From: laurence@cco.caltech.edu (Dustin Lee Laurence)
Subject: Re: CHAMP: 1/2d6 vs d6-1
Organization: California Institute of Technology, Pasadena
Distribution: usa
Date: Fri, 10 Apr 1992 01:35:07 GMT

cleggp@aix.rpi.edu (Paul Jason Clegg) writes:

>I've been meaning to ask this question for a while.

>When do you use "xd6-1" vs. "x 1/2d6" for things like killing attacks?
>According to the "DC" table, they're both on the same "level", but:

>1) They never really explain how to use the "d6-1" concept in the rules, and
>2) It would seem to me that the "d6-1" is better than a 1/2d6, and thus
>   shouldn't be considered "equal".

>I normally use 1/2d6es, because that's all that's ever mentioned in previous
>editions.  However, in the listings for weapons, some weapons are rated at
>"1 1/2d6K" and some at "2d6-1K".  What's the difference?  When do you use
>which?  Why did they make them different?  How do you use a "1d6-1" for
>STUN and BODY purposes?  What's the deal?

>...Paul

Well, lets see.  Hero wants there to be three damage classes per killing
die, so what is really called for are 1/3d6 and 2/3d6 rolls.  I usually
do this, as I don't mind, but I suspect that most people would dislike
it.  So, you have to have a reasonable substitute.  The mean roll on a
killing die is 3.5.  Clearly, we need to get as close to rolls with means
of 1 1/6 and 2 1/3 as possible.

The sixth of a body is negligible, so instead of 1 1/3d6 just roll 1d6+1.
Simple.

Now, 1d6-1 averages to 2.5, which differs from 2 2/3 by 1/6, so that is
a similarly acceptable substitute for 2/3d6.  On the other hand, hero
always says that numbers should be rounded in the characters favor, so
that if you roll a die and divide by two, what is nominally a half die
averages to 2.  This differs from 2 1/3 by 1/3 of a body, so this is
a worse aproximation.  However, it's still small enough to be acceptable
to most people.

So, to the accuracy that hero cares about, 1/2d6 and 1d6-1 are the same.
On the other hand, their difference is 1/2 a body, so you might notice
the difference if you use them both.

If you really want to go to the trouble, then roll the third dice:
rounded correctly, a 1/3d6 rolls 0-1-1-1-2-2 and a 2/3d6 rolls
1-1-2-3-3-4.  Their averages are 7/6 and 7/3, so they actually are
exactly correct in the mean.  Their higher moments are going to be off,
but if this bothers you then you should be confined for your own safety.

By the way, if you really want a true half die, then you need to make
half the rounds to be against the character rather than for.  Since
there are three rounds, you can't do this exactly, but you can come
closer.  Since I have to err one way or the other, I choose to err in
the character but as little as possible, to follow the spirit of the
rounding rule.  Rounding one .5 down rather than up gives a mean of
1 5/6, which differs from the correct mean of 7/4 by 1/12 of a body;
surely a negligible error.  I choose to round a single pip down to
zero, because I can remember it easily, but it doesn't matter whether
you round the 1/2, the 3/2, or the 5/2 down.

As with most things hero, if you figure out the intent then you don't
need the official ruling.

-- 
Dustin Laurence            "Someone please stop me, before I net again."

laurence@alice.wonderland.caltech.edu