Where Did Prot Holo Come From?

[Crozame.4098]

1 hour ago, JusticeRetroHunter.7684 said:

 

Here's the real issue...forget the solution. You don't even know the parameters of the problem or how to model it. If you learned anything about what I just said above, you'd realize that the problem itself is much larger in scope.

 

This is completely false. You do this because you can't actually GET the unknown variables...it requires measurement you can't do in practice...so you just have to trust that your hidden variables will cancel out given a large enough statistical sampling (or until you get a better measurement apparatus)

 

 

This here is an ape level analysis of the problem. Because this skill hitting for 20k, is dependent on the existence of how well other classes are able to defend themselves. Even looking at the damage equation on the wiki points to the fact that this number is not even a static quantity. it may hit 20k against your super glass naked staff ele. but it hits for 4k, if at all, against a dodge bot Strength Warrior.

 

About complexity, you are just making ridiculous assumptions about what you think the solution is to a problem you don't even fully understand in any meaningful scope. Increasing complexity is not "adding more absurd numbers."

 

If you actually did look into anything on complexity theory, you'd realize it is the same THING as Network theory that you said you studied before. I think if you actually took the time to listen and learn from other people and to stop lying, you wouldn't even be here making these kinds of really thoughtless comments. 

 

 

 

1) Again, a bunch of nonsense without any specific idea of how to balance. Besides saying increase complexity, bla bla bla, you have nothing concrete to offer.

2) You do not understand what is a omitted variable and what is an error term that will not lead to bias. 

3) do you understand the meaning of "suppose"?

4) You are right, I dont give a kitten about complex/chaos. 

5) Your explains / posts, still do not address properly how it will help balance the game.

 

Edited June 8, 2021 by Crozame.4098

[JusticeRetroHunter.7684]

28 minutes ago, Crozame.4098 said:

1) Again, a bunch of nonsense without any specific idea of how to balance. Besides saying increase complexity, bla bla bla, you have nothing concrete to offer.

2) You do not understand what is a omitted variable and what is an error term that will not lead to bias. 

3) do you understand the meaning of "suppose"?

 

Omitted variable's ARE hidden variables...do you not understand this? you do not have access to them...therefor when you do analysis on the system it will be APPROXIMATE. You treat hidden variables like NOISE because the average of those variables you don't have access too will cancel each other out if you have a lot of them (they will also reflect all range of behaviors as an average)

 

Very simple example, take white noise, and tell me what do you think is the average proportion of white pixels to black pixels Go on and take a wild guess,

 

and then once you answer that question, ask what would be the average color of a noise image in a 256 color space?. Maybe this will help you understand where it got it's name from

 

Honestly If you don't understand the above, then i can't help you any longer...go look it up on Wikipedia or take a class. Your not arguing with me anymore, your arguing with stuff that's been established for hundreds of years. 

Edited June 8, 2021 by JusticeRetroHunter.7684

[JusticeRetroHunter.7684]

@Crozame.4098 

 

Okay since it seems people are confused, here's a good example of an omitted variable.

 

Crozame : 

Quote

"True shot is hitting 20k.... Lets nerf it."

 

An omitted variable is the fact that it doesn't ONLY hit 20k in all scenarios...it hits 20k on a naked glass ele maybe...but it hits 4k on a bunker warrior build that dodges alot...it hits 600 damage on a target that inflicts weakness, It is reflect-able, it is Losable so on and so on and so on. There's a huge number of variables you OMMITTED by saying that it only hits for 20k....there are so many variables most of which you can't  even measure and these are called hidden variables.

 

Does anyone not understand this very simple fact, and how Crozame is a hypocrite and is actively omitting variables himself when talking about balance change?

Edited June 8, 2021 by JusticeRetroHunter.7684

[Kolzar.9567]

8 hours ago, Crozame.4098 said:

1) I said data is informative? I did not say it will provide the definite answer? The devs can then investigate further by watching vids or trying out themselves. Why you are assuming I meant randomly nerfing something?

2) Because it is not possible to define the strategy space during game play.

3) Because you cannot assume players are rational or even optimising something, this is a game, without a competitive scheme, no one cares that much. This is not true for using economics modelling to study real life interactions, because 1) it matters a lot to people, 2) there are firms, institutions and others that are close to rational and 3) there are markets and the price of the power is huge -- you know the market efficient hypothesis?

4) I said experts right in simple and short terms, they do not explain stuff by posting hour long vids.

5) You know for level-k reasoning, you need to have some knowledge about the distribution of types to conduct meaningful analyses?

6) I am confused. Utility functions are required also in extensive form game: the definition of utility function in game theory is mapping from actions to payoffs. Tell me, which branch of game theory does not require utility functions? You trying to be smart here, but please understand the basics first.

