+ armor 

2 boons*  1 fatigue  2 boons*  1 fatigue  
1 comet  +1 dam +1 crit  1 comet  +2 crit  
1 chaos  delay this attack 
# from the Critical Rating of the weapon
* all physical actions have this as a possible result so it isn’t listed on the card
Comet use
On the conservative side comet priority was: increase 0 successes to 1 > increase 1 boon to 2 > increase 2 or 3 successes to 3 or 4 > comet line.
On the reckless side comet priority was: increase 0 success to 1 > increase 2 successes to 3 > increase 1, 2, or 4 boons to 2, 3, or 5 > increase 1 success to 2 > increase 0, 3, or 5 boons to 1, 4, or 6 > comet line
From a pool of 1 Yellow, 1 Purple, and 2 Black plus 5 characteristic dice from 3 Green to 3 Red
3 Green  2 Green  1 Green  0 Green (Blue)  0 Red (Blue)  1 Red  2 Red  3 Red  

Percent Hit  86%  83%  79%  76%  76%  78%  80%  81%  
Average Damage  13.4  12.8  12.1  11.4  11.3  11.7  12.1  12.4  
Versus 3+ Armor  12.8  13.3  13.7  14.1  
Average Criticals  0.34  0.32  0.29  0.27  0.04  0.04  0.05  0.06  
Average Fatigue  0.04  0.04  0.05  0.05  0.05  0.27  0.46  0.63  
Percent 3+ Armor Fatigue  4.1%  6.7%  9.7%  13.2%  
Percent Delay  49%  36%  20%  0%  
Percent Delay Attack  4.0%  4.2%  4.5%  4.7%  12.5%  12.5%  12.5%  12.5% 
Interestingly, this is the only card I’ve examined so far that yielded better damage on the conservative than reckless side for 5 Blue dice. While the reckless side has some very high damage potential, D +12, it isn’t so much better than the conservative side, D +9, and requires 6 boons and 3 successes. The steep requirement for boons from Red dice combined with a 2 Black die penalty means that those really high results are quite rare, only around a 6% chance of scoring D +7 or higher damage with 3 Red dice. Without the bonus piercing effect the reckless side fairly consistently yields lower damage than the conservative side, making this actually a very nice attack for a conservative fighter. However, against high armor opponents reducing their armor by 2 on the reckless side effectively increases the damage by 2. This makes it a very strong attack against armored opponents as seen in the figure showing a damage curve for 5 Blue dice.
The extra Black dice also result in a high overall chance of missing, around ¼ for 5 Blue dice. Given the short duration of combats missing is pretty horrible. This, combined with the very low chances of scoring the high end rolls, suggests that Mighty Swing is better for more skilled characters. It would be interesting to see how increasing the positive dice pool would affect Mighty Swing especially compared to an attack with fewer lines like Reckless Cleave.
Conservative  Reckless  

1 success  base damage  1 success  base damage  
3 successes  D +1 critical  2 successes  D +1 critical  
2 boons  +1 critical  1 boon  +1 critical  
2 boons#  +1 critical  2 boons#  +1 critical  
2 boons  1 fatigue  1 boon  1 fatigue  
2 boons*  1 fatigue  2 boons*  1 fatigue  
1 comet  +7 dam  
1 chaos  delay this attack 
# from the Critical Rating of the weapon
* all physical actions have this as a possible result so it isn’t listed on the card
Comet use
On the conservative side comet priority was: increase 0 successes to 1 > +1 critical
On the reckless side comet priority was: increase 0 successes to 1 > comet line
From a pool of 1 Yellow and 1 Purple plus 5 characteristic dice from 3 Green to 3 Red
3 Green  2 Green  1 Green  0 Green (Blue)  0 Red (Blue)  1 Red  2 Red  3 Red  

