default header

Theory

On Complexity, Depth and Skill

Moderator: JC Denton

On Complexity, Depth and Skill

Unread postby Kuzdu » 14 May 2008 21:48

http://insomnia.ac/commentary/on_comple ... and_skill/

I was wondering about the suggestion that the relationship between complexity and depth is "exactly linear".

It seems to me that some games with simple rulesets can nonetheless have a lot of depth. For instance, Go has just a handful of rules, and yet the distance between a master and an amateur is immense.

On the other hand, a game like Settlers of Catan has quite a few rules, and yet there are only a few truly viable strategies. If all the players choose one of those strategies then the game really comes down to who the dice favor.

First of all, am I misunderstanding the definitions of the terms given in the article? If I'm not misunderstanding, are these definitions simply specific to video games?

It seems to me that the two examples I've given point to the relationship between complexity and depth in games being something less than exactly linear. I would be really interested to hear Kierkegaard's response to this.
Kuzdu
 
Joined: 14 May 2008 21:19

Re: On Complexity, Depth and Skill

Unread postby JoshF » 15 May 2008 06:27

Kuzdu wrote:I was wondering about the suggestion that the relationship between complexity and depth is "exactly linear".

They relate to/modify one another in succession.

Umm... read this part:
Alex wrote:Each new meaningful rule makes a game more complex, and gives the player some extra work to do in order to learn it. Each new rule interacts with the existing rules in new and increasingly complicated ways, creating an ever-widening realm of possibilities which the player is called upon to grasp. The better he grasps them the more capable he becomes in using them to his advantage, and thus the more skillfully he can play.


Kuzdu wrote:It seems to me that some games with simple rulesets can nonetheless have a lot of depth. For instance, Go has just a handful of rules, and yet the distance between a master and an amateur is immense.

Situations (maybe there's a better word?) can be part of the rules too. For instance you won't find "Dee Jay's jumping light punch will beat T. Hawk's Condor Dive" on an instruction card, but it is a rule nonetheless, as it is unalterable.
User avatar
JoshF
 
Joined: 14 Oct 2007 14:56

Unread postby Kuzdu » 15 May 2008 09:21

Ah, then maybe the case is that I misunderstood.

What I took "exactly linear" to mean was that whenever you increase the complexity of the ruleset you inevitably increase the depth of the game. My example, Settlers of Catan, is a game that has many rules, but really comes down to luck in the end, and is therefore not really skill-based at all.

BUT, I suppose if you count "situations" that arise from a ruleset, the 'meta-rules', then it is reasonable to suggest that complexity, depth, and skill do in fact have a linear relationship.

What this suggests though, and this is by no means a bad thing, is that we might never really know all the rules of a given game. If the rules interacting gives rise to "situations", new rules, and then through the interaction of those new rules we discover even more rules, then that could proceed on forever.

Hmm, very interesting...
Kuzdu
 
Joined: 14 May 2008 21:19

Unread postby raphael » 15 May 2008 09:51

Edit: this was written before Kuzdu's previous post. I hope it is still interesting. But I think he understood on his own what I tried to explain here.


The case of Go is certainly interesting and enlightening. Being myself a player I think I can understand how Alex's assertion still applies. I will try to explain.

Go truly has one of the smallest set of rules in a board game. But once you try to play it with seasoned players you will soon realize you can not compete because they don't play by these rules only. If they did, it would take them much longer to make their decisions right about the very complex matters one always meets in this game. Because yes, despite the simple set of rules there is a lot of complexity.

The main reasons for this complexity are:
1- the important size of the board, making the number of possibilities (meaningful or not) just huge.
2- there are very few limitations to were you can put your stone at each turn, thus the number of possibilities are not reduced as they would be in a game were you move the pieces
3- situations can be reverted, making the possibilities (again meaningful or not) virtually endless.

So how do seasoned players take their fast and meaningful decisions ?
Well, this is history. Making it very short, japanese imperial court held the chinese game of Go very high. It was considered one of the main arts an high spirit should master. So the problem of sorting meaningful from meaningless was taken and addressed very seriously. For centuries they worked on it and transmitted their experiences. Thus the knowledge on the game and the quality of the players raised immensely.

So, back to our seasoned player, how does he take his decisions ? It's by using a set of advanced rules that help recognize meaningful and efficient decisions from meaningless possibilities, the very rules centuries of japanese high spirits passion has helped building.