7) I am also confused about your definition of history... Loosely speaking a history is just a set of moves taken by the players -- yes it is  unrelated to preferences. But history ends at a terminal node. And you should know that terminal nodes is followed by utilities. And utilities already taken into account players preferences.... You trying to be smart here, but please understand the basics first.

 

You already seem pretty convinced that your level knowledge is enough, have gone into making assumptions about my knowledge/occupation/expertise so I am not going to even address the argumentative points.

 

2-6-7) You are just ill informed and you don't seem to have understood what was suggested. In extensive form games/stochastic games you can describe the environment and the set of actions and the resulting history of play without making any assumptions on preferences/knowledge. Extensive form games are not limited to finite sequential action extensive form games only and you can have repeated games with random matching which are still a sort of extensive form game, which i believe is the appropriate for GW2. Just to address the point of a terminal node, you might also want to brush up on your knowledge of repeated games with or without perfect information and see what the set of histories look like. Regardless, even on finite extensive form games, you can draw the game tree just by knowing the set of available actions to the players. In such games a sequence of actions, will lead to an outcome, the players will have preferences over such outcomes. If those preferences are well behaved enough, then you might try to say there is a utility representation. Again, you can define notions on the history of play without making any assumptions on behavior or even a solution concept. That was what I did.

 

To illustrate the point in a simple example that is hopefully accessible to everyone, suppose you collect some number of actual monkeys and some players from this forum, put them each in a cubicle that has three buttons R,P,S. At random intervals in time, you pair up some of those (not necessarily all concurrently) cubicles randomly and have them pick a button have them effectively play RPS over this small internet. The rules for determining the winner are the same as regular RPS, but winner gets a candy, if its a draw they get a juice and the loser listens to 15 seconds of Justin Bieber. If the monkeys or humans don't play you can assign a random action to them, or just assume they lost by taking an additional action F, but lets stick with the first one. You keep doing these randomized matchings and keep recording the frequency of R,P,S that was played, . Congratulations you have defined a random process over the histories. You can even add random timed information release announced into these cubicles, where you say in the last 5 games played R had this frequency, P had this frequency, S had this frequency. So people and monkeys get matched, play a game, maybe get some reward, make their inferences about their own experience or don't and adjust their actions for their next pairing or don't. Now if it at some point after having been randomly matched the players (including the monkeys) the frequency of RPS that was played did not change, you have reached a stable meta (a.k.a a fixed point on the mapping from distribution over actions do distribution over actions) of this jointly controlled process. Now if at that point suppose only R,P is played, then you can say directly well that is not a very diverse meta because only two things are viable, alternatively you can incorporate the standard deviation or some characteristic of the distribution, and say if the deviation is large or not. I suggested both as viable alternatives. Now, to define these notions, what have I assumed about the rationality/knowledge/preferences of the humans or the monkeys? Nothing. Maybe some people prefer juice, maybe some people like Justin Bieber, maybe the monkeys have learned game theory before and know how to bid in a first price auction, I don't care and it is unnecessary. You can vaguely assume they do what they like limited to their tastes/knowledge/preferences/learning along the way and it will buy you a little bit about the fixed point (mind you still no utilities just basic maybe incomplete, intransitive preferences, because variants of theorem of the maximum/zorn's lemma start becoming applicable but it is not even necessary) It does not matter, I don't need it just to describe a strategic environment and a notion on it.  On a side remark, utility functions are just ordinal representations of preferences, when these preferences satisfy some assumptions, they are not the primitive to do any economic analysis, they are just convenient.

 

5) I did not impose a solution concept (like Nash equilibrium) above, you assumed I did.  Nash equilibrium does have stringent requirements on rationality and knowledge of the game which limits its applicability. I gave several examples where such requirements are relaxed, just to illustrate the point that if someone wanted to, they might attempt to use a solution concept that is appropriate for whatever kind of relaxation they think is fit. There is an entire subfield of economic theory called decision theory that deals with a large swath of such relaxations. Maybe people are ambiguity averse, maybe people have wrong models in their head that they keep updating, maybe people are loss averse, maybe people are time inconsistent. Most of these models start with a preference relation on acts and you may or may not get a utility representation or even a proper probability measure. If people think their assumptions on these bounded rationality is good enough, they can impose it on the environment and may attempt to make predictions, then you can refute if the assumptions are indeed good enough or ill fitting. 

 

4) Once again I have not posted any videos and once again when writing a paper or giving a talk, you know that referees/editor/seminar audiences will have a basic knowledge of the topic and at the very least will have a PhD (and therefore completed a core sequence) as well as being familiar with the conventions of the profession.  This is not the case here, using only technical terms without explanation is just going to alienate everyone.

Edited June 8, 2021 by Kolzar.9567

[Eugchriss.2046]

@JusticeRetroHunter.7684 Can you give simple and concrete stuffs of what to do in order to balance? Like imagine I am the programmer who implements the balance decisions. What would you tell me to do?

