[MUD-Dev2] [DESIGN] Expected value and standard deviation

[Travis Casey]

> * Original Poster:  Jeff Cole
> * Thu Aug 28, 2003 1:27 pm

> And that got me to thinking. In MUDs/MMO* advancement entails
> (ridiculously?) increasing the expected value of a player's
> performance. Gameplay would certainly be more complex if, like
> poker, advancement required one to balance expected value with
> standard deviation--if advancement involved more decreasing of
> standard deviation and less increasing of expected value.
>
> My concern, though, would be that players, like my friends, would
> have a difficult time recognizing such "advancement." Dunno. Such
> an approach would necessarily require rethinking other "standard"
> gameplay systems.

A few paper RPGs do this sort of thing.  In the hopes of inspiring  
someone, here's a rundown of three that I know of:

_Don't Look Back: Terror Is Never Far Behind_ rates attributes,  
skills, and difficulties with plus and minus ratings, most commonly  
in the -3 to +3 range, but sometimes moving farther out.  To resolve  
an action, the applicable modifiers are totaled, and then a number of  
six-sided dice are rolled equal to:

abs(total modifier) + 3

If the total modifier was positive, then the three highest die rolls  
are added together for the result; if it was negative, then the three  
lowest die rolls are used.  A die sum of 11 or higher is a success,  
with higher results being greater success, while those of 10 or less  
are failures, with lower results being worse.

The end result is that all characters have the same possible range of  
results on actions.  As a character gets better, though, their  
average result becomes higher, and the "peaking" becomes sharper,  
resulting in smaller standard deviations.


Another system, used in _Heavy Gear_ and its related games, also uses  
six-sided dice, but has two sorts of modifiers.  One sort is simple  
pluses or minuses, which are added directly to the die roll.  The  
second sort is additional dice to roll, which are not added to the  
one die one normally gets; rather, one rolls the dice and takes the  
highest among the individual dice that were rolled.


Lastly, _Ironclaw_ uses a system with a mixture of dice sizes:  d4,  
d6, d8, d10, d12, and d20.  When rolling multiple dice, the highest  
result is used, and different mixtures are possible -- e.g., 2d4 
+d10.  (The system notates the dice being rolled in this way, even  
though the dice are not being added together.)

Increasing the size of the largest die raises the maximum possible  
result, but adding extra dice increases the consistency of results,  
making low results much less likely.


--
Travis Casey
efindel at gmail.com