So novice players don't stand a chance as long as they don't learn those rules. Actually, these are not considered rules because they only derive from the basic set of rules. They are merely consequences. But still, the knowledge of these derivative rules makes a dramatic difference, so people play by them. And when you start learning it you discover they are very complex... and numerous.
User avatar
raphael
 
Joined: 04 Mar 2008 19:31
Location: Paris

Re: On Complexity, Depth and Skill

Unread postby icycalm » 16 May 2008 18:03

Josh pointed towards the answer to the original question, without directly providing the answer. So let me do that here in detail.

Kuzdu wrote:I was wondering about the suggestion that the relationship between complexity and depth is "exactly linear".

It seems to me that some games with simple rulesets can nonetheless have a lot of depth. For instance, Go has just a handful of rules, and yet the distance between a master and an amateur is immense.


What makes you think that all rules are equal? I.e. that all rules affect the level of complexity of a game equally? Obviously, that's not true. I made the distinction between 'meaningful' and 'meaningless' rules, but of coure there are degrees of meaningfulness. Go may have few rules, but those rules, and the realm of possibilities which they create by interacting with each other (i.e. the game's depth), is much greater than the realm of possibilities created by the rules of something like, say, Lost Odyssey, which has millions of rules, most of them completely meaningless (and many of the rest even going as far as to cancel out complexity created by other rules and sets of rules!).

So this is the point where you go wrong (along with practically everyone who writes about games today):

Kuzdu wrote:It seems to me that some games with simple rulesets can nonetheless have a lot of depth.


There is nothing "simple" about the ruleset of Go, just as there is nothing simple about the ruleset of Mushihime-sama or KOF XI. Just because you can easily recite something (a poem, say, or a ruleset comprised of six rules) doesn't mean you understand it.

So when some journalist hack writes that a "simple" game has "a lot of depth", all he is doing is abusing the terms 'simple' and 'depth'. A simple game is by definition shallow, and a complex game by definition deep. If we start calling simple games 'deep' then our whole terminology becomes meaningless -- which is of course what these people are doing on purpose in order to muddy the waters and hide in them their own ignorance. Since they cannot even begin to understand complexity, their adoption of doublespeak helps ensure that their readers have no chance of doing so either.

JoshF wrote:Situations (maybe there's a better word?) can be part of the rules too.


There is no better word than 'rule'. A rule defines what is possible in a game, and therefore also what is not possible. A situation is nothing more than one of those allowable posibilities.

JoshF wrote:For instance you won't find "Dee Jay's jumping light punch will beat T. Hawk's Condor Dive" on an instruction card, but it is a rule nonetheless, as it is unalterable.


Exactly. There is a rule in the game which says, "Dee Jay's jumping light punch will beat T. Hawk's Condor Dive". Videogames have hundreds of thousands of rules like this. There are even rules which determine what font the "Game Over" logo will be, or what color the top-right pixel in the sixth frame of the the third-from-last cinematic will be. Obviously, those rules are meaningless, because if you change them the game will remain the same, and that's what we call "atmosphere".

This comment by raphael, by the way, is dangerously misleading:

raphael wrote:So novice players don't stand a chance as long as they don't learn those rules. Actually, these are not considered rules because they only derive from the basic set of rules. They are merely consequences. But still, the knowledge of these derivative rules makes a dramatic difference, so people play by them. And when you start learning it you discover they are very complex... and numerous.


Introducing superfluous terms like "derivative rules", "consequences", "situations", etc. only serves to muddy the waters and make it harder for people to understand what you are trying to explain to them.

In games there are only rules. This is a sufficient concept to explain whatever it is that needs explaining.

And I'll close this reply with the issue of linearity, which perplexed Kuzdu:

Kuzdu wrote:It seems to me that the two examples I've given point to the relationship between complexity and depth in games being something less than exactly linear.


The relationship between complexity and depth is the same as that between distance and length: i.e. depth is nothing but the measure of complexity, as length is the measure of distance. We could as well speak about "height" of complexity or "length" or "width" of complexity if we wanted to. So obviously this so-called "depth" will be linearly related to complexity, since it measures it.

As for the relationship between complexity/depth and skill... it is obviously linear, and we can say this by experience. More possibilities* means more ways to gain an advantage, means a higher degree of skill is necessary to exploit them. If you require mathematical proof... well, I bet if I worked on it I could give it to you. At the moment, however, I lack the necessary mathematical tools (Frege's logic, mostly, as well as some way to quantify skill).

At any rate, it would be a boring enterprise. I am satisfied with my current, qualitative, explanation. Doubtless the scientist monkeys will one day give us the proof, and doubtless none of us will bother reading it.