[JusticeRetroHunter.7684]

1 hour ago, Eugchriss.2046 said:

@JusticeRetroHunter.7684 Can you give simple and concrete stuffs of what to do in order to balance? Like imagine I am the programmer who implements the balance decisions. What would you tell me to do?

 

So there's two answers. The first answer would be an answer that skips all the relevant mathematical detail for why this is the answer.

The 2nd answer, is the more detailed mathematical reason for why I told you the first answer. 

 

First Answer

The first answer: Make game mechanics more complex. Don't be fooled by the word. The definition of complexity is very nuanced here, because something being complex does not mean "making it harder to read the skill tooltip" or something naïve like that. Complexity refers to the possibility space, in which skills can interact with other skills. Another aspect of complexity is called "complex computation." If you have Skill A that does 10 damage, and Skill B that does 11 damage, then it's obvious almost immediately that Skill B is a better skill.

 

So an example of a more complex skill then the example above, is the following: That Skill A's damage, is dependent on Skill B's healing, which is dependent on Skill A's cooldown. This means that casting Skill A will do damage according to skill B's healing, which is dependent on the cooldown of A...so if you Spammed Skill A, it's damage would be low, while if you used it less often, Skill A's damage would be higher. Skill B's healing is dependent on Skill A's cooldown too. The interplay between skill A and Skill B become defined by this complicated relationship, and this elongates the time in which it takes someone to make the decision that skill A is more optimal then skill B or vice versa. The whole point is to slow down the process of optimal decision making, and at a certain point in a game where the possibility space is significantly high, it takes a huge amount of time to make any kind of optimal decision, and the game becomes an exploration of different arrangements of these skills. This is the cornerstone reason for why games like gw1, and card games like Magic the Gathering (the game gw1 was based on) was so successful. The game was highly complex, while the skills could remain simple... where the complexity, was in the very large possibility space, in which players could explore all the different relationships that skills could have with each other. This is what solves the diversity problem and the balance problem, in that the game is now just a very long exploration of different combination of skills, and determining the optimal configuration of the game becomes a very hard problem to solve.

---------------------------------------------------------------------

Second Answer

First thing is to take a look at all of Kolzar's responses, as he is detailing how to model a game like gw2, because that is the first step, is modeling the game.

 

The purpose of a model, is to analyze how changes you make in the game effect the behavior of the game as it marches through time. From now on I'll be referring to "the game" as a system, and i will sometimes refer to a "model" as a measuring apparatus.

 

Before you can create a model of a system, you need knowledge about the things in your system. "Things" encompasses two pieces of information, which are the number of those things, and then how those things effect other things (which from now on i will call a relationship). So you have Skill A and Skill B...you need to define what these things are first, and then you need to describe how these two things are related to each other, and then you can see how this system evolves through time. So if you were to change Skill A, you need to know what it is that you are changing, and then you need to know how that change, effects other things in the system like Skill B. The level at which you can actually KNOW these pieces of information, is based on how well you are able to account for all that information. You can imagine that if you have 1000 skills that are all correlated to some degree, your level of knowledge about the system become difficult. This difficulty in acquiring knowledge about a system is essentially chaos theory. The less you know about a system, the more unlikely you are to make accurate predictions about them, or how changes effect them. 

 

Given the above, if you are a game developer, and you wanted to make a change to the game to fix a balance problem, you have to make a prediction about what that change will do, and this prediction is going to be based on how much information you have over your system. This information is gathered by measuring the things in your system, and measuring the relationships those things have to other things. If the game has a million things with a million relationships, and your measuring apparatus only accounts for 30 things and 10 relationships, then how well of a prediction can you make? You can guess it will be very inaccurate.

 

So if you were to make a change say : "Nerfing this Skill by 1000 damage" or "Buffing this skill by 500 healing" then how accurately do you know that these skills will balance the game or give it more diversity? The answer is that it's dependent on your measuring apparatus (your model). A poor model of the system means a poor prediction, and in this way, balance changes you make are basically meaningless because you have almost no idea how it actually changes the system.

 

Complexity comes into play here, when you realize that balance dev's are essentially fighting an uphill battle. In a game with as many components and relationships in gw2, making a balance change with any level of accuracy in your prediction for how it changes the game becomes insanely difficult. Currently Arenanet uses the model of DPS on DPS golems to balance PVE, and they also use a model of Automated Tournament "performance" to make balance changes for PVP. These models are way WAY too primitive and they do not work, because they poorly approximate the things and relationships those things have with each other.

 

You can thus think of Complexity as a river heading downstream. It's easier to make mechanics have a richer possibility space, then it is to balance them with very poor approximations.

