Solving the +1 Dilemma in Fudge
by Steven Hammond
Introduction
Probably the biggest problem I have faced when running Fudge, particularly
in fantasy games, is dealing out bonuses and penalties to players. In many
game systems a magical +1 sword is a good weapon, but in Fudge it is very
powerful. If combined with a +1 from another source, such as a deity's blessing,
it becomes even more powerful -- perhaps too powerful. Where does the GM
go from there? The same issue exists with penalties; a -1 penalty is very
harsh in Fudge.
Many proposals for solving this problem have been posted to the Fudge
mailing list over the years. Typically they involve adding more levels, or
using different dice systems. What I really wanted was a system that worked with standard Fudge
dice and used the 4 dice and seven levels everybody is familiar with, but
allowed finer grain bonuses and penalties that could easily be accumulated.
What if I had a Sword?
At the time, I was primarily focused on magical swords, so I started
thinking about things a sword could do other than give a +1 bonus in combat.
I came up with a lot of ideas. In particular, I wondered what if the sword
didn't actually help in combat, but it never hindered either? It would never
over penetrate and get stuck, its balance would allow its user to quickly
recover from a missed blow, etc. How could that be represented as a game
mechanic? The answer, and the basis for this system, is simple. Use a colored
Fudge die and ignore any -'s that show up. That die is the sword and it never
contributes negatively to a combat roll. It provides a bonus the player can
measure and perceive that is less powerful than a full +1. There is another effect; the player can see the sword's effect on
his character's skill. Every time he rolls the dice he can see the sword's
impact. "Whoa, good thing I had my sword, I would have missed without it."
The Dice Colors
Once the idea is out, it is easy to create a variety of patterns and
assign them to dice colors. Table 1, below, lists the ones I use.
| Color | Pattern |
| Black | Always rolls a - |
| Red | A roll of + or - is read as a - |
| Blue | Any + is ignored |
| Ivory | Normal dF |
| Green | Any - result is ignored |
| Purple | Any - roll become a + |
| White | Always read as a + |
Table 1: Dice Colors and Patterns
The colors used were arbitrarily selected from the available dice
colors. In the context of this article, the colors provide an easy way to
reference a particular pattern. In practice, any color can be used as long
as everybody knows what pattern it represents for the roll. The following two tables show out the probabilities for each result
when rolling 3dF and a single colored die. The probabilities for 4dF, 4dF+1
and 4dF-1 are also provided for comparison.
| | 4dF-1 | | Black | | Red | | Blue | | 4dF | |
| | Prob. | Cum. | Prob. | Cum. | Prob. | Cum. | Prob. | Cum. | Prob. | Cum. |
| -5 | 1.23% | 1.23% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% |
| -4 | 4.94% | 6.17% | 3.70% | 3.70% | 2.47% | 2.47% | 1.23% | 1.23% | 1.23% | 1.23% |
| -3 | 12.35% | 18.52% | 11.11% | 14.81% | 8.64% | 11.11% | 6.17% | 7.40% | 4.94% | 6.17% |
| -2 | 19.75% | 38.27% | 22.22% | 37.03% | 18.52% | 29.63% | 14.81% | 22.21% | 12.35% | 18.52% |
| -1 | 23.46% | 61.73% | 25.94% | 62.97% | 24.70% | 54.33% | 23.46% | 45.67% | 19.75% | 38.27% |
| 0 | 19.75% | 81.48% | 22.22% | 85.19% | 23.46% | 77.79% | 24.70% | 70.37% | 23.46% | 61.73% |
| 1 | 12.35% | 93.83% | 11.11% | 96.30% | 14.81% | 92.60% | 18.52% | 88.89% | 19.75% | 81.48% |
| 2 | 4.94% | 98.77% | 3.70% | 100.00% | 6.17% | 98.77% | 8.64% | 97.53% | 12.35% | 93.83% |
| 3 | 1.23% | 100.00% | 0.00% | 100.00% | 1.23% | 100.00% | 2.47% | 100.00% | 4.94% | 98.77% |
| 4 | 0.00% | 100.00% | 0.00% | 100.00% | 0.00% | 100.00% | 0.00% | 100.00% | 1.23% | 100.00% |
| 5 | 0.00% | 100.00% | 0.00% | 100.00% | 0.00% | 100.00% | 0.00% | 100.00% | 0.00% | 100.00% |
Table 2: Negative Dice Probabilities
| | 4dF | | Green | | Purple | | White | | 4dF+1 | |
| | Prob. | Cum. | Prob. | Cum. | Prob. | Cum. | Prob. | Cum. | Prob. | Cum. |
| -5 | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% |
| -4 | 1.23% | 1.23% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% |
| -3 | 4.94% | 6.17% | 2.47% | 2.47% | 1.23% | 1.23% | 0.00% | 0.00% | 1.23% | 1.23% |
| -2 | 12.35% | 18.52% | 8.64% | 11.11% | 6.17% | 7.40% | 3.70% | 3.70% | 4.94% | 6.17% |
| -1 | 19.75% | 38.27% | 18.52% | 29.63% | 14.81% | 22.21% | 11.11% | 14.81% | 12.35% | 18.52% |
| 0 | 23.46% | 61.73% | 24.70% | 54.33% | 23.46% | 45.67% | 22.22% | 37.03% | 19.75% | 38.27% |
| 1 | 19.75% | 81.48% | 23.46% | 77.79% | 24.70% | 70.37% | 25.94% | 62.97% | 23.46% | 61.73% |
| 2 | 12.35% | 93.83% | 14.81% | 92.60% | 18.52% | 88.89% | 22.22% | 85.19% | 19.75% | 81.48% |
| 3 | 4.94% | 98.77% | 6.17% | 98.77% | 8.64% | 97.53% | 11.11% | 96.30% | 12.35% | 93.83% |
| 4 | 1.23% | 100.00% | 1.23% | 100.00% | 2.47% | 100.00% | 3.70% | 100.00% | 4.94% | 98.77% |
| 5 | 0.00% | 100.00% | 0.00% | 100.00% | 0.00% | 100.00% | 0.00% | 100.00% | 1.23% | 100.00% |
Table 3: Positive Dice Probabilities
A close look at the tables will reveal a few interesting features of the probability curves.
First, note that the colored dice never exceed the +4 to -4 range
of the standard 4dF roll. Comparing Black and 4dF-1, you will see that they
are both centered around -1. However, the Black curve only covers the range
from 2 to -4. It is a little "steeper" and favors the -1 result more strongly.
The Red, Blue, Green and Purple curves are not symmetrical bell
curves. They are weighted more towards the negative (Red and Blue) or positive
(Green and Purple) in addition to having the curve's peak shifted away from
0. These features can more easily be seen in the graphs below. The first graph shows all the curves. The second shows a subset
of them. The second graph is easier to read. Blue and Red are a mirror image
of Green and Purple. The curves are the same shape, just reflected across
the 0 line. Similarly, White and 4dF+1 are reflections of Black and 4dF-1,
respectively.

Chart 1: All dice probability curves (Click on graph for a larger view.)

Chart 2: Subset of the curves (Click on graph for a larger view.)
Multiple Colored Dice
Accounting for multiple bonuses and penalties is easy in this system.
Replace one Ivory (normal dF) with an appropriate colored die for each modifier.
GMs may choose to limit the number of dice that can be replaced. I use a
limit of three, although I can't explain why I don't like the idea of replacing
all four dice. Other GMs may disagree and allow all of the dice to be replaced.
If there are more bonuses and penalties than allowed substitutions
then select the ones with the highest magnitude (i.e. select the Blacks and
Whites first, then the Reds and Purples, then the Greens and Blues). If you
have to choose between a positive and a negative of the same magnitude then
it's the GMs choice. I I usually favor the positive modifier.
Colored Dice In Practice
As usual, each GM needs to decide how they want to use these dice in
practice. I use the following guidelines when translating other Fudge material
to this system.
| -3 | Black |
| -2 | Red |
| -1 | Blue |
| +1 | Green |
| +2 | Purple |
| +3 | White |
Individual bonuses or penalties greater than three are rare and I handle those as needed.
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