*and remember: we are always referring only to meaningful possibilities -- because complexity/depth can only be defined in terms of those. In fact "meaningless possibilities" do not exist; the expression is an oxymoron.
User avatar
icycalm
Hyperborean
 
Joined: 28 Mar 2006 00:08
Location: Tenerife, Canary Islands

Unread postby icycalm » 16 May 2008 18:24

Also, just in case it's not crystal-clear from the above, all of Kuzdu's second post is nonsense:

Kuzdu wrote:My example, Settlers of Catan, is a game that has many rules, but really comes down to luck in the end, and is therefore not really skill-based at all....


I've never played the game, but if it has many rules while at the same time not being skill-based at all, it means most of its rules are meaningless, or even worse, meaning-cancelling. Therefore it's a shallow game.

Kuzdu wrote:BUT, I suppose if you count "situations" that arise from a ruleset, the 'meta-rules', then it is reasonable to suggest that complexity, depth, and skill do in fact have a linear relationship.


"Meta-rules" my ass. See above.

Kuzdu wrote:What this suggests though, and this is by no means a bad thing, is that we might never really know all the rules of a given game. If the rules interacting gives rise to "situations", new rules, and then through the interaction of those new rules we discover even more rules, then that could proceed on forever.


Complete and total horseshit. Obscurantism at its best. You pull a bunch of nonsensically-defined terms out of your ass, then you throw them haphazardly in a paragraph, and when you can't make heads or tails from the resulting mess, you say:

Kuzdu wrote:Hmm, very interesting...


lol
User avatar
icycalm
Hyperborean
 
Joined: 28 Mar 2006 00:08
Location: Tenerife, Canary Islands

Re: On Complexity, Depth and Skill

Unread postby Ichigo Jam » 17 May 2008 01:13

icycalm wrote:As for the relationship between complexity/depth and skill... it is obviously linear, and we can say this by experience. More possibilities* means more ways to gain an advantage, means a higher degree of skill is necessary to exploit them.

About the word linear: maybe it's just the mathematician in me, but your use of the word linear implies things I don't think you mean.
I.e. a relation of the form f(x)=kx+c (with k and c constant and k non-zero). For example it's correct (if pointless) to say that the number of pieces remaining on a chess board is linearly related to the number of pieces taken (i.e. f(x)=32-x).

But anyway, my real question is: does this mean that increasing the size of the dartboard in a game of darts reduces the complexity? It seems to reduce the skill required, does it not?
User avatar
Ichigo Jam
 
Joined: 22 Apr 2008 17:24

Unread postby JoshF » 17 May 2008 03:53

What do you mean? Simply making it bigger reduces the difficulty. Unless you're talking about adding areas the rules are the same, so it is no more or less complex. I think this proves what Alex said, that depth, complexity, and skill must go in a certain order to effect one another.

Also, on the notion that "more space = more depth," it is a bit tricky. In some games having a limited playfield is what forces the strategy, like Chess or 2d fighters.
User avatar
JoshF
 
Joined: 14 Oct 2007 14:56

Re: On Complexity, Depth and Skill

Unread postby TreeFrog » 17 May 2008 11:26

Ichigo Jam wrote:But anyway, my real question is: does this mean that increasing the size of the dartboard in a game of darts reduces the complexity? It seems to reduce the skill required, does it not?


At some point this will clearly become true - once the areas are big enough that even the most rubbish player can hit them, then the game has almost no scope for skill.

The choices are then reduced to only which number to hit, without the error prediction/recovery that makes the game interesting.

In 'meaningful' terms the rules will eventually become simpler. To illustrate:

A darts player will have a larger chance of hitting a single than a double, and a double than a triple. This requires some trade off between score and reliability when picking the optimal move.

e.g. with 62 points and 2 darts remaining, it would normally be better to go for 2x20, 2x11 rather than 3x20, 2x1.

As the board becomes bigger, this trade off will become less and less relevant until you reach a point where it'll never be worth aiming for anything other than the shortest path to 0.

Thinking about it another way, the current size of the dartboard is (hopefully) set to maximise the meaningfulness of most players choices. If the board were too small, then only masters could make meaningful choices - everyone else would be lucky to hit the board, so they'd probably always aim to hit the middle.
Last edited by TreeFrog on 19 May 2008 12:28, edited 1 time in total.
User avatar
TreeFrog
 
Joined: 01 May 2008 18:53

Re: On Complexity, Depth and Skill

Unread postby Ichigo Jam » 17 May 2008 13:05

JoshF wrote:I think this proves what Alex said, that depth, complexity, and skill must go in a certain order to effect one another.

icycalm wrote:It is logically impossible for us to conceive of them separately, as they are in fact related in an exactly linear fashion

After re-reading the article, it seems to all come down to me mis-understanding the above statement of icycalm's.

