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.

The Basic Model

Mechanics

The model was based on the FATE combat system in the Dresden Files, Diaspora, and to a great extent Starblazer Adventures. Starblazer Adventures uses d6 – d6 the others use fudge dice.

Mechanically characters have a certain number of Stress boxes representing how much damage they can take. This can vary depending of the type of conflict involved, physical combat can use physical Stress while social conflict can use mental Stress and these numbers can be different for the same character.

When a character is attacked in a conflict the attacker rolls four fudge dice, dice with an equal chance of rolling -1, 0, or +1, and adds the results generating a number between -4 and +4 highly skewed towards 0 (see FATE Minus d6 and Counting). The roll is added to their attack skill. The attack roll is then compared to the defender’s defense roll, also four fudge dice plus their defense skill. If the attack total is equal to or higher than the defense total the defender suffers Stress equal to the difference between the attack and defense totals. Yes, that can be 0. That’s because these games also use equipment/ powers that may do bonus damage or provide protection that reduces damage. These will increase or decrease the Stress by the appropriate amount. For example, an attack with a gun that does +2 damage would increase the Stress by 2 while armor that protects against 4 points of damage would reduce the Stress by 4, to a minimum of 0. Note that the modifications for equipment/ powers happen after the roll to hit so that an attack with +9 damage would do nothing if the attacker’s roll was lower than the defender’s, even by a point.

Characters add Stress as it is taken and if the total ever exceeds their number of Stress boxes of that type of Stress then they are Taken Out. In other words, they lose the conflict and bad things happen to them. Stress can be avoided by taking Consequences instead. These are bad things that happen to the character depending on the type of conflict. So Consequences in a fight are basically wounds, “twisted ankle” or “broken arm”. Consequences run from mild to severe with correspondingly longer recovery times and more difficulty dealing with the consequence. Starblazer Adventures also has an extreme consequence level.

Barring certain abilities characters can only take 3 Consequences and none of them can be of the same level. So most of the time a character can take 1 mild, 1 moderate, and 1 severe Consequence. Taking a Consequence reduces the Stress that the character just took, to a minimum of 0, by a certain amount, 2 for mild, 4 for major, and 6 for severe. As a result a character with 5 physical Stress could take at most 17 Stress and still be in the fight, 5 for the Stress with 12 points absorbed by taking Consequences.

Assumptions

Bonuses to damage and armor are really a subject for a different post and I didn’t incorporate them into the model. I also assumed that a character would stay in the fight as long as possible so that they would use Consequences to eliminate Stress. The heuristic I used was employing the largest Consequence that would reduce the Stress to 0 or more first. In other words, if a character took 4 or 5 Stress they would take a major Consequence reducing the damage to 0 or 1. If they had taken 6 or more Stress they would take a severe Consequence reducing the damage by 6 instead.

Then if the Stress would still result in being Taken Out I used the smallest available Consequences until either the character was still in play or ran out of Consequences. For example, if a character took 3 Stress the model would normally reduce that to 1 by having them take a mild Consequence. However, if that character had already taken a mild Consequence they would not take a major Consequence, -4 Stress damage, unless that 3 Stress would result in them being Taken Out.

Overall the goal was to “waste” as little of the Stress reduction from the Consequences as possible. Once again, I ignored initiative thus enabling fights to end in ties if both characters were Taken Out in the same round.

Testing the model

The first thing to do was test the model to make sure there were no programming/ logic errors and that it generally behaved as expected. The simplest test is to use two equal skilled opponents and see if they have equal chances of winning. As shown in Figure 1, two opponents both with 5 Stress boxes and combat skills at 2 had equal chances of winning the fight. Combats also most commonly lasted 10-12 rounds.

Figure 1. Combat Between Equal Opponents

Since the combat rolls are all opposed rolls as long as the attack and defense skills are equal the results should remain unchanged. Setting the combat skills to 0 or 4 or setting one opponent to Attack 2, Defense 0 and the other to Attack 0, Defense 2 all yielded results indistinguishable from Figure 1, just as expected.

Even if the attack skills were higher or lower than the defense skills, as long as the difference was the same for both combatants they should have even chances of winning. However, if the attack skills were higher, damage would be expected to be higher and thus combats shorter, and vice versa for lower attack skills. Figure 2 shows the effects of changing the attack skills from 2 lower to 2 higher than the defense skills. Only one curve is shown for each attack value since, as expected, the two combatants had indistinguishable results for each value. As can be seen, changing the relative attack value radically changes the duration of the fights, from typically 5 or 6 rounds at two better than defense to typically 32 to 40 rounds at two lower.

