From: Jacob Fugal <lukfugl@...>
Date: 2006-01-10T00:57:44+09:00
Subject: Re: Dice Roller (#61)

On 1/7/06, Reinder Verlinde <reinder@verlinde.invalid> wrote:
> Notation: [x,y] is any distribution with minimum x and maximum y. I then
> get:
>
> (5d5-4)d(16/d4)+3 =        (adb = [a,a*b], so 5d5 = [5,25])
>
> ([5,25]-4)d(16/d4)+3 =     ([x,y] - c = [x-c,y-c])
>
> ([1,21])d(16/d4)+3 =       (adb = [a,a*b], so d4 = 1d4 = [1,4])
>
> ([1,21])d(16/[1,4])+3 =    (c/[x,y] = [c/y,c/x]  if x and y > 0)
>
> ([1,21])d([4,16])+3 =      ([a,b]d[c,d] = [a*c,b*d] if a,b,c, and d > 0)
>
> [4,336]+3 =                ([x,y] + c = [x+c,y+c])
>
> [7,339]

As pointed out by others, the result should actually by [4,339]. The
error above is in the second to last step. [a,b]d[c,d] != [a*c,b*d],
it should be [a,b]d[c,d] = [a,b*d]. The minimum effective value on a
die roll is always one, regardless of the number of sides (ie. whether
using a c-sided die or d-sided die). The minimum number of rolls being
a, the minimum roll total would then be a*1 = a. So we have:

  [1,21]d[4,16]+3 =
  [1,21*16]+3 =
  [1+3,336+3] =
  [4,339]

Jacob Fugal