I took "impossible for us to conceive of them separately" to mean that the three concepts are nearly interchangeable. (Not helped by my reading of linear as a mathematical concept.)
This interpretation was reinforced by the fact that it seems reasonable for depth/complexity.
User avatar
Ichigo Jam
 
Joined: 22 Apr 2008 17:24

Unread postby icycalm » 17 May 2008 16:01

First off, Ichigo Jam and Treefrog, PLEASE separate your paragraphs with spaces. I am sick and tired of editing other people's posts. It will only take you like a few fucking milliseconds. So just fucking do it.

Ichigo Jam wrote:About the word linear: maybe it's just the mathematician in me, but your use of the word linear implies things I don't think you mean.


Mathematician my ass. What is this, kindergarten? I have to now explain to you what 'linear' means? "Two linearly related qualities increase in proportion to one another." How hard can that possibly be to grasp? You need equations in order to do that?

Also, Jesus fucking Christ:

Ichigo Jam wrote:I.e. a relation of the form f(x)=kx+c (with k and c constant and k non-zero). For example it's correct (if pointless) to say that the number of pieces remaining on a chess board is linearly related to the number of pieces taken (i.e. f(x)=32-x).


Why don't you just copy-paste the whole Wikipedia article in here and be done with it? Then there will be no reason for you to think about how the concept of linearity applies in the present context. Pedantism at its worst.

Ichigo Jam wrote:I took "impossible for us to conceive of them separately" to mean that the three concepts are nearly interchangeable.


What a stupid thing to imagine! How did you come up with that hallucination? My advice: stay off drugs when you are reading my articles. And what the hell is "nearly interchangeable" supposed to mean? Two concepts are either interchangeable (in which case they are really ONE concept for which we have two words), or they are not. That's it. There's no "nearly".

Ichigo Jam wrote:But anyway, my real question is: does this mean that increasing the size of the dartboard in a game of darts reduces the complexity? It seems to reduce the skill required, does it not?.


Stay on-topic. If you want an answer to this question start a "Darts" thread.

JoshF wrote:I think this proves what Alex said, that depth, complexity, and skill must go in a certain order to effect one another.


Using the word 'must' carries the implication that this order may be changeable. It isn't. This is how this mechanism works, and there is nothing we can do to change it. It is a fact of logic, which is to say a fact of nature.

Now please note that I didn't read Treefrog's reply because it is off-topic. So he may be right or he may be wrong; either way I don't have much interest in darts so I don't care. You guys must realise that we are talking about general concepts here. General concepts are useful, because once they are sufficiently developed (as they have been in this article and thread, after my clarifications) they can be applied to ANY game.

Now of course those who have trouble grasping the theory immediately may need some additional examples (i.e. apart from the coin toss and Go) in order to do so. That's fine and well, I guess, so thankfully the "Darts" example will help them. But let's not turn this thread into a series of discussions of individual games. Let's try to keep the thread at an abstract level, as much as that is possible.

PS. (Not that there remains anything to discuss, of course. The purpose of this thread is for me to answer questions and make clarifications in order to help those who have trouble understanding the original article.)
User avatar
icycalm
Hyperborean
 
Joined: 28 Mar 2006 00:08
Location: Tenerife, Canary Islands

Unread postby Kuzdu » 17 May 2008 21:57

I guess I misspoke when I said "simple" ruleset when what I really meant was "small". That is, Go has a very small ruleset, if we're not taking the emergent situations as rules.

I think we agree that a game's rules define its possibility space. What I'm suggesting though, is that as you map that possibility space through play, at a certain point the game actually starts to have a less depth, not more, as more of the formerly meaningful rules prove to actually be meaningless.

I was being (perhaps inappropriately) facetious when I said that this mapping could go on infinitely. "Skill" is really a matter of being able to effectively navigate a possibility space, but when the space has been entirely or mostly mapped, as it has been in Tic-Tac-Toe or Checkers or Catan, then navigating it becomes trivial.

I started this thread in order to clear up some of my misunderstandings though, so as you said, I'll start a new one if I want to keep hashing these things out.

Thanks for clarifying! I understand what you were getting at.
Kuzdu
 
Joined: 14 May 2008 21:19

Unread postby hypsup » 18 May 2008 10:23

Hi, This is my first post anywhere ever on anything.

A few things:
Great site. Very thought provoking.

I am not sure I agree with your assertion that the absolute complexity of a game can be measured by the maximum distance between the best and worst players. This will really only tell you whether not the game is a pure game of chance or not.

