[MUD-Dev] Cognitively Interesting Combat (was Better Combat)

[David Kennerly]

(I'll reply to all three letters with the same subject line in this
one.)

Paolo Piselli wrote:
> kennerly at finegamedesign.com wrote:

I share the stated assumptions, except:

> I am assuming that making combat more interesting amounts to
> modifying the combat task such that it places more demands on the
> player.

Interesting combat requires more definition than only cognitively
demanding combat.  Integral calculus is demanding.  And so is a
first person shooter.  Some, but not all, cognitive demands promote
interest for some, but not all, players.

But before continuing, I need to know: What is a metric of cognitive
demand?  When two systems are compared, what rules dictate which
demands more or less than the other?

> It is my position that cognitive analysis is part of the future of
> making a *science* of game design.

The incomplete list of working-memory-elements for Puzzle Fighter is
an excellent start.  I see what you mean about the cognitive
complexity that the set of chunks suggests.

Yet, while aiming for new science, it would be a pity to overlook
prior art.  I doubt how theorems of games can deny their pixelated
roots in discrete mathematics, which may include game trees, tree
algorithms, and game mechanics.  I have no disparages for what
cognitive task analysis can offer, but it would be folly, as Newton
said, not to stand on the shoulders of the intellectual giants that
have preceded us.

> Rather, what I propose is that if the player must spend hundreds
> of hours in the game, lets try to make them as interesting hours
> as possible.

You can safely say "we" as in all of MUD-Dev and every MMP player
who has ever lived or will live.

> These decisions need to be made over and over again during the
> course of one "combat" because the conditions have changed for
> each iteration of the high-level goal-loop.

One unrepresented class of working memory elements (or "chunks") is
not any of these steps but is the goal itself.  The decision to
break-big-blocks itself requires tactical assessment.  Against a
human opponent, which often happens in Puzzle Fighter (if a second
player is present) or Yohoho Puzzle Pirates, the opponent can adjust
to these strategies, in which case a player needs to adopt, if to
win, a contingent strategy.

Any interesting game has this property.  It is almost implicit in
the defintion of "interesting."  It sustatins attention precisely
because failure to pay attention to the strategies employed is a
sufficient condition to lose against an opponent who, e ceritibus
paribus (all things being held constant), only differs in that his
strategy includes responding to the other player's strategy.

> The combination of uncertainty and decision-making means that
> Puzzle Fighter can never be "solved" by a discovering a single,
> optimal procedure, even though the game has incredibly simple
> mechanics and memory footprint.

Uncertainty is insufficient critertia in decision-making to prevent
a game from being solved.  A mixed strategy is what game theorists
call the solution to a game with uncertainty, and it's nearly
trivial.  Simply assign the optimal probability to each pure
strategy.

Uncertainty is, strange as it seems, theoretically necessary to
prevent a pure strategic solution in a game of perfect information.
However, that doesn't matter in practice.  For example, Chess is a
game of zero uncertainty and perfect information.  Reasoning implies
a solution exists.  But combinatorics implies that the solution is
intractable.

Thus, in practice, uncertainty is neither sufficient nor necessary
for obfuscating optimization.  This is not to rule out uncertainty.
Uncertainty is an RPG designer's (and casino designer's) best
friend.

What is necessary seems, as best as I have found any (always)
necessary trait, is NP-hardness.  That is, no polynomial-time
complexity algorithm exists to solve it.  According to a researcher,
Tetris is NP-complete.  But I am wildly generalizing.  Is Puzzle
Fighter NP-hard?

>>  - how fast of a reaction time will the player be required to
>>  have?

>> No faster than the roundtrip lag of the network, so about 1
>> second lower-bound is safe in the US on 56 kbps modem?

> I would probably give them more time than one second.  With
> network latency that would require the HPBs to have near
> instantaneous client-side reaction time.  This affects things such
> as: what should the minimum casting time on interruptable spells
> be?  Assuming that, due to latency, the client sees his foe
> casting 0.5 sec after the casting starts, he reacts in X amount of
> time, his interrupt command takes 0.5 sec to reach the server,
> then the minimum casting time should be 1 sec + upper bound for X
> (client-side player-reaction-time).  My preference would be to set
> that lower bound at 2 seconds to keep things from being too
> twitchy.

You are right.  I was wrong.

>>  - how frequently will the player have to make decisions?

> John Buehler proposed no more often than once each 3 seconds.  But
> that's just one pacing preference.  How about a range from 1
> second to 15 seconds?

> Have you ever played the custom "Defense of the Ancients" style
> maps that are popular with online Warcraft III?

No.  I haven't finished the single-player game of Warcraft III.

> The hero-vs-hero combat has a very PvP flavor to it, with the
> intersting strategy coming in the spatial posturing (analogus to
> the proposed "fighting stances"?) and in the use of the abilities
> on timers (each hero usually has several abilities each on 10-30
> second timers).  I find that these combats have a nice pacing that
> is exciting yet not twitchy.  As a player you constantly monitor
> the combat state, evaluating wether to advance or retreat or burn
> some mana on an ability.  I'm pretty sure the pacing of ability
> usage or "posture change" falls in your suggested range.

"Spatial posturing" as in a formation of units?

>>  - how much information will the player have to remember during
>>  combat?

> Depends on the desired combat.  To continue my magic number trick:
> between 0 and 3 preceding game states?  Let's say each state has
> no more than 10 bits of

> Hmm, I wasn't really thinking of the game-tree itself as a
> working-memory element.  I was more referring to things pertinant
> to decision-making that are not made explicit in the interface.
> Stuff like "this enemy can cast FOOBIE BLETCH" or "this enemy
> easily blocks standard melee attacks" or "Chun Li's super combo
> goes like: jump-in, kick-high, kick-medium, kick-high ..."
> Speaking of Street Fighter, an elite player may know the precise
> timing of 40 super moves, but during a match he will only need to
> actively remember the few that belong to his opponent.