 

Edited June 8, 2021 by JusticeRetroHunter.7684

[Crozame.4098]

3 hours ago, JusticeRetroHunter.7684 said:

 

Omitted variable's ARE hidden variables...do you not understand this? you do not have access to them...therefor when you do analysis on the system it will be APPROXIMATE. You treat hidden variables like NOISE because the average of those variables you don't have access too will cancel each other out if you have a lot of them (they will also reflect all range of behaviors as an average)

 

Very simple example, take white noise, and tell me what do you think is the average proportion of white pixels to black pixels Go on and take a wild guess,

 

and then once you answer that question, ask what would be the average color of a noise image in a 256 color space?. Maybe this will help you understand where it got it's name from

 

Honestly If you don't understand the above, then i can't help you any longer...go look it up on Wikipedia or take a class. Your not arguing with me anymore, your arguing with stuff that's been established for hundreds of years. 

 

If you regress X on Y, and you omit an important variable Z. Then your result is biased. If you regress X on Y, and the error term only consists of noise, there is no other important variables that affect both X and Y, then your results are not biased. Therefore, you cannot treat omitted important variables as noise.

[Crozame.4098]

1 hour ago, Eugchriss.2046 said:

@JusticeRetroHunter.7684 Can you give simple and concrete stuffs of what to do in order to balance? Like imagine I am the programmer who implements the balance decisions. What would you tell me to do?

 

He answered, again, make the game more complex. Do you know how to code it?

 

[Eugchriss.2046]

From all the wall you wrote, I believe this seems to be your answer

9 minutes ago, JusticeRetroHunter.7684 said:

if you are a game developer, and you wanted to make a change to the game to fix a balance problem, you have to make a prediction about what that change will do, and this prediction is going to be based on how much information you have over your system.

 

Well, what you described here is the job of the balance team. The balance team call for decisions and the game developer apply them. So again what decisions should I apply, and not make, if you were the balance team?

[Crozame.4098]

2 hours ago, Kolzar.9567 said:

You already seem pretty convinced that your level knowledge is enough, have gone into making assumptions about my knowledge/occupation/expertise so I am not going to even address the argumentative points.

 

2-6-7) You are just ill informed and you don't seem to have understood what was suggested. In extensive form games/stochastic games you can describe the environment and the set of actions and the resulting history of play without making any assumptions on preferences/knowledge. Extensive form games are not limited to finite sequential action extensive form games only and you can have repeated games with random matching which are still a sort of extensive form game, which i believe is the appropriate for GW2. Just to address the point of a terminal node, you might also want to brush up on your knowledge of repeated games with or without perfect information and see what the set of histories look like. Regardless, even on finite extensive form games, you can draw the game tree just by knowing the set of available actions to the players. In such games a sequence of actions, will lead to an outcome, the players will have preferences over such outcomes. If those preferences are well behaved enough, then you might try to say there is a utility representation. Again, you can define notions on the history of play without making any assumptions on behavior or even a solution concept. That was what I did.

 

To illustrate the point in a simple example that is hopefully accessible to everyone, suppose you collect some number of actual monkeys and some players from this forum, put them each in a cubicle that has three buttons R,P,S. At random intervals in time, you pair up some of those (not necessarily all concurrently) cubicles randomly and have them pick a button have them effectively play RPS over this small internet. The rules for determining the winner are the same as regular RPS, but winner gets a candy, if its a draw they get a juice and the loser listens to 15 seconds of Justin Bieber. If the monkeys or humans don't play you can assign a random action to them, or just assume they lost by taking an additional action F, but lets stick with the first one. You keep doing these randomized matchings and keep recording the frequency of R,P,S that was played, . Congratulations you have defined a random process over the histories. You can even add random timed information release announced into these cubicles, where you say in the last 5 games played R had this frequency, P had this frequency, S had this frequency. So people and monkeys get matched, play a game, maybe get some reward, make their inferences about their own experience or don't and adjust their actions for their next pairing or don't. Now if it at some point after having been randomly matched the players (including the monkeys) the frequency of RPS that was played did not change, you have reached a stable meta (a.k.a a fixed point on the mapping from distribution over actions do distribution over actions) of this jointly controlled process. Now if at that point suppose only R,P is played, then you can say directly well that is not a very diverse meta because only two things are viable, alternatively you can incorporate the standard deviation or some characteristic of the distribution, and say if the deviation is large or not. I suggested both as viable alternatives. Now, to define these notions, what have I assumed about the rationality/knowledge/preferences of the humans or the monkeys? Nothing. Maybe some people prefer juice, maybe some people like Justin Bieber, maybe the monkeys have learned game theory before and know how to bid in a first price auction, I don't care and it is unnecessary. You can vaguely assume they do what they like limited to their tastes/knowledge/preferences/learning along the way and it will buy you a little bit about the fixed point (mind you still no utilities just basic maybe incomplete, intransitive preferences, because variants of theorem of the maximum/zorn's lemma start becoming applicable but it is not even necessary) It does not matter, I don't need it just to describe a strategic environment and a notion on it.  On a side remark, utility functions are just ordinal representations of preferences, when these preferences satisfy some assumptions, they are not the primitive to do any economic analysis, they are just convenient.