If after 1000 matches of a game each player has won 500 it is clear that the game is a game of chance. However, what if the results of the the game are 600 to 400? You know the game has a sizeable element of chance, but the rules can obviously be exploited to win. It’s hard to say anything about it’s complexity.

When it comes to absolute complexity it is more useful to look at the top tier alone. If the top 100 players all have exactly the same high score for example you can bet that the rules of the game can be and have been perfectly exploited. The absolute complexity of the game is now a known quantity.

For every other game:
Is a game complex? If I understand the rules of a game, but don’t understand how a top player exploits them to win the answer is probably yes.
hypsup
 
Joined: 17 May 2008 00:59

Unread postby icycalm » 18 May 2008 15:57

Kuzdu wrote:I guess I misspoke when I said "simple" ruleset when what I really meant was "small".


No, you didn't misspeak, you said exactly what was on your mind, which was stupid, and now that you understand that it was stupid because you had it explained to you, you are making a pathetic attempt at covering your original stupidity.

So don't. We all make mistakes. Just take it like a man.

Kuzdu wrote:That is, Go has a very small ruleset, if we're not taking the emergent situations as rules.


Hello stupidity again. THERE ARE NO "EMERGENT" SITUATIONS -- only situations PERIOD. What you call an "emergent situation" is simply a situation the possibility for which has always existed, but which you were too stupid to see before you actually played the game and came face to face with it. So stop trying to introduce meaningless terms into this thread.

Kuzdu wrote:I think we agree that a game's rules define its possibility space.


You "think" that we agree? You are still not sure? Did I not explain this very thing in the original article? And now, after all these clarifications which were prompted by your questions, you are still not sure that you agree with me? (PS. Please don't bother answering.)

Kuzdu wrote:What I'm suggesting though, is that as you map that possibility space through play, at a certain point the game actually starts to have a less depth, not more, as more of the formerly meaningful rules prove to actually be meaningless.


How can a "formerly meaningful" rule later prove to actually be meaningless? The only thing that this "discovery" proves was that you were too stupid to discern each rule's degree of meaningfulness in the first place.

Also, a game's depth has been defined the moment the game is created. It cannot at some later point "start to have less depth".

You are again and again confusing the attributes of the thing which you are trying to examine, with your ability to grasp them. Just because you can't see something doesn't mean it doesn't already exist for christsake.

Kuzdu wrote:I was being (perhaps inappropriately) facetious when I said that this mapping could go on infinitely.


You were not being facetious when you said that, you were being stupid. I am sorry, but in this forum we call a spade a spade.

Kuzdu wrote:"Skill" is really a matter of being able to effectively navigate a possibility space, but when the space has been entirely or mostly mapped, as it has been in Tic-Tac-Toe or Checkers or Catan, then navigating it becomes trivial.


For the person who has mapped it, yes. Which is why I am saying that increasingly complex games are necessary to maintain the interest of an intelligent human being (but don't go off on a tangent now -- this subject already has its own thread).

Kuzdu wrote:I started this thread in order to clear up some of my misunderstandings though, so as you said, I'll start a new one if I want to keep hashing these things out.


Hash things out on which subject? Obviously not on this subject, because this subject already has its own thread. On a different subject? Be my guest -- as long as that subject doesn't have its own thread already.

Kuzdu wrote:Thanks for clarifying! I understand what you were getting at.


Yes, I now believe that you do, at least to a great degree. And don't let my tone bother you. I just don't have the time nor the inclination to sugar-coat my replies. They still get the job done though, which is what you really want after all.
User avatar
icycalm
Hyperborean
 
Joined: 28 Mar 2006 00:08
Location: Tenerife, Canary Islands

Unread postby icycalm » 18 May 2008 16:04

As for hypsup's post: I am thinking about it. I'll think about it some more.
User avatar
icycalm
Hyperborean
 
Joined: 28 Mar 2006 00:08
Location: Tenerife, Canary Islands

Unread postby Molloy » 19 May 2008 16:03

hypsup wrote:When it comes to absolute complexity it is more useful to look at the top tier alone. If the top 100 players all have exactly the same high score for example you can bet that the rules of the game can be and have been perfectly exploited. The absolute complexity of the game is now a known quantity.



I'd say that assertion is pretty much on the money from what I've seen in multiplayer games. Supreme Commander had a ranking system and GPG involved the top 10 players in all the beta tests.

The balance was too defensive and this meant to the matches played out in a pretty repetitive manner. The noobs loved this. The pros wanted something faster and more aggressive, that offered more opportunities to disrupt the opponent in the early game without having to tech up for 30 minutes. It was taking ages for expert players to finish off average players.