Percent Hit  95%  93%  91%  88%  88%  89%  90%  91%  
Average Damage  11.4  11.2  10.9  10.6  11.8  11.9  12.0  12.1  
Average Criticals  1.18  1.08  0.98  0.89  1.39  1.39  1.39  1.39  
Average Fatigue  0.01  0.02  0.02  0.02  0.08  0.33  0.55  0.74  
Percent Delay  49%  36%  20%  0%  
Percent Delay Attack  12.5%  12.5%  12.5%  12.5% 
Thunderous Blow is designed to do critical hits. It does so. As can be seen in the results table it does yield pretty consistent amounts of critical hits. Unfortunately, critical hits are generally not all that useful except against henchmen where they do extra damage. So even with the critical hits the fact that the conservative side does less damage than Melee Strike, the game’s basic melee attack, means that the conservative side of Thunderous Blow just isn’t all that useful. This is the first card that I’ve examined where a character really wouldn’t want the action depending on which stance they favored. In this case, conservative fighters should avoid Thunderous Blow.
The high damage hits are only available on the reckless side and only with a comet roll. Comets are only found on skill dice (Yellow) which have a 1/5 chance of rolling a comet. Thus the utility of this attack is going to depend heavily on the number of weapon skill dice the character has. Also, the chance of doing the high damage hit doesn’t vary all that much with the rest of the dice pool. It went from 16.8% chance with 5 Blue dice, since the attack has to hit and the comet can’t be spent making the attack hit, to a 17.4% chance with 3 Red dice.
]]>For reasons that will become apparent in future articles I chose to switch the base weapon for the simulation. Instead of using 5 strength and a hand weapon I used 5 strength and a great weapon giving a base damage of 12 and a Critical Rating of 2. For those unfamiliar, a Critical Rating is the cost in boons for any attack made with that weapon to generate a critical hit, as will be seen in the card description.
Here are the available results for Reckless Cleave
Conservative  Reckless  

1 success  base damage +2  1 success  base damage +1  
3 successes  D +3  
2 boons  +Str^ dam, delay this card  1 boon  +Str^ dam, delay this card  
2 boons#  +1 critical  2 boons#  +1 critical  
1 boon  1 soak  1 boon  1 soak  
2 boons*  1 fatigue  2 boons*  1 fatigue  
1 comet  +2 critical  
1 chaos  delay defense  1 chaos  delay defense 
^ assumed to be 5 for this example
# from the Critical Rating of the weapon
* all physical actions have this as a possible result so it isn’t listed on the card
Comet use
On the conservative side comet priority was: increase 0 successes to 1 > increase 1 boon to 2 > +1 critical
On the reckless side comet priority was: increase 0 successes to 1 > increase 0 boons to 1 > increase 2 successes to 3 > comet line
For boons extra damage was chosen before the critical and reduced soak was chosen before fatigue.
From a pool of 1 Yellow and 1 Purple die plus 5 characteristic dice from 3 Green to 3 Red
3 Green  2 Green  1 Green  0 Green (Blue)  0 Red (Blue)  1 Red  2 Red  3 Red  

Percent Hit  95%  93%  91%  88%  88%  89%  90%  91%  
Average Damage  15.7  15.3  14.9  14.3  15.7  15.7  15.7  15.7  
Average Criticals  0.16  0.15  0.14  0.13  0.27  0.30  0.32  0.34  
Average Fatigue  0  0  0  0  0  0.20  0.37  0.51  
Percent Delay  49%  36%  20%  0%  
Percent 1 Soak  7%  7%  7%  8%  8%  12%  17%  23%  
Percent Delay Defense  12.5%  12.5%  12.5%  12.5%  12.5%  12.5%  12.5%  12.5% 
Several of the patterns seen with TrollFeller Strike were repeated here. The reckless side was stronger without stance dice. Adding in Green dice increased the chance to hit and average damage. However, there were some differences. While for TrollFeller Strike the conservative side gained lower and middle damage hits in exchange for the high damage hits from the reckless side, here there are no middle damage hits on the conservative side. However, its big damage hit is only 1 point lower than the reckless big damage hit and more likely. So it is a solid conservative attack. However, reckless damage is usually better. 3 Red dice give better damage than 3 Green dice 62% of the time while 3 Green does more damage only 32% of the time. Some favoritism towards the reckless side didn’t seem unreasonable for an action called reckless cleave.
Ironically, however, you don’t want to be too reckless using the attack. Average damage did not go up as Red dice were added. Actually it went down slightly but not enough to change the rounded numbers in the chart. Given that Red dice increased the chance to hit this meant that any extra damage the attack was gaining from hitting more often it was losing in high damage attacks. For attacks that hit, 5 Blue dice did on average 0.6 more damage per hit than 2 Blue plus 3 Red. This is because of the large damage boost from rolling 1 boon and the lack of higher value boons that add damage. Red dice roll fewer boons than Blue dice. So as Red dice were added the chance of getting the boon result, which is the entire reason people take this attack in the first place, goes down. This can be seen in the 18 or better damage line in the figure. Red dice can result in rolls with really high numbers of boons, but with no more damage boons to spend them on they were mostly wasted. Maybe it should have been called SortofReckless Cleave, though it is still a great attack. This also implied that characters in reckless stance may really have to manage their stance from round to round while conservative characters can just go more and more conservative.
]]>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.
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
Percent  Result 