 

5) I did not impose a solution concept (like Nash equilibrium) above, you assumed I did.  Nash equilibrium does have stringent requirements on rationality and knowledge of the game which limits its applicability. I gave several examples where such requirements are relaxed, just to illustrate the point that if someone wanted to, they might attempt to use a solution concept that is appropriate for whatever kind of relaxation they think is fit. There is an entire subfield of economic theory called decision theory that deals with a large swath of such relaxations. Maybe people are ambiguity averse, maybe people have wrong models in their head that they keep updating, maybe people are loss averse, maybe people are time inconsistent. Most of these models start with a preference relation on acts and you may or may not get a utility representation or even a proper probability measure. If people think their assumptions on these bounded rationality is good enough, they can impose it on the environment and may attempt to make predictions, then you can refute if the assumptions are indeed good enough or ill fitting. 

 

4) Once again I have not posted any videos and once again when writing a paper or giving a talk, you know that referees/editor/seminar audiences will have a basic knowledge of the topic and at the very least will have a PhD (and therefore completed a core sequence) as well as being familiar with the conventions of the profession.  This is not the case here, using only technical terms without explanation is just going to alienate everyone.

Repeated game, games with imperfect information -- information sets are not singletons anymore, games with incomplete information -- you do not know others type but only know the distribution of types. For all these games, you need a mapping from strategy space to a number?

 

Think most common solution concepts: NE, Subgame perfect NE, sequential NE, and Bayesian NE. For all these, you need number to compute the expected payoff of some strategies in order to solve it.

 

The setting of a game usually consists (N (players), S (strategies), T (types), and U), where U must be a function (it does not need to be continuous) because if the same strategy maps into different numbers, then the game is not well defined. 

 

Give me a text book or something saying that we do not need the U element to analyse a game.

 

[JusticeRetroHunter.7684]

19 minutes ago, Eugchriss.2046 said:

From all the wall you wrote, I believe this seems to be your answer

 

Well, what you described here is the job of the balance team. 

 

If you actually want this to be constructive, first you need to read the entire comment, because I said this.

 

Secondly, you need to not skip sections in the comment, and understand everything that is being said here. I clearly state what the proposed answer is, and I give you a very detailed reason as to why the answer is what it is....this was the first sentence of the comment (lol)

 

Lastly, I'm not using that much math...I'm breaking it down into plain English for you...but the nature of the problem is mathematical. You can't just skip over everything as if the answer to your question is going to be some small line of text somewhere in that comment. Do the proper diligence of following the logic, which i placed out for you in order, so that you can easily understand it without math. 

 

 

Edited June 8, 2021 by JusticeRetroHunter.7684

[Kuma.1503]

Skill interaction is precisely why I main engi in the first place.

 

A basic (but effective) version of that does exist with the combo system. You can combine skill A (combo) with skill B (finisher) to create an effect that is greater than the sum of its parts. It's a shame Anet has been taking repeated strides to nerf/remove combo field gameplay. Cleverly weaving finishers into combat is one of the more fun and skillful parts of this game. 

[Eugchriss.2046]

I read the whole thing. How would I have found that specific sentence in that huge wall of text if not?

I specifically picked that sentence because it had the most concretes "what to do" steps. Now if your answer is this : 

52 minutes ago, JusticeRetroHunter.7684 said:

Make game mechanics more complex.

Then.... that's not really concrete to me. As long as there is room for interpretions in your balance decisions, then it's more like hints than decisions. Look those 2 examples : 

1. Increase X specific trait of Y specific skill by specificallyZ%
2. Make trait X more complex

Can give me your answer again by having a functional specification in mind?

Edited June 8, 2021 by Eugchriss.2046

[Kolzar.9567]

58 minutes ago, Crozame.4098 said:

Repeated game, games with imperfect information -- information sets are not singletons anymore, games with incomplete information -- you do not know others type but only know the distribution of types. For all these games, you need a mapping from strategy space to a number?

To describe the environment and the path of play you don't need preferences, to impose a solution concept you do. How do you think people are even thinking about strategic environments where people are not fully rational? Once again what kind of assumptions did you need to describe what was happening on the monkeys and humans playing RPS. You could literally just write down the path of play. If I assumed monkeys or humans preferences over paths of play that are well behaved enough you can define utility representations for them and try to solve the game, I have not attempted to do so. This is a basic modelling concept beyond game theory even any kind of single player stochastic control problem has the same virtues. Suppose I am literally typing paragraphs using random letters,  the set of letters I include in each paragraph is going to be a process, regardless of the objective I have and if you see that I start typing the same letters you can say something. Now, you can say I know some languages and I am typing coherent sentences, or not, you do not that bit of information to see whether I have started repeating myself. 