After 9 months of rebalancing they eventually ended up with a much more Total Annihilation style balance. Now If the players are unevenly matched the game ends in 15minutes at the first tech level. If they're evenly matched it goes to tech 2, tech 3 etc. until someone makes a big mistake. Of course the noobs hate this and complain "Waaah! Level 1 is too powerful. Stupid rushing fags!' but that's how it should be. Once you learn to survive the tech 1 phase, then you deserve to play with the tech 2 toys. If people get to play with the superweapons before they understand the basics properly then they'll never improve.

I think World of Warcraft is a good example of how to spoon feed complexity so people don't get too snowed under. Any casual player can handle it at the start. There are only two or three buttons on the screen. But by the time you reach level 70 the screen looks like something off a helicopter HUD. More needs to be done to ease the less competitive players into hardcore gaming.

Kuzdu is sounding like a politician. They're newest thing is not saying they made a mistake but they 'misspoke'. Absolutley ridiculous.
User avatar
Molloy
 
Joined: 29 Mar 2006 20:40
Location: Ireland

Unread postby Molloy » 19 May 2008 21:06

David Sirlin has a new interview where he talks about complexity and depth and the challenges of balancing.
http://www.gamecyte.com/2008/05/14/inte ... -of-2/1342

He's also sort of suggesting that the more complexity you add, the harder it is to make sure all the things you add are meaningful. In an ideal world everybody would still be playing your game 10 years on from release and you could keep adding further layers of sophistication but even then you're going to reach a point of diminishing returns.
User avatar
Molloy
 
Joined: 29 Mar 2006 20:40
Location: Ireland

Unread postby icycalm » 20 May 2008 14:59

Molloy wrote:I think World of Warcraft is a good example of how to spoon feed complexity so people don't get too snowed under. Any casual player can handle it at the start. There are only two or three buttons on the screen. But by the time you reach level 70 the screen looks like something off a helicopter HUD.


I understand what you are saying here, but your example is a poor one. There are no winners and no losers in WoW (in fact it is impossible to lose), hence ALL complexity in it is fake.

Molloy wrote:More needs to be done to ease the less competitive players into hardcore gaming.


Why? If someone is "less competitive" as you say, no amount of "easying" him into "hardcore" gaming will make him "more competitive". Competitiveness is one of the defining human characteristics -- you can't teach people to be competitive. They either have it in them -- they either feel it as a need and constantly crave it -- or they don't. And most people simply don't.
User avatar
icycalm
Hyperborean
 
Joined: 28 Mar 2006 00:08
Location: Tenerife, Canary Islands

Unread postby icycalm » 20 May 2008 15:26

Okay, so here is my answer to hypsup's post. He managed to misunderstand the key concepts to such a degree that he even confused me for a while.

hypsup wrote:I am not sure I agree with your assertion that the absolute complexity of a game can be measured by the maximum distance between the best and worst players. This will really only tell you whether not the game is a pure game of chance or not.


Nope. It will tell you how much work the worst player needs to do in order to reach the best. In other words, it will tell you how much work the worst player needs to do in order to master the game's complexity to the degree which the best player has. In other words, it will tell you the game's complexity.

hypsup wrote:If after 1000 matches of a game each player has won 500 it is clear that the game is a game of chance. However, what if the results of the the game are 600 to 400? You know the game has a sizeable element of chance, but the rules can obviously be exploited to win. It’s hard to say anything about its complexity.


Of course it is. Because you are not doing what I told you to do (i.e. measure skill disparity between best and worst players); you are doing something completely different. Because WE TAKE AS GRANTED that the best player will ALWAYS beat the worst player in a game which is not dominated by chance (see coin toss). The point is to measure how overwhelmingly he wins. This is no easy task, of course, but it's possible. In practice you'll need different criteria for each game.

Molloy wrote:
hypsup wrote:When it comes to absolute complexity it is more useful to look at the top tier alone. If the top 100 players all have exactly the same high score for example you can bet that the rules of the game can be and have been perfectly exploited. The absolute complexity of the game is now a known quantity.


I'd say that assertion is pretty much on the money from what I've seen in multiplayer games.


This is a rather useless assertion. Correct, of course, to a certain extent, but not very useful. And this is because what we want here is to set the procedure by which we can compare the complexities of different games, not to find the "absolute complexity" of a single game. I mean, yeah, if we look at the top 100 Pac-Man players and see that they all have exactly the same high score that means that "the rules of the game can be and have been perfectly exploited" (assuming we perform this investigation a long time after the game has been released, of course). And so what? How does that help to compare different games and determine which of them is more complex? We need a theory for that.

In fact, in this case we don't even know this "absolute complexity", since we haven't even devised a unit for measuring it.

