House of Cards: Putting it Together

I ended up analyzing more attack actions than I had intended, but that allowed me to compare them to each other.

Troll Feller Strike

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.

Stance 2 With and Without 1 Black Die


Comparing Attacks

Average Damage Summary Table

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.  Continue reading


Reckless or More? Damage and Stance in Warhammer

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.


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 Continue reading

The Correlation Effect

The Warhammer Fantasy Roleplaying Game 3rd edition (from now on WFR3) employs an unusual resolution mechanic with specialized dice. The results are very non-linear and the resulting probabilities are not intuitive. As a result there have been a number of good statistical analyses of the new mechanic. So why am I doing another one? One aspect of the mechanics is generally left out of these analyses because it is such a pain to deal with. So, in my fine tradition of dealing with stupidly complicated game mechanics for no good reason, I decided to see just how important this aspect really is to the game.

The Question

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.  Continue reading

The Importance of FATE

Add FATE Points and Stir

The previous article talked about setting up and testing a basic Monte Carlo model of FATE combat. This one tackles the task of introducing FATE points to the model. Most of the article covers testing and optimizing the model. Readers not interested in finicky details of model building are really encouraged to skip to the Results section at the end. Seriously, it’s ten pages of details, just look for the picture of fudge dice.

FATE point mechanics

While different versions of the mechanics change things up a bit most FATE systems use FATE points. FATE points are a limited pool of points that can be spent for a number of different bonuses. However, in order to spend a FATE point the character not only needs a FATE point but needs an appropriate Aspect.

Aspects are character abilities that are usually a phrase or description like “Veteran of Normandy” or “World’s Greatest Mechanic”. In order to use a FATE point in a situation the character has to have an Aspect appropriate to the circumstance. So a “Veteran of Normandy” could spend points on combat rolls or getting along with other veterans while the “World’s Greatest Mechanic” could spend points repairing things or to have a special gadget rigged up in their car.

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Coming to terms with FATE

This series has taken a number of looks at the FATE system in various of its incarnations. One thing that I have diligently avoided is looking at the use of FATE points in combat results. The reason for this is the difficulty of the FATE point rules. They offer a number of choices for a limited resource and their use is situationally driven. However, they represent a very important part of the FATE system and a full understanding of the system requires taking a look at FATE points. In order to bite the bullet and take a look at how FATE points change combat, I first needed a model of FATE combat. Previous articles have looked at Spirit of the Century and FATE 2.0 but I’m not really a fan of those particular versions of FATE. I prefer the overall layout of combat in Starblazer Adventures or the Dresden Files.

This article describes building and testing a Monte Carlo model of an entire fight between two combatants, not just a single roll of the dice, using the Dresden Files FATE combat system. I have used these types of models frequently and the goal here is to take a detailed look at what I’m doing when I put one of these models together. Those uninterested in the model and wanting to cut to the chase should just skip to Table 1. Once I have a functioning basic model I then intend to incorporate FATE points. The actual results of incorporating FATE points will be in the next article.

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The Limits of Wealth: a boundary problem in Diaspora

Diaspora is a FATE based game aimed at creating a somewhat hard sci fi feel similar to Traveler, rather than a science fantasy setting like Star Wars or Star Trek. One of the qualities that it tries to emulate from Traveler is the economics of running a small merchant vessel. However, the economic mechanics of FATE do not mesh well with a business simulation and I feel that the resulting rules are simply terrible. What makes it interesting is that it is a different type of failure than the previous articles have discussed, a boundary problem.


Rolls in Diaspora use a typical FATE set up, roll four fudge dice, each numbering from -1 to 1, yielding a roll from -4 to +4 and adding a skill. If a target number or better is rolled, the roll succeeds with possible bonuses for how much the roll exceeds the target. If the roll is lower than the target, the roll fails and may result in penalties for how much the roll is short of the target.

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Teaming in PDQ

Over the course of several products Atomic Sock Monkey has generated many variations on its basic PDQ mechanic. One set of mechanics that has received multiple treatments are the rules for teamwork.


For non-conflict rolls in PDQ players roll 2d6 and add the result to the character’s skill, which will be divisible by 2 i.e. 0, +2, +4 etc. If the total equal or exceeds the target number set by the game master the roll succeeds. Conflicts are slightly more complicated. In The Zantabulous Zorcerer of Zo and Truth and Justice rolls in conflicts are basically the same as normal but instead of rolling against a target number the attacker rolls 2d6 and adds their attack skill while the defender rolls 2d6 and adds their defensive skill. For every point that the attacker’s total is higher than the defenders the defender takes a point of damage. In Swashbucklers of the 7 Skies players get to divide 3 dice between attack and defense rolls, so an attack will be 0 to 3 d6 plus the attacker’s skill against 0 to 3 d6 plus the defender’s skill. The point of this article is to compare the teamwork rules, not the huge change in the basic combat mechanic. So for this article it will be assumed that all rolls are made on 2d6.

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