 

If you have a full fledged well behaved utility function with an nice accompanying objective probability measure you can say well I will try to use these well behaved solution concepts such as NE, SPNE, SE etc. If you have instead subjective probability measures for example, then you end with preferences with ambiguity, you may have a representation, but it will probably at best be of Epstein-Zin form (which you can actually put into formal models and use it to try to explain various puzzles in finance), at worst could be just an integral of a charge you get out of Savage or Anscombe-Aumann axioms. You want to learn about such constructions (this is the largest branch in non-rational models) you can start from Kreps' book, notes on theory of choice and eventually catch up to the frontier. If you want to think people have misspecified learning, say I don't understand whether candy is good for me or not, but as I keep eating it and I learn you will have a model of misspecified learning, google Berk-Nash equilibrium, you will find wonderful bits of research. If you just want to understand how to define a history space, literally pick any graduate textbook, MWG, Mailath Samuelson, Fudenberg Tirole etc. You will see that they will first define the set of actions, then the set of histories, which is all I have done. In fact you will see they will add different monitoring structures, behavioral types, or limitations of rationality and then compare to the fully rational case. And once again these are textbook examples so they are approximately 10-15 years behind the frontier. Just to highlight that you don't need a valid and known utility function look up rationalizability (it should have a section on MWG). Notably if you look up at any of these books you would see that they will usually start with either a choice correspondence or a preference relationship. Any strategic interaction again, you will need to have description of outcomes to actions, and you have preferences over such outcomes. Just to hammer this in, RPS has actions, and outcomes, who wins who loses, then the players will have preferences over those to have utilities to write it succinctly. You don't need to tell me I get 5 utils from winning 0 from draws or 7 from losing (the preferences need not align by the notion of winning or losing), just to say in this environment the set of allowable actions is RPS, and an outcome will be a tuple of the form (R,P), (R,R) etc and so on and so forth. If I keep repeatedly playing this game the set of histories will be sequences of the form ((R,P),(R,P),(R,P).....). I am not sure what is missing here, that prevents from saying well these guys are playing some stage repeatedly and have some preferences, but they seem to be repeating (R,P).

 

I thought the example with the monkeys and the set of histories above was crystal clear and I don't see an argument about what you didn't understand about that. Did you not understand the description of distribution of actions over time? Did I need to make any assumptions on utility to describe the process and a notion of diversity over there? Clearly you can simply extend it to GW2, instead of having RPS, you just pick a build out of which there are finitely many of. Instead being paired as 2, you get paired as groups of 5, and the random information that is released can be thought of the forums/metabattle whatever.  But as I previously mentioned you seem more convinced of your extent of knowledge, rather than trying to look up the things or even entertain the idea that other people might actually know more on certain topics. I am certainly not appreciative of you demanding references a) because you can look them up yourself, b) because again it would just be alienating the people further. I thought the argument I was making was clear enough that I do not need to appeal to any authority including my own, that was the reason of giving so many pedestrian examples. If there is a flaw in the descriptions I have provided you are certainly welcome to point it out directly instead of appealing to some irrelevant half knowledge. As long as you keep it civil I can keep trying to explain it you, but unfortunately I can't understand it for you.

Edited June 8, 2021 by Kolzar.9567

[Crozame.4098]

8 minutes ago, Kolzar.9567 said:

Just to highlight that you don't need a valid and known utility function look up rationalizability

Rationalizability relies on best response function/correspondents, how do you apply it without utilities?

 

You also talked about preferences, then at least you need to understand people's motives to specify which action is weakly preferred to others? Also, preferences can be represented as utility function under mild conditions. This is more than 20 years old.

 

Also, I explained before, given the complexity of the game and the  game play as well as people play this game mostly for leisure, it is not a good idea to use game theoretical models to analyse it etc. As long as you keep it civil I can keep trying to explain it you, but unfortunately I can't understand it for you.

Edited June 8, 2021 by Crozame.4098

[Kolzar.9567]

3 minutes ago, Crozame.4098 said:

Rationalizability relies on best response function/correspondents, how do you apply it without utilities?

Look up rational preferences and rationalizable choices, you will immediately see that it is not your run off the mill VNM expected utility. Although at this point I give up, you are just being argumentative without answering where we needed utility functions to describe the dynamics. At your next step you can proceed to correct my grammar as well. As you alluded regarding the other poster I don't know how to argue with someone like "you".