What we need is the relative complexity, and the only way I can see for us to measure it is the one I described.

But getting back to "absolute complexity", there may indeed be a way for us to measure it, but, like I've already said, I do not currently have the necessary mathematical tools for that. I think the key is in the so-called "truth-functions" and the logic of Frege, Russell, et al.
User avatar
icycalm
Hyperborean
 
Joined: 28 Mar 2006 00:08
Location: Tenerife, Canary Islands

Unread postby wateyad » 03 Sep 2008 23:29

There is a meaningful difference between written rules and the interactions that arise out of them, it's just not immediately apparent when your primary frame of reference is videogames.

You'd rather be actually playing a game than reading a rulebook right? There's a fairly well known and popular school of thought in tabletop game design that a player should have to learn as few rules as possible in order to sit down and play a game without having to constantly reference the rulebook but those rules should produce as many meaningful decisions as possible. In short, it should be as easy as possible to learn what you can do in any given situation but as hard as possible to figure out what you should do.

icycalm wrote:For the present case I'll just say that even if Twelve's final, say, five battles were the best SRPG battles ever made, that would STILL not have convinced me to spend even a SINGLE extra hour playing the kind of boring scenarios I played in the first six hours.


It's pretty much analogous to this only with "boring scenarios" replaced with effort that must be expended before you can even begin to play the game. Although I'll admit that there's a much higher chance of the payoff to passing through the high barrier to entry being worth it.

Now I'll admit to being a little fuzzy on how this concept applies to videogames in particular. This is less obvious and possibly less direct, due to most of even the written rules of a videogame only being dealt with by the computer. I think an example of this kind of barrier to entry, although obviously one that has been deemed worth it and passed through by most of the people, if not everyone, here may be found in learning fighting game move lists (especially for someone who had never played one before, who would also have to learn to recognise and perform the common directional motions) but if anyone can think of a better (and if it exists, probably at least somewhat more direct) example I'd be interested to hear it. I have a feeling that I'm missing something that I'll kick myself when I find.
wateyad
 
Joined: 03 Sep 2008 12:36

Unread postby icycalm » 03 Sep 2008 23:56

wateyad wrote:There is a meaningful difference between written rules and the interactions that arise out of them, it's just not immediately apparent when your primary frame of reference is videogames.


I don't even have to read the rest of your post. If you do not manage to understand that the RULES ARE EVERYTHING, and that they completely define every possibility in the game, you'll be stuck at this point all your life. There's no understanding games for you if you do not understand this. I'll address the rest of your points anyway, but they are mostly off-topic and it's mostly a waste of time.

wateyad wrote:You'd rather be actually playing a game than reading a rulebook right?


Retarded question. Save it for Action Button. WTF do rule books have to do with videogames? A video game has like A TRILLION rules. You usually only need to know 5-6 of them. Do not pursue this point any further, it's just retarded.

wateyad wrote:There's a fairly well known and popular school of thought in tabletop game design that a player should have to learn as few rules as possible in order to sit down and play a game without having to constantly reference the rulebook but those rules should produce as many meaningful decisions as possible. In short, it should be as easy as possible to learn what you can do in any given situation but as hard as possible to figure out what you should do.


Completely off-topic. I am not even going to address whether it's correct or not. Re-read the article.

wateyad wrote:
icycalm wrote:For the present case I'll just say that even if Twelve's final, say, five battles were the best SRPG battles ever made, that would STILL not have convinced me to spend even a SINGLE extra hour playing the kind of boring scenarios I played in the first six hours.


It's pretty much analogous to this only with "boring scenarios" replaced with effort that must be expended before you can even begin to play the game. Although I'll admit that there's a much higher chance of the payoff to passing through the high barrier to entry being worth it.


More off-topic nonsense. The article was NOT about HOW TO DESIGN A GOOD GAME. It was about explaining in plain words what is meant by "complexity", "depth" and "skill" in a game. End of story.

wateyad wrote:Now I'll admit to being a little fuzzy on how this concept applies to videogames in particular.


Of course you are fuzzy. And not "a little" but a lot. You don't even have to "admit it" -- it is obvious. There are no easy formulas to PERFECT GAME DESIGN that apply in all genres and in all situations. There's one or two obvious truths (such as the need for challenge, for example), but apart from that you have to take it on a game per game basis. This is still all off-topic of course.

wateyad wrote:This is less obvious and possibly less direct, due to most of even the written rules of a videogame only being dealt with by the computer. I think an example of this kind of barrier to entry, although obviously one that has been deemed worth it and passed through by most of the people, if not everyone, here may be found in learning fighting game move lists (especially for someone who had never played one before, who would also have to learn to recognise and perform the common directional motions) but if anyone can think of a better (and if it exists, probably at least somewhat more direct) example I'd be interested to hear it. I have a feeling that I'm missing something that I'll kick myself when I find.


More random off-topic stuff. You should start a blog.
User avatar
icycalm
Hyperborean
 
Joined: 28 Mar 2006 00:08
Location: Tenerife, Canary Islands

Re: On Complexity, Depth and Skill

Unread postby Worm » 21 Dec 2008 08:50

icycalm wrote:There is nothing "simple" about the ruleset of Go, just as there is nothing simple about the ruleset of Mushihime-sama or KOF XI. Just because you can easily recite something (a poem, say, or a ruleset comprised of six rules) doesn't mean you understand it.
I understand all there is to know about how to follow the rules of Chess, but I am poor Chess player. Do you say that I don't understand the rules of Chess?

To ask it another way: are you contrasting recitation (i.e. parroting the syllables) with the ability to follow the rules? Or do you mean (as I think you do) that to "understand" a ruleset you must grasp the realm of possibilities that it creates? In the former case, understanding the rules of Chess is a trivial task. In the latter, well, who can ever be said to understand them?

In any case, the distinction between rulesets that are difficult to learn (e.g. Dungeons and Dragons) vs. those that are easy (Chess) seems an important one. Can you suggest words, instead of "simple" or "complicated," that we can use to mean "low/high barriers to entry?" Although the journalists may use trite phrases like "minutes to learn, a lifetime to master," it's useful to note such characteristics.
User avatar
Worm
 
Joined: 20 Dec 2008 21:06

Unread postby JoshF » 21 Dec 2008 09:10

I understand all there is to know about how to follow the rules of Chess, but I am poor Chess player. Do you say that I don't understand the rules of Chess?

Yes. Just like a Street Fighter player who knows all the combos but gets killed in mixup and can't perform the combos when he's not against a training mode dummy.
User avatar
JoshF
 
Joined: 14 Oct 2007 14:56

Unread postby Vert1 » 21 Dec 2008 11:23

So, application equals understanding in this case?

(a) knows the rules (inputs) on performing combos
(b) cannot apply the rules (inputs) on performing combos
(c) bad at Street Fighter

If (a) and (b), then (c).

Sorry about the boring presentation— just trying to break it down.

Worm wrote:
icycalm wrote:There is nothing "simple" about the ruleset of Go, just as there is nothing simple about the ruleset of Mushihime-sama or KOF XI. Just because you can easily recite something (a poem, say, or a ruleset comprised of six rules) doesn't mean you understand it.
I understand all there is to know about how to follow the rules of Chess, but I am poor Chess player. Do you say that I don't understand the rules of Chess?


All I am reading from this is that knowing does not equal understanding when dealing with rulesets. I don’t see where being a good/bad player with regards to things that follow rulesets comes in.
User avatar
Vert1
 
Joined: 19 Nov 2008 18:27

Re: On Complexity, Depth and Skill

Unread postby Gnarf » 21 Dec 2008 13:09

Worm wrote:
icycalm wrote:There is nothing "simple" about the ruleset of Go, just as there is nothing simple about the ruleset of Mushihime-sama or KOF XI. Just because you can easily recite something (a poem, say, or a ruleset comprised of six rules) doesn't mean you understand it.
I understand all there is to know about how to follow the rules of Chess, but I am poor Chess player. Do you say that I don't understand the rules of Chess?


You understand enough to not break the rules. (Which is hardly relevant in most videogames, as it is usually easier to follow the rules than to break them.)

Worm wrote:To ask it another way: are you contrasting recitation (i.e. parroting the syllables) with the ability to follow the rules? Or do you mean (as I think you do) that to "understand" a ruleset you must grasp the realm of possibilities that it creates? In the former case, understanding the rules of Chess is a trivial task. In the latter, well, who can ever be said to understand them?


A better players can be said to have a better understanding of them. A lot of people (fully) understand the ruleset of tic-tac-toe. Because it is a simple game (/has a simple ruleset).

Vert1 wrote:All I am reading from this is that knowing does not equal understanding when dealing with rulesets. I don’t see where being a good/bad player with regards to things that follow rulesets comes in.


Your ability to follow a the rules is your ability to not break the rules is your ability to not cheat. Obviously, if you're not even able to not break the rules, you're not a good player. But being able to follow them doesn't mean you are good. For example, you do not have to know the combos in Street Fighter in order to not cheat.
Gnarf
 
Joined: 27 Aug 2008 18:31

Next

Return to Theory