From: Reinder Verlinde <reinder@...>
Date: 2006-01-08T01:58:00+09:00
Subject: Re: Dice Roller (#61)

In article <m2fyo0gs8o.fsf@lilith.local>,
 Christian Neukirchen <chneukirchen@gmail.com> wrote:

> "Matthew D Moss" <matthew.moss.coder@gmail.com> writes:
> 
> > Hopefully this ASCII art comes through clean:
> >
> > Parse tree for: (5d5-4)d(16/d4)+3
> >
> >                 _______________ + _______________
> >                 |                               |
> >         _______ d _______                       3
> >         |               |
> >     ___ - ___       ___ / ___
> >     |       |       |       |
> > ___ d ___   4       16  ___ d ___
> > 5       5               1       4
> 
> So what are the maximum and minimum values of this?

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]

Reinder