[MUD-Dev] Better Combat

[David Kennerly]

Brendan O'Brien wrote:

> However, in terms of fighting strategies and how players spec
> their characters, it is very common to see players focus almost
> entirely on offensive-based skills.  They like the bragging rights
> and shock value of landing a huge hit, and are certainly willing
> to sacrifice a bit of defense in order to achieve it.  If nothing
> else, just think of how many games have ended up with a very
> popular "glass canon" template.

I'm assuming these are quasi-D&D derivatives.  If so, then being
offensive IS a risk-averse strategy when in a team.  And even as a
solo character, a high-offense is more efficient than a high-defense
character.  It seems counterintuitive, but in D&D derivatives, the
usual victory condition is reducing the opponent to 0 or less hit
points.  No amount of defense will do that.

Yet what we were talking about with your proposal was not really
like this.  In D&D terms the only approximation is "fighting
defensively", "expertise", "power attack", "charge", and things like
this, which is a tradeoff various amounts of attack bonus or damage
(offense) for armor class (defense).  Since we're talking about
better combat, I certainly don't want to restrict our conversation
to D&D!  Just want to clear up the terms so we can progress beyond:
Hello.

>> Also, how does the payoff matrix of this aggression differ from
>> Rocks, Papers, Scissors?  That is, given player 1 and 2, both
>> with options {1, 2, 3, 4, 5}, forming a 5x5 matrix, how do the
>> payoffs differ from the 3x3 RPS matrix?

> I wouldn't really consider it a matrix in the same way at all.  At
> least not in the terms of thinking that choosing one option will
> always work when used against another option.

No.  Certainly not just one matrix.  But given a specific example
with all parameters set, the only variables remaining are (for two
combatants) their decisions.  If they have 5 options, as you said on
a scale of 1 (cautious) to 5 (aggressive) then, one simple model of
this example is a 5x5 payoff bimatrix.  Since this is a combat, it
would not be inappropriate to consider that their player utility
functions are diametrically opposed, so the victory of player 1 is
the defeat of player 2, and vice versa.  In this case, we could
easily assign single matrix (instead of bimatrix) values.  That is
each cell has a value.  To do this properly, we can use Zermelo's
algorithm, which is just backwards induction.  Start at the victory
conditions (for either player) and work backwards.  Having done so,
there now exists a complete game tree with all vertices at a
particular value.  Since all parameters except decisions have been
set, there are 5^2 (25) out-arcs from each game vertex.  Each of
these points to another game vertex.  If it points to a victory
vertex, then it has a value of 0 or 1.  If lotteries are used (i.e.,
randomness) then there can be an intermediate vertex of each
instance of randomness in which a virtual player, named Chance,
takes a turn, choosing the arc to the next as dictacted by the
random distribution.

So, now that we have that cleared up.  Suppose an example
situation--any that you please--How does this example's payoff
matrix differ from Rocks Papers Scissors?  A repeated rocks papers
scissors, combat might go as follows, with 0.5 being draw, 0 being a
win for player 2, and a value of 1 being a win for player 1:

  p1    \   p2

           r          p          s
  r       0.50       0.25       0.75
  p       0.75       0.50       0.25
  s       0.25       0.75       0.50

Each of these numbers is not the outcome of the game necessarily; it
is just the value of the next vertex.  The vertices can each have
different values in their own matrices.  But this representative
case explains the nature of RPS... which already knew.  Dave Morris
applied RPS to fighting game, with obvious correlations (e.g.,
rock==defense, paper==feint, scissors==aggressive).  But by covering
this familiar territory, now we can start to seriously discuss the
design you wrote about.  In the simplest example of 5x5 matrix, what
differences cause it stand apart from the intransitive, reflexive,
and asymmetric relation above (i.e. RPS)?

I don't mean to be a pendantic bore.  It isn't necessary that you
fill out a matrix, but some sort of concrete, shared vocabulary must
be employed if we are to get pass barroom quality chat.  :)

I totally agree with your sentiments:

> The harder you hit your opponent, the more likely you are to gain
> control of the fight (by injuring him, making him lose his
> balance, or just putting him on the defensive).  However, the risk
> is that if you misjudge the opportunity, a harder blow is more
> difficult to get off, which could result in your opponent taking
> control (your move can be prevented from being executed if your
> opponent is able to turn the round of combat into his favor).

I would just like to understand what you game mechanically mean by
them.  In this example, there is a big difference, game mechanically
between ye-old D&D style such as "power attack" which does just what
you say:

> However, the risk is that if you misjudge the opportunity, a
> harder blow is more difficult to get off, which could result in
> your opponent taking control

But is as fun as you said: like watching a lumberjack.  In OGL (open
gaming license, the "open source" that D&D now rides on) power
attack is a simple subtract attack bonus and add to damage, which
meets this above sentiment precisely, yet it is dull.  Dull!  There
is an optimum result to input for a tuple of (armor class, attack
bonus, damage, 2-handed or not, and a few others), but the result is
fairly mindless, and has the flair of a lumberjack ... without the
singing.

Power attack could be modeled as a matrix as well, and the problem,
as would be seen in that matrix, is that it's surface (if a matrix
were continuous) is smooth and has a very small slope.  Even it's
optimum is not treacherous.  Declaring +1 power attack is optimum
under most cases, and it requires highly irregular circumstances to
deviate, which a matrix (or set of matrices of typical encounters)
reveals.  So, in this example of determining how hard to swing and
"taking control" what would be some of the game mechanical effects?

Again, I apologize for the use of D&D, which I disfavor, in part for
its "Worse Combat".  :) Just a vocabulary aid, and hopefully a
lukewarm baseline to judge the excitement your intended system
evokes.

David
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