[Crozame.4098]

2 minutes ago, Kolzar.9567 said:

Look up rational preferences and rationalizable choices, you will immediately see that it is not your run off the mill VNM expected utility. Although at this point I give up, you are just being argumentative without answering where we needed utility functions to describe the dynamics. At your next step you can proceed to correct my grammar as well. As you alluded regarding the other poster I don't know how to argue with someone like "you".

 

Rational preference. Let me rephrase my concern: given the complexity of the game, it is a game for leisure. and people have different incentives for playing the game. Even preferences are not well defined: how can you decide which strategy is preferred over others?

[JusticeRetroHunter.7684]

5 minutes ago, Eugchriss.2046 said:

I read the whole thing. How would I have found that specific sentence in that huge wall of text if not?

I specifically picked that sentence because it had the most concretes "what to do" steps. Now if your answer is this : 

Then.... that's not really concrete to me. As long as there is room for interpretions if your balance decisions, then it's more like hints than decisions. Look those 2 examples : 

1. Increase X specific trait of Y specific skill by specificallyZ%
2. Make trait X more complex

Can give me your answer again by having the functional specification in mind?

 

Complexity is formalized in the form of using what's called network graphs. It's very simple, in that the only thing network graphs show, is how well things are connected to each other in a network. Formally in mathematics, The skills (called vertices) on this network can be described as a set, it's components are subsets of those sets, and a line connecting these sets is the relationship of those sets called an edge. traditionally, graphs do not overlap their edges like i have here, because they map all subcomponents to their own vertex, but for the sake of the example I just did it this way to illustrate the point.

 

https://i.imgur.com/bDCJVUe.png

 

If you were to describe the difference between the each edge on this graph, for why some lines are longer and others are shorter, it's only a reflection of the number of sets a function has an effect on. In terms of gw2, I took a few traits that I could easily classify from Elementalist and categorized them in terms of their complexity:

 

Minimally Complex Skills

Empowering Flame

Soothing Power

Bountiful Power

Arcane Restoration

 

Mildly Complex Skills

Pyromancer's Training

Power Overwhelming

Soothing Disruption

Soothing Mist

 

Highly Complex Skills

Smothering Auras

Powerful Aura

Cleansing Water

 

I don't know if you notice a trend, but the more complex skills, are the ones that effect the most things, which have things that effect a lot of other things. For example, Cleansing Water cleanses conditions when you apply regeneration. Regeneration is attached to elements that they themselves have relationships to other things to do with aura's, and this kind of continues on and on for a bit. You can see how a well connected network of things actually makes it possible for "good" builds to be created.

 

Second trend you might notice... but the most complex skills just so happen to be some of the the most simple ones to understand...Their tooltips aren't exactly long at all.

 

So from this you should be getting an intuition, that understanding complexity is like an artform, as it's the study of relationships between things...it's not exactly a complicated subject at all. It takes a bit of perspective to create something simple, that exhibits highly complex behavior... When you look at it in terms of a graph, then that intuition becomes a bit more obvious. 

 

So in terms of functional specification, and dumbing it down to a less formal level, skills that effect only themselves, or REQUIRE a connection to them in order to work is minimally complex. A mildly complex skill would be a binary or one way relationship. Skill A effects Skill B or Skill B effect Skill A or a combination of both. A highly complex skill is something that has polygamous relationships with other skills that have polygamous relationships. and something I would consider a level above being highly complex would be recursive relationships...where monogamous or polygamous relations effect themselves in loops.

[Kolzar.9567]

33 minutes ago, Crozame.4098 said:

 

Rational preference. Let me rephrase my concern: given the complexity of the game, it is a game for leisure. and people have different incentives for playing the game. Even preferences are not well defined: how can you decide which strategy is preferred over others?

For the very last time, look up my post from 4ish hours ago, regarding points you raised 2-6-7) and the following example. I am not trying to solve a game, I am defining histories and defining a notion of diversity on these histories, no solution concept, no need for utilities or preferences or whatever, just a description of the environment. As an outside observer, monkeys do whatever monkey like, I am not trying to make any prediction. I simply say look at the history, if it is repeating look at the support of the actions in the history. I don't care where that history comes from. The references to notions of bounded rationality and how to evaluate outcomes in such environments only came up because you brought them up and I elaborated, with references at your request which evidently was my mistake.  If you are unsatisfied with this answer, you can simply assume I am wrong, you are right, and conclude the argument as such, but I would appreciate if you would stop quoting me to ask questions.

[Crozame.4098]

4 minutes ago, Kolzar.9567 said:

For the very last time, look up my post from 4ish hours ago, regarding points you raised 2-6-7) and the following example. I am not trying to solve a game, I am defining histories and defining a notion of diversity on these histories, no solution concept, no need for utilities or preferences or whatever, just a description of the environment. As an outside observer, monkeys do whatever monkey like, I am not trying to make any prediction. I simply say look at the history, if it is repeating look at the support of the actions in the history. I don't care where that history comes from. The references to notions of bounded rationality and how to evaluate outcomes in such environments only came up because you brought them up and I elaborated, with references at your request which evidently was my mistake.  If you are unsatisfied with this answer, you can simply assume I am wrong, you are right, and conclude the argument as such, but I would appreciate if you would stop quoting me to ask questions.

