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.

Any number of FATE points can be spent on a roll within two limits. First, the character has to have the points. Second, only one point can be spent per Aspect on a given roll. So a character with “Crack Shot” and “Veteran of Normandy” could spend two points on a roll to shoot someone but without a third applicable Aspect couldn’t spend three.

Several different bonuses can be purchased with FATE points. Most iterations allow some world editing like declaring that one of the character’s war buddies is in the bar in the middle of nowhere. In terms of dice rolls players can usually choose between rolling the dice again or simply adding +2 to the roll. Obviously, which of these is preferable depends on the original roll. Adding 2 to a roll of -4 only gives a total of -2 while rerolling will give -1 or better over 4/5 of the time. In contrast, adding 2 to a +3 roll gives a total of +5, more than any roll can ever yield. Table 1 shows how a reroll compares to just adding 2 for different original rolls.

Table 1. Comparing Rerolling the Dice to Adding 2

Roll Chance Reroll
Better (%)
Chance Reroll=
+2 (%)
Chance +2
Better (%)
-4 81 12 6
-3 62 20 19
-2 38 23 38
-1 19 20 62
0 6 12 81
1 1 5 94
2 0 1 99
3 0 0 100
4 0 0 100

For very low rolls, -4 or -3, rerolling will generally give better results. For moderate rolls, -1 or better, adding 2 is generally the best plan. At -2 the average results are the same and the choice would depend on how much randomness a player wanted.

Model Assumptions

The huge number of variables shows why I’ve been trying to avoid FATE points. How many points does the character have, do they have the right Aspects, reroll versus add 2, spending multiple points on the same roll, etc. In order to put this in a program some pretty restrictive assumptions needed to be made and so the results will at best be an approximation of the effects of FATE points.

For ease of handling, the model assumed that the characters had appropriate Aspects but would never spend more than one point on a single roll.

Then there was the question of which rolls to spend the points on. The model could easily separate out attack and defense rolls so was able to take a look at only spending for attack, only spending for defense, or both attack and defense.

However, it also needed a criterion for when to spend points on these rolls. For attacks, missing by 1 is just as much of a miss as missing by 3. Because of this it seemed likely that only increasing rolls that were already pretty good would yield better results. So the model used a cutoff for spending on attacks. Only rolls making the cutoff or higher caused a FATE point to be spent. For attacks this was always adding 2 to the roll, since rolls of -4 or -3 wouldn’t really meet the criterion for pretty good roll. The opposite is true for defense rolls. Once damage is 0 increasing the defense roll is meaningless. Ok, for aficionados, some versions of FATE have a special bonus for beating an attack roll by 3 or more but I didn’t worry about that. So the model used a cutoff for spending on defense. Only rolls making the cutoff or lower caused a FATE point to be spent.

Timing can be very important for spending FATE points. Spending the character’s only point to reroll a -1 defense roll may seem a poor choice if the next round they roll a -4. However, it’s a program and so the choices needed to be hard coded. It was set up as a first come, first serve model so points were spent whenever they were available and a roll made the cutoff for FATE point use. Since the program made attack rolls before defense rolls this also meant that attack rolls took precedence over defense rolls in a given combat round.

Testing and Fine Tuning

Attack!

Because the attack algorithm of always adding 2 was so simple, I started testing with attacks. The first test was to see whether adding in FATE points for attacks was symmetrical. If both opponents were given a FATE point they should have equal chances of winning the fight. Figure 1 shows the results for 1 FATE point each with an attack cutoff of 0 or better and, as expected, there was no bias between the opponents.

Figure 1. Equals Attacking with 1 FATE Point

Like increasing attack values over defense, using FATE points to increase the attacks should shorten combats. 1 FATE should produce a shorter fight than no FATE points though not as much as setting attack skills 2 points higher than defense, which would be like using a FATE point for every attack. This is confirmed in Figure 2 which shows that using FATE points to increase attacks shortens the fights.

Figure 2. Attacking with FATE Shortens Fights

The next question was where to put the cutoff for attacks. Changing this should have little effect when both opponents had FATE points so the test was run with Pain having 1 FATE point for attacks and Suffering 0. Table 2 shows that the optimal choice for opponents of equal skill is 0, though the differences are generally very small. Flipping the number of FATE points flipped which opponent had the advantage, but the advantage was unchanged indicating no bias in the model.

Table 2. Attack Cutoff for Equal Opponents

Attack Cutoff Pain Wins (%) Suffering Wins
(%)
Ties (%)
-2 54.0 40.1 5.9
-1 54.5 39.7 5.9
0 54.6 39.5 5.9
1 54.1 40.0 5.9
2 52.4 41.7 5.9
3 49.7 44.4 5.8

Defense

With attacks working as expected the next step was to test using FATE points for defense. I started with a system that used rerolls for any roll of -4 or -3 that made the defense cutoff and +2 for any roll -2 or higher that made the cutoff. Once again symmetry between the combatants was tested. Each opponent was set to equal skill and 1 FATE point to be spent only on defense with a 0 or lower cutoff. As seen in Figure 3 there was no bias between the opponents.

Figure 3. Equals Defending with One FATE Point

Just as FATE points for attacks shortened fights, FATE points for defense should lengthen them. Figure 4 shows a comparison between no FATE points, 1 point spent for defense, and setting attack skill 2 lower than defense skill. As can be seen spending for defense increased the length of the fight.

Figure 4. Defending with FATE Lengthens Fights

Next came the question of cutoffs for the defensive roll. Also, how the dynamic system of rerolling or adding 2 depending on the original roll fared against always rerolling or always adding 2. As with attacks, Pain was given 1 FATE point and Suffering 0 and the simulation run for different cutoffs. Table 3 shows that the optimal defense cutoff for equal skilled opponents is -2. As expected this is a lower cutoff than for attacks. However, comparing Table 2 and Table 3 shows that spending on defense seems to win more fights.

Table 3. Defensive Cutoff for Equal Opponents

Defense Cutoff Pain Wins (%) Suffering Wins
(%)
Ties (%)
-3 53.5 40.9 5.6
-2 55.5 38.9 5.6
-1 54.8 39.5 5.7
0 53.4 40.8 5.8
1 52.4 41.8 5.8
2 51.8 42.4 5.8

I also compared the algorithm of rerolling for -4 or -3 and adding 2 for higher rolls with always rerolling or always adding 2. As expected, the algorithm performed better than the other strategies.

Both Attack and Defense

The next test was to run fights with the option of attacking and defending with fate points. Both combatants were set to equal skill and 1 FATE point using an attack cutoff of 0 and a defense cutoff of -2. The results confirming symmetry are shown in Figure 5.

Figure 5. Equals Attacking and Defending with FATE

It should be noted here that the model used in this and the previous article is the second version of the model. The first version failed this test. That model calculated one set of attack and defense rolls and then the other set. The result was that Pain would decide on whether to use FATE points for attacks then defense while Suffering would decide on defense and then attacks. Given the limited pool of FATE points the timing of the choice mattered and the results were not symmetrical. The new version decides for attack and then defense for both combatants.

This shows the importance of running tests on the model. Also, it shows how subtle an error can be. When no FATE points were used or they were used only for attack or only for defense the original model worked just fine. The timing error only showed up when testing both attack and defense.
Given the availability of both attack and defense bonuses it was unclear what affect the FATE point would have on combat length. Figure 6 compares spending for both attack and defense to no FATE points as well as FATE only for attack or only for defense.

Figure 6. How Attacking and Defending Changes Combat Length

The results mostly resembled that for attack only use of FATE points. The reason became clear when I tried to determine the optimum cutoffs for the combined attack and defense. Running through all the possible combinations from -4 to +4 for both variables would have been too time consuming so I looked at permutations around the previously determined cutoffs. Defense cutoffs of -1, -2, and -3 for different attack cutoffs were tried as well as different defense cutoffs for an attack cutoff of 0. Table 4 shows the results with the best results for any given attack cutoff shown in red.

Table 4. Combined Attack and Defense Cutoffs for Equal Opponents

Attack Cutoff Defense Cutoff Pain Wins (%) Suffering Wins
(%)
Ties (%)
-2 -3 54.0 40.1 5.9
-2 54.1 40.0 5.9
-1 54.0 40.1 5.9
-1 -3 54.5 39.6 5.9
-2 54.6 39.6 5.9
-1 54.5 39.7 5.9
0 -4 54.7 39.4 5.9
-3 54.8 39.3 5.9
-2 54.9 39.2 5.9
-1 54.8 39.3 5.9
0 54.4 39.7 5.9
1 53.9 40.2 5.8
2 53.7 40.5 5.9
1 -3 54.6 39.5 5.9
-2 54.7 39.4 5.9
-1 54.5 39.6 5.8
2 -3 53.9 40.2 5.9
-2 54.5 39.7 5.8
-1 54.3 39.9 5.8
3 -3 53.5 40.7 5.8
-2 54.9 39.4 5.7
-1 54.4 39.8 5.7
4 -3 53.5 40.9 5.7
-2 55.5 39.0 5.6
-1 54.7 39.6 5.7

The first thing to note is that the best value for defense only, 55.6% for a -2 cutoff (Table 3), is higher than the highest value, 55.4 for a 4 attack and -2 defense cutoff, in this table. A mix of using a single FATE point for both attack or defense is not as good as using it solely for defense. Consistent with the defense only cutoff calculations, the best values were obtained for a defense cutoff of -2 or lower.

One odd result was that at a defense cutoff of -2 there were two maximums for the attack cutoff. This is probably easiest to see as a plot.

Figure 7. Mixed FATE Use at Defense Cutoff -2

This appeared to be the result of the superposition of two effects. One is the optimal attack cutoff of 0. The other is that using the point for defense gave better results. Thus when the attack cutoff became strict enough that the point was more likely to be spent on defense than attack, a cutoff of 3 or higher, the percentage wins started to rise again. An attack cutoff of 5 or higher, which could never be rolled, would be the equivalent of spending only for defense. Note that this also explains why in Figure 6 the attack and the attack and defense curves are very similar. With a defense cutoff of -2 and an attack cutoff of 0 the program was much more likely to spend the single FATE point on attack than defense and so the curve was very similar to the attack only curve.

Results

After that overly long preamble, here are the results. Keeping in mind that these results are an approximation, Table 5 shows the percentage chance of winning a fight against an equal skilled opponent with different numbers of available FATE points. The table shows results for using FATE points only for defense, only for attack, or for both, though at most one point on any roll. The results are shown graphically in Figure 8.

Table 5. Effectiveness of FATE Points in an Even Fight

Fate Points Attack Only
(% wins)
Defense Only
(% wins)
Both (% wins)
0 47.1 47.1 47.1
1 55.6 54.7 54.9
2 62.2 62.8 63.3
3 66.7 70.7 71.2
4 69.3 77.5 78.2
5 70.5 82.6 84.0
6 71.2 85.2 88.5
7 71.4 86.1 91.6
8 71.5 86.4 93.6
9 71.5 86.4 94.7
10 71.5 86.4 95.3

Figure 8. Effectiveness of FATE Points in an Even Fight

As expected, spending FATE points to increase attack or defense rolls increases the likelihood of winning combats. Having more FATE points to spend increases the benefit. However, at a certain point the increase levels off as the character has more FATE points than they will be spending for the fight.

Overall, spending points on both attack and defense rolls as applicable gave the best result. However, the defense results have some interesting quirks. The effectiveness of defense only spending falls off quite dramatically. This is likely the result of how the model was constructed. FATE points were only spent to increase defense rolls of -2 or lower, approximately a 1 in 5 chance on any roll. Even in fights with high numbers of FATE points available the vast majority lasted fewer than 18 rounds. 18 rounds would require 18 defensive rolls, on average fewer than 4 rolls of -2 or lower. This would explain the very minimal gains in having more than 4 FATE points.

However, the only time the mixed attack and defense expenditures were exceeded was for pure defense spending with only 1 FATE point, all be it not by much, 0.7%. My best guess is that it comes from rerolling really poor defense rolls. Rolls of -4 or -3 are reasonably rare at about 1 in 17. Thus it is unlikely that two such rolls would happen in any combat but one very well might. If the worst thing that could happen in a fight was a terrible defense roll then saving and using the character’s 1 point for that roll might be the best use of a single point.

The number of available FATE points is going to vary dramatically with the exact rules set and the campaign’s style. It seems unlikely that more than 3 or 4 points would be spent on an even combat. Fortunately, those are the most effective points in terms of increased wins per point spent, a little less than 8% per point.

Once again the article has gone on far too long. The next will cover the results of FATE points for uneven fights.

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5 Responses

  1. I’m curious to know what process you use to model this. Do you have software that works it out? A spreadsheet? A slide rule?

  2. I think he has a near infinite supply of monkeys banging away at abacuses.

    Another great article Erik!

  3. Each combat round has an attack and defense roll for two combatants, so 4 rolls per round. Combats will last 10 or more rounds usually and I ran 2 million fights for each calculation. So each box in one of those tables represents some 100 million die rolls. After my monkeys quit citing serious labor violations I moved over to using Perl scripts.
    Erik

  4. Ook!

  5. […] 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 […]

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