There is an additional problem: A competent player must search the
game tree (which is, for our purposes, isomorphic to the decision
tree and can be derived from a problem space).  A necessary strategy
to success in Puzzle Fighter is the ability to anticipate potential
game states.  The whole notion of breaking a block is the simplest
and shortest search of a game tree.  Yet more complex versions
include looking five or ten moves ahead.  Although I do not know how
the game trees for Puzzle Fighter compare to Chess, in my limited
experience with both, it ain't easy.

Our lurkers will remember reading the comments on how human and
computer players search a Chess game tree, at least in broad
strokes, as we were saved from painful details.  Although I do not
wish to tie us to Chess, we are stuck with a (unless someone can
bring something better to the table) game tree and algorithms to
search a subtree.  As you know, but some readers might not,
alpha-beta is not a Chess algorithm.  Chess is merely one of its
applications.  Alpha-beta pruning used in several game playing
algorithms (and non-game algorithms).  It's not the only one, but
it's not to be left out of consideration.  A* also, is not a Chess
algorithm.  It's popularly mentioned as an efficient path-finding
algorithm.  It so happens that a game tree is composed of potential
paths.

These are not the way a human searches the game tree, but a human
does search the game tree.  The structure of the tree (or the set of
rules for its generation) is necessary to even construct the WME of
Puzzle Fighter.  Break block has no meaning without understanding
the rules of the game.  Break block has no strategic value without
understanding what the subtree from one's current vertex (AKA node)
in the game tree is.

>> However, as soon as the player has an optimal strategy, meaning
>> she has solved the game, then it's not fun any more.  The

> For a fixed game tree this is possible, but this is where the
> uncertainty of the opponent's move comes in.  If everyone is
> constantly responding to their opponent, and there is a bit of
> chance thrown in to boot, then you can't really "solve" combat in
> a way that requires no decision making.

But a player can solve it.  Game theorists call such a solution a
mixed strategy.  It is a set of pure strategies, each with a
probability assigned to it.  Optimization of a mixed strategy is no
more cognitively interesting than a pure strategy, once it has been
optimized.  For example: Rock Paper Scissors has a solution.  As a
tuple, it is (1/3, 1/3, 1/3).  Randomly select one of R, P, or S.
Game theorists call a mixed strategy over all elements with a
uniform distribution a pure random strategy.  In the case of RPS, it
is the solution.  Having solved it, it's no more interesting than
another solved game, such as tictactoe.

A solved game, for a rational player, is just a chore.  By chore, I
mean a procedure without interesting decisions.  By a rational
player, I mean one that does not care about anything except his
utility function.  To keep their guards up, a game theorist may
clarify that the payoff function is equivalent to the utility
function for the game in question.  In short, points are all that
matters and in solved games, the solution is the maximal point (AKA
payoff) strategy.

> So long as the player has to think and react, I would say the
> experience stays interesting.

After solving the game, the player only has to remember the
solution.  Remember and react is no more a game than a reflex test
during a doctor's physical examination is a game, or turning off an
alarm and going back to sleep is a game.  It is a single
working-memory-element (or chunk).

> Good point, a user's motivations do play heavily into how much
> something interestes them.  But I don't think there is any problem
> with players being motivated to quest for fame, glory, and phat
> lewt.

Motivation is necessary but not sufficient.  Several boring MMP, MP,
and SP combat systems exist that result in fame, glory, and phat
lewt.  What is sufficient, as we've already agreed, is the intrinsic
fun of the process of performing the task.

>> natural conclusion is to increase cognitive-load over time.

> Which a decent MMP does: Over time a player gains new items and
> new skills that require new and more complicated tactics.

> This sounds like a great method for adding interest - what do you
> think are some good examples of non-linear skill advancement that
> achieve this?

When a rogue learns Ambush in the The Kingdom of the Winds.  When a
warrior learns Wind Blade in Dark Ages.  When a druid or necromancer
learns his first minion spell in Diablo 2.  When a priest learns his
first debuff.  When a White Mage learns his first buff in Final
Fantasy XI.

In general, any new ability that dramatically alters the structure
(not just the values of the vertices) of the game tree complicates
tactics.  Such a new ability is analogous to a paradigm shift in the
player's model, and indeed, in the game itself.

>> Or increase combinations over time, which an MMP does (and many
>> non-MMPs do).  A player doesn't start out in Lineage, EverQuest,
>> or any of the other MMP with all the abilities or access to every
>> tactic.  I thought CoH was

> But again, if there is a known optimal strategy for a given comabt
> instance, it does not matter how many options you have.  Perhaps
> discovering this strategy is fun, but discovery can only happen so
> many times.  I still think that making the combat process itself
> inherently interesting is the way to go.

Although I have been representing game theorists (surely someone
here can represent it better than me, a math coward), I have to
introduce a caveat to optimal strategies and their utility in
design.  PacMan took over 20 years to have performance of its
solution recorded.  The theory of the solution was obvious far
before that.  So, it is not necessary that no optimal strategy
exist.

Even at MMP rates of consumption, a solution on the order of
PacMan's is more than enough to entertain players long enough to
release the sequel.  PacMan's solution, as best I read of it (I'll
never have the time to know it in practice), includes several long
sequences of pure strategy.  That is, no uncertain decisions.  As
strange as it struck me, I take it on good faith that it is so.
PacMan's solution is mostly pure; meaning certain.  Thus uncertainty
is not necessary for cognitive interest, at least within the domain
of PacMan players.  A domain expert (should we call her a
PacManiac?)  reading this could explain the errors and declare the
true Laws of PacMan.  :)

David
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