Ok ok, that's fine, you dont need well defined preferences or utilities for defining histories.

 

Then, if you build a model or describe a environment with no intention to solve or to make any sort of predictions out of it, then what is the point of doing that?

[Crozame.4098]

40 minutes ago, JusticeRetroHunter.7684 said:

 

Complexity is formalized in the form of using what's called network graphs. It's very simple, in that the only thing network graphs show, is how well things are connected to each other in a network. Formally in mathematics, The skills (called vertices) on this network can be described as a set, it's components are subsets of those sets, and a line connecting these sets is the relationship of those sets called an edge. traditionally, graphs do not overlap their edges like i have here, because they map all subcomponents to their own vertex, but for the sake of the example I just did it this way to illustrate the point.

 

https://i.imgur.com/bDCJVUe.png

 

If you were to describe the difference between the each edge on this graph, for why some lines are longer and others are shorter, it's only a reflection of the number of sets a function has an effect on. In terms of gw2, I took a few traits that I could easily classify from Elementalist and categorized them in terms of their complexity:

 

Minimally Complex Skills

Empowering Flame

Soothing Power

Bountiful Power

Arcane Restoration

 

Mildly Complex Skills

Pyromancer's Training

Power Overwhelming

Soothing Disruption

Soothing Mist

 

Highly Complex Skills

Smothering Auras

Powerful Aura

Cleansing Water

 

I don't know if you notice a trend, but the more complex skills, are the ones that effect the most things, which have things that effect a lot of other things. For example, Cleansing Water cleanses conditions when you apply regeneration. Regeneration is attached to elements that they themselves have relationships to other things to do with aura's, and this kind of continues on and on for a bit. You can see how a well connected network of things actually makes it possible for "good" builds to be created.

 

Second trend you might notice... but the most complex skills just so happen to be some of the the most simple ones to understand...Their tooltips aren't exactly long at all.

 

So from this you should be getting an intuition, that understanding complexity is like an artform, as it's the study of relationships between things...it's not exactly a complicated subject at all. It takes a bit of perspective to create something simple, that exhibits highly complex behavior... When you look at it in terms of a graph, then that intuition becomes a bit more obvious. 

 

So in terms of functional specification, and dumbing it down to a less formal level, skills that effect only themselves, or REQUIRE a connection to them in order to work is minimally complex. A mildly complex skill would be a binary or one way relationship. Skill A effects Skill B or Skill B effect Skill A or a combination of both. A highly complex skill is something that has polygamous relationships with other skills that have polygamous relationships. and something I would consider a level above being highly complex would be recursive relationships...where monogamous or polygamous relations effect themselves in loops.

Empowering Flame: + 150 power in fire. It potentially interacts with all the strike attacks. Why it is minimally complex?

Soothing Power: More healing --> survive longer --> can use more skills --> can help teammates. Therefore it interacts with many elements, why it is minimally complex?

 

Smothering Auras: just remove some condis. many other classes can cleanse for me. Or given people say power builds are much stronger than condi builds. Then cleanse condis does not matter. So, why it is highly complex skills?

 

[JusticeRetroHunter.7684]

23 minutes ago, Crozame.4098 said:

Empowering Flame: + 150 power in fire. It potentially interacts with all the strike attacks. Why it is minimally complex?

Because in the formal definition where the lines on a graph are just functions, then the lines (functions) between elements(variables) can be thought of as a math problem. Adding +150 power to an attack is a very simple math problem. So even though an element can connect to 1000 other elements, doesn't mean that relationship is complex...the function (the relationship) is just as important if not more so then number of elements it's connected to. Soothing Power: works very much in the same way, where the function is a rather simple addition problem.

 

You can definitely argue about how complex the current mechanics are in comparison to how complex the mechanic could be, given the space of all mathematical problems. That's really all the game is really...we're all just solving little math problems, and our brain does this very easily when the math problems are easy. How hard are those problems depends on the relationships these variables have. Addition subtraction...those are easy problems. Add more variables? slightly harder problem. Richness of the function? very much a harder problem. 

Edited June 8, 2021 by JusticeRetroHunter.7684

[Kolzar.9567]

34 minutes ago, Crozame.4098 said:

Ok ok, that's fine, you dont need well defined preferences or utilities for defining histories.

 

Then, if you build a model or describe a environment with no intention to solve or to make any sort of predictions out of it, then what is the point of doing that?

This is literally the way to have a meaningful discussion in a sensible framework. