From: Jacob Fugal <lukfugl@...>
Date: 2006-01-07T09:17:31+09:00
Subject: Re: [QUIZ] Dice Roller (#61)

On 1/6/06, James Edward Gray II <james@grayproductions.net> wrote:
> On Jan 6, 2006, at 5:35 PM, Jim Freeze wrote:
>
> > What do you need to roll to get a 0 and 100?
>
> A zero on the tens dice is 10.  On the one's dice, it's zero.  00 is
> 100.

Clarification: presented in short, long and practical. :)

Short clarification:

Actually, when rolled together, both dice are zero-based. The
double-nought is the only special combination of 00 -> 100. When
rolled singly, a d10 has 0 -> 10. Rolling a 0 is never possible.

Long clarification:

Normally, a d% is rolled as a combination of a "d100" and a d10.
"d100" is in quotes, because it's actually just a special d10 -- 10
sided die, that is -- except the numbers on the "d100" are 00, 10,
20... 90. The numbers on the d10 are 0, 1, 2... 9. Rolling the two
together and adding you have a range from 0..99. However, since the
tables that require a d% roll are normally 1-based (1..100), the
'double-nought' -- a 00 on the "d100" and 0 on the d10 -- is
considered 100, everything else is face value. Some examples:

  00 / 5 -> 5
  10 / 5 -> 15
  20 / 0 -> 20
  00 / 0 -> 100

Similarly, when asked to roll a d10, the face numbers are 0..9, but
are interpreted as 1..10 by making the 0 a 10 and leaving the other
faces at face value.

All other dice (in my experience) are always interpreted as face value
(the sides being 1-based).

Regarding the probability curve of a d% versus a true d100 (100-sided
die), they are the same. Consider the d100: there are 100 faces, each
with a 1% probability. With a d% roll ("d100" + d10), each integer
between 1 and 100 (again, double-nought counting as 100) is produced
exactly once, and with the same probability. 53 (produced only by 50 +
3) is no more likely than 99 (90 + 9) or 1 (00 + 1). So for all
intents and purposes, a d% is equivalent to a d100.

Practical clarification:

As mentioned above, rolling two ten-sided dice versus rolling a
100-sided dice produce the same distribution (given the method of
combination). Rolling a ten-sided zero-based die then converting 0 to
10 versus rolling a ten-sided one-based die produce the same
distribution. So if you see dM then rand(M) + 1 will produce the
correct distribution. d% counts as d100.

Now if you'll excuse me, I'm late for an appointment with *my* dice.
Your die-rolling lesson for the day was brought to you by the numbers
3, 5 and the letter D. :)

Jacob Fugal