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(TFT) H3 System Revisited: Skewing the Bell Curve

                             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 

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