From: Matthew Smillie <M.B.Smillie@...>
Date: 2006-01-08T04:27:31+09:00
Subject: Re: Dice Roller (#61)

On Jan 7, 2006, at 18:32, Christian Neukirchen wrote:

> Gavin Kistner <gavin@refinery.com> writes:
>
>> On Jan 7, 2006, at 9:55 AM, Gavin Kistner wrote:
>>> On Jan 7, 2006, at 5:03 AM, Christian Neukirchen wrote:
>>>> "Matthew D Moss" <matthew.moss.coder@gmail.com> writes:
>>>>> Parse tree for: (5d5-4)d(16/d4)+3
>>>>
>>>> So what are the maximum and minimum values of this?
>>>
>>> Max: (5*5+4)*(16/4)+3 = 29*4+3 = 119
>>
>> Man, *and* I flipped the sign on that -4. *shakes head sadly*
>>
>> One more shot.
>>
>> Min: (5*1-4)*(1)+3 = 1*1+3 = 4
>> Max: (5*5-4)*(16/4)+3 = 21*4+3 = 87
>
> I claim 4 and 339.

Both (4, 87) and (4, 339) are correct depending on your definition of  
'max'.  You get the former if you assume maximum rolls for each die,  
and the latter if you want the maximum possible result of the  
expression.

In any case, the extremal results aren't particularly useful from a  
testing point of view, as different distributions can have the same  
extremal points, and you could potentially erroneously pass an  
incorrect case.  For example: 2d2d6

left-associative:
(2d2)d6 -> 4d6 -> 24 max

right-associative (oops!):
2d(2d6) -> 2d12 -> 24 max

But the distributions are different in each case (the latter result  
could include 2 and 3, for instance).

matthew smillie.