SKEWING THE BELL CURVE
One of the core premises of Melee/Wizard is its implementation of
success or failure; you roll 3D6; a total of 5 or less means you succeed,
16 or more means you fail. The less likely the outcome, the more
spectacular the result; a 3 is a magnificent success while an 18 is a
disastrous failure. The combined probabilities of these rolls means
that 5% of the time you are going to succeed in a task and 5% of the
time you are going to fail.
As a means of modifying this roll, TFT employs an "add or subtract a
D6" method: if a task is more difficult, add a D6 (or two, or three...)
and
if easier, subtract a D6 from the roll. TFT still clings to this +/- 5%
law
however, so that if you are rolling 4D6, you have to consult a special
table to determine your chances of auto success/failure, for 5D6
another chart, for 6D6 another chart, ad infinitim. If you are lucky
enough to be rolling 2D6, well you still have a chance of auto success
or failure, but now it is only if you roll a 2 or a 12. And some tasks
(at
the GMs discretion) are deemed to be so easy (or so hard) as to not
require a roll at all.
Such a system ignores a basic premise of reality: it is easier for
skilled characters to perform simple tasks and harder for unskilled
to perform more difficult ones. The TFT system flies in the face of
that: no matter what your skill level, you are going to succeed or fail
5% of the time.
In July 2000, I proposed a new system of modifying dice rolls to
address this problem: it was dubbed the "Highest Three" system.
Basically, the idea was that if you were attempting a 4D6 roll, you
rolled the 4D6 as normal but instead of totalling all of the dice, you
totalled only the highest three, which gives you a result of 3-18 which
you then interpret as per the basic rules. The system had the benefit
of being easy to implement and was infinitely expandable on both
ends of the spectrum. The proposal generated some discussion
and, despite its initial appeal, it was eventually abandoned due to
the steepness at which it generated success/fail results.
After a lot of thought at trying to save the system, I've come up with a
method which works and, though a bit more difficult to implement, is
still playable and generates good results. In order to implement it, a
GM will need a red die, a green die and several white dice.
Before rolling the dice, the GM determines the difficulty level of the
roll by summing the relevant disadvantages and subtracting the
relevant advantages. Under the old TFT method, this was adding
and subtracting a D6: A character wishes to avoid an ambush, he
has the advantage of Alertness which produces a difficulty level of -1;
A character searches for a specific herb, it is rare in these parts (two
disadvantages) but the character has Nature Lore (one advantage)
which gives a difficulty level of +1. The GM then throws the red die,
the green die and the required number of white dice and consults
the following table:
DL #W Red Result
P(5-) P(16+)
...
-4 5 Sum Lowest 3 of 5 White dice
.2342 .0027
-3 4 1-3 Sum Lowest 3 of 4 White dice .1823
.0072
4-6 Sum Lowest 3 of Green & 4 White dice
-2 4 Sum Lowest of 4 White dice
.1304 .0116
-1 3 1-3 Sum 3 White dice
.0884 .0290
4-6 Sum Lowest 3 of Green & 3 White dice
0 3 Sum White dice
.0463 .0463
+1 3 1-3 Sum 3 White dice
.0290 .0884
4-6 Sum Highest 3 of Green & 3 White dice
+2 4 Sum Highest 3 of 4 White dice
.0116 .1304
+3 4 1-3 Sum Highest 3 of 4 White dice .0072
.1823
4-6 Sum Highest 3 of Green & 4 White dice
+4 5 Sum Highest 3 of 5 White dice
.0027 .2342
...
This may seem confusing at first but it gets easier to use over time
and has the advantage of allowing the GM to interpret the result in
just one throw of the dice. The long and short of it is this: if the DL
is even, use only the white dice. If the DL is odd, then the red die is
used to interpolate the results between the two surrounding DL
values.
Dan
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