50%  1 success 
25%  1 boon 
25%  nothing 
Average 0.5 success, 0.25 boons
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.
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.
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.
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.
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 TrollFeller 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 TrollFeller 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.
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 TrollFeller 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 TrollFeller 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.
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 TrollFeller 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.
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).
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 TrollFeller 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 TrollFeller Strike example is shown in Figure 3.
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.
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.
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 TrollFeller 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.
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.
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.
]]>So what is this aspect? That takes a bit of explaining. Thanks to the different specialized symbols rather than just numbers like an ordinary die WFR3 has several axes for resolution on any roll.
What do I mean by that? The classic d20 system only has one axis. Roll a d20 and add a number to it. The result can be higher or lower but it just produces one number. This is why in d20 systems everything uses a separate roll. In contrast the One Roll Engine, as the name indicates, resolves entire actions from initiative to hit location with a single roll. Its dicing mechanic has two axes. A player rolls a number of 10 sided dice and looks for matching numbers. For example if 3 of the dice showed the number 2 this would be 3 2’s, while 2 dice showing 8’s would be 2 8’s. The number of matching dice and the number on the die give two different results to use to resolve an action. This is why I don’t care for the One Roll Engine. It only has two axes. However, those two results are used to determine every aspect of a roll leading to strange links. So an attack will have initiative, damage, to hit, and target location, four different things but using only two numbers for them. Thus the earlier an attack goes in the round the more damage it does and it is easier to avoid an attack that might hit your feet than it is to avoid one that might hit your head.
WFR3 has five different axes. It has success, boons (basically side effects, negative side effects are called banes but are really just negative boons), a special bad effect called a Chaos Star, a wild card called a Comet, and the possibility of a separate penalty. For those that know the game a roll can produce a delay penalty or an exertion penalty. While these are different only one type is possible on any roll so there is only one extra penalty possible and not two. Having this many axes allows the game to make task resolution as complicated as they wish with many possible outcomes including succeeding but with problems or failing but with some positive outcome.
Now to the question. When conducting statistical analyses of the rolls these different axes are treated as independent. If a roll has a 50% chance to succeed and a 50% chance of getting a positive side effect this is treated as 25% chance of succeeding with a positive side effect. However, they are not independent. If the good die that can roll successes or positive side effects rolls successes then it didn’t roll positive side effects. Likewise a bad die that rolled negative side effects wouldn’t have rolled negative successes. As a result rolls with large numbers of success should tend to have worse side effects while rolls that fail should tend to have positive side effects.
This would be irrelevant if the side effects didn’t have anything directly to do with success or failure. However, interpreting the results from the die roll is done based on the action the character is taking. Talking to someone has different possible outcomes than swinging a sword. For many of these actions the positive side effects amplify the results of a success. This means that positive side effects are often only useful if the task succeeds. So if positive side effects are skewed to occur when the task fails this could significantly change the distribution of the final results.
In order to test how boons (side effects) correlate with success I chose to look at a dice pool of 2 blue, 2 red, and 2 purple dice. This is just gibberish to those unfamiliar with the game. In brief, blue dice are good, purple dice are bad, and red dice basically good but with some bad results on them. Relatively small numbers of dice were chosen to try to maximize the correlation. Larger numbers of dice will tend to even out across the outcomes as it becomes less and less likely that all of the dice will roll the same result and so the results will behave closer to true independence.
In order to model the exclusionary effects of actually rolling the dice I constructed a Monte Carlo model of WFR3 dice rolls. 1,000,000 rolls of the dice pool were generated.
(As a side note: the number of distinct results generated by the Monte Carlo program given the five different axes, well four really as I didn’t use any dice that give Comets, was 390. This gives some idea of just how complicated they could make results using this system. Fortunately, most cards only have 3 different levels of success and often only 4 or 5 levels of boons so rolls only yield dozens rather than hundreds of different results.)
The basic distribution of boon results, ignoring successes for the moment, was compared to calculated results. This provided a test of the Monte Carlo model. As can be seen in Figure 1 the Monte Carlo results are effectively the same as the calculated results.
To see how the boons are affected by success I broke the results down by type of success. In this case I chose three categories, failure, success, and three or more successes. This is how most actions are broken down. Some use two or more successes, or four or more instead of three, but three is the most common break point for succeeding very well on a roll. Figure 2 plots the distribution of boons within each category along with the distribution if they really were independent variables.
There is a very pronounced skew in the results. On rolls that fail the roll is less likely to score 0 or fewer boons than would be the case if the results were independent but more likely to score 1 or more boons. At the level of 3 or more successes the chance of also scoring 3 or more boons is around a tenth of the independent result.
The extra penalty associated with red dice is exhaustion. What’s interesting from a correlation point of view is that the exhaustion result is linked to a success result. This means that rolls that result in exhaustion should be more common for successful rolls compared to rolls that fail. In addition, because the red dice also have a 2 success roll, which wouldn’t be rolled if the 1 success plus exhaustion side came up, there may be a skew against rolling exhaustion in the high success results. Breaking the results down as above, Figure 3 shows how exhaustion correlates with success.
As can be seen, failed results are less likely to result in exhaustion. The effect is very low when it comes to 3+ successes but there is a tiny reduction compared to a simple success. Of course, this doesn’t mean all that much. Exhaustion is a cumulative penalty that only causes problems over time and so it is irrelevant whether exhaustion occurs with failed or successful rolls. While the results may not be independent, from a game stand point they might as well be.
As mentioned above, even if a skew exists it may not matter much from a game mechanical point of view. In order to test the results of an action I applied the rolls to the action Trollfeller Strike. For those unfamiliar with the game this is an attack developed by Dwarfs to kill big monsters like Trolls. It is also a commonly used action example. It has two levels of success, base damage +1 and for 3+ successes base damage +3. Since all successful results include the base damage and the overall chance of success is identical between the independent and Monte Carlo models the actual level of the base damage is not that important so I’ll indicate it with a D. Trollfeller also has three levels of positive boons, +1 damage and ignore armor, +3 damage and 1 critical hit, and +4 damage, ignore armor, and 1 critical hit. Table 1 shows the percentage chance to obtain each of these results for both models as well as the average bonus damage per attack, average critical hits per attack, and percent of hits that ignore armor.
Result  Percent  

Independent  Monte Carlo  
D+1  26.1  27.2 
D+2 no armor  7.6  7.6 
D+4 critical  4.3  4.1 
D+5 no armor critical  2.5  1.7 
D+3  11.8  14.7 
D+4 no armor  3.5  2.7 
D+6 critical  2.0  0.9 
D+7 no armor critical  1.1  0.1 
Bonus damage  1.40  1.28 
Criticals  0.10  0.07 
Ignore armor percent  25  21 
There certainly is a difference when nonindependence is taken into account. However, that difference is pretty small (0.12 points of damage). If D were 10, pretty common for this attack, then the average damages would be 7.29 and 7.17 respectively, a difference of less than 2 percent. If ignoring armor were worth 2 extra damage done, it would barely break 2 percent. The effect is present but even in an example chosen to maximize the difference it’s just not large enough to matter.
This is good news for modelers since assuming independence makes calculations so much easier.
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