Figure 2. Effect of Relative Attack Skill

Similar behavior would be expected from raising or lowering the number of Stress boxes. Figure 3 shows what happens if the characters have 3, 5, or 7 Stress boxes. As expected changing the amount of Stress, i.e. damage, the combatants can take changes the length of the combat. However, the effects were nowhere as pronounced as changing relative attack skill.

Figure 3. Effect of Stress Levels

Establishing a Baseline

The controls indicated that the model was working as expected. Next a baseline needed to be established. Table 1 shows the chances for Pain or Suffering winning a fight depending on relative skill.

Table 1. Effects of Relative Skill on Combat

Pain’s Skill Relative
to Suffering
Pain Wins
(%)
Suffering
Wins (%)
Ties (%)
-3 0 100 0
-2 0.01 99.98 0.01
-1 2.6 96.4 1
Even 47 47 6
+1 96.4 2.6 1
+2 99.98 0.01 0.01
+3 100 0 0

The results are symmetrical indicating no errors biasing the results between combatants. As with other FATE combat models even small skill differences have a huge effect on the results.

Next up, adding FATE points to the model.

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7 Responses

  1. A comment from the Diaspora Forums on your article:

    “The only thing it looked like that article proved was that if the opponents are equal, then they have an equal chance of winning. There was excruciating detail about that, but then he threw this table at the end that said with a difference of only one skill level, the stronger would have over 95% chance of winning. No math showing why. No calculations of fate dice probabilities, not even a small paragraph stating how he put the data together to get that table.

    He’s clearly not factoring in fudge dice percentages, because he stated that with a difference of 3 skill levels, the stronger has a 100% chance of winning, which is statistically impossible. A character with a three skill level only has a %38.29 of rolling something unbeatable to a character with a 0 skill level. Even with multiple rounds of combat, the stronger would never gain a %100 to win. That would only happen if the characters skill level was 8 vs his opponent of 0, something that cannot happen in Diaspora.”

  2. Partly my bad here. I assumed that anyone reading the article would have been following the series. Jumping in in the middle would make things less clear.
    They seem to have three concerns. The first is that there was excruciating detail about the model. I’ve used these sorts of models for many articles and the point of this one was to show the details of setting one up. The next article will have more actual results, this one was about building the model. I tried to be explicit with this in the opening line saying that if you are not interested in the model in and of itself skip to the end.
    The second and third are related, that the table comes from nowhere and that I’m not factoring in fudge dice percentages. The key here is that the entire point of building the model is that it is a Monte Carlo simulation of an entire combat, not just a single die roll. I should have been more explicit in saying that it was a Monte Carlo model but was lazy and figured that everyone reading these knew that by now. The figures are “showing the math” by showing that the model works as predicted. While some complex equations might be able to explicitly calculate the odds of winning a fight that is beyond my skill, hence the Monte Carlo analysis. Build a program that will run the fights for you and then have it run 1 million fights and see who wins. Since the calculations cover an entire fight, not just one set of dice rolls, the odds of winning are very different than the odds of winning a single dice off. Simple example, if you need to roll a 6 on a d6 to win then the chance if you’re rolling once is 1 in 6. If you need two 6’s in a row, 1 in 36. It rapidly gets to the point where your chance is basically 0.
    Hope this helps
    Erik

  3. Just to encourage you, this article has had 45 hits since you published it. And you got some nice comments over in the Diaspora General forum. One of them even said that they can’t wait for the next installment.

  4. […] 1Seattle gaming linksToon City Vice: Arms DealsHow To Make Paper FiguresRole-Playing Games for KidsComing to terms with FATESpace Race 1895 Actual […]

  5. […] to his articles on variance and game design, variance in Spirit of the Century, combat in Fate 2.0, combat in The Dresden Files RPG and other Fate-derived systems, and the use of fate points to counter the difference in skill […]

  6. By my definition of challenge, this makes an Even encounter “Incredibly hard”; a 1 lower encounter “interesting”; and a 2 lower or easier encounter “easy”. That’s not a lot of resolution. How do you gauge conflict challenge in FATE?

  7. Jon,
    I agree with you. It was experiencing this in a FATE game that was part of the reason for calculating these things out. FATE isn’t very granular. The difference between no skill and world expert is 4 to 5 points. It makes gauging challenges difficult. I talked a little about this in the article on Fighting FATE and how introducing mook rules helped in FATE 2.0. Another possibility is separating out attack and defense skills, SotC does this for guns and athletics. Then lower the opponent’s defense. The can still hit but the PCs can take them out much easier. The new FATE game goes the opposite route where the opponent is supposed to be much better than you and everyone spends their time creating new aspects with free uses and then hits them with an attack at +8 or some such. If you’re good at juggling Fate points that might also help.

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