Re: (TFT) 3d6

[raito@raito.com]

I take that bet, I think. 

Both 3D6 and D20 can be used for attack rolls, and we could convert the 
math such that any 3D6 roll could be roughly converted to a D20 roll 
and vice versa. So, if one can be completely converted to the other, 
why is one better than the other?

The answer lies partially in the mechanic of TFT character development. 
The typical human character begins with attributes of 8 (with the 
points to spread around, but bear with me). A 3D6 vs 8 will succeed 
only 56/216 of the time. That's about 26% of the time, or about a 5 on 
a D20. But the 'average' attribute for a human is 10, which succedds on 
a 3D6 exactly half the time, or a 10 on a D20. 

Now look at those attribute numbers, and their 3D6 and D20 
counterparts. Using 3D6, a gain of 2 points gets you a 24% gain. But if 
I use an attribute of 5 (for D20), it takes a gain of 5 points to get 
the same benefit! (This assumes that each attribute point in D20 raises 
success by 5%). 

Because human (and human-like) characters have their average attributes 
at 10, using 3D6 works 'better' because as one's attribute approaches 
the average, one's chances for success not only improve, but improve in 
proportion (roughly) to how close to the average the character is. One 
improves more as a percentage the closer one is to the average. In 
fact, the gain from 10 to 11 is about 12.5%, or 2.5 pips on a D20. 

And because the game is mostly about human (and human-like) characters, 
this works better. (I have another argument that it doesn't scale well, 
that points to this average attribute thing, but stay with me for now). 
Not only do those near the average get more out of their gained 
attribute, those near the ends get less. So you're the greatest 
swordsman -- what's another DX point really going to get you? And you, 
you're incompetent, so your next point doesn't get you much, either. 

Now let's look at the ends of the scale, the hoped-for triple and 
double damage, and the dreaded drop and break weapon. It is not 
possible with a single roll of a D20 to get a chance of something 
hapening down below 5%. Yet that's an awful lot of dropped and broken 
weapons (assuming that we use rolls of 19 and 20 for those). Using 3D6, 
we get a dropped weapon 3/216 of the time, and a broken weapon 1/216 of 
the time. We can use the characteristics of the roll to put 
low-percentage outcomes at the ends of the scale -- something we can't 
do (without extra rolls) with a D20. 

Now let's look at difficulty. 

Sure, it's easy to apply a bias to a roll to make something easier or 
more difficult. But again, look at that average. If you have an 
attribute of 16 (which is really high for a human), your actual penalty 
with a -2 on your roll is about 8%. But the same conditions for someone 
with an 11 is a hit of 25%. For a D20, a penalty of -2 is always 10%. 
With 3D6, if you're really good, you can take a chance, and similarly, 
if you're really bad, a penalty doesn't hurt you much. 

But look again at a 3D6 mechanic for difficulty -- the extra die. With 
3D6, the usual range is 3-18, with 4D6, it's 4-24. But the percentages 
shift so that being average is no longer a 50% chance. Now look at the 
D20. It's normal range is 1-20. But the range for 2D20 is now 2-40. 
That moves the eprcentages around by a very large amount compared to a 
D6. Yes, you can figure out how much to bias everything, but that's 
dancing around the issue, ebcause every bias in a D20 system results in 
the same percentage. The 3D6 system wins for this mechanic because it's 
very easy for the GM to fine-tune rolls. 

One of the things I've always liked about the TFT 3D6 system is that 
it's like meta-rules. The PC figures out what the character wants to 
do. The GM declares which Talents are applicable, which attribute to 
roll against, and how many dice for difficulty. Then fine tune with 
biases for the current situation, and roll. And if the situation comes 
up again, you already know how to handle it. 

Neil Gilmore
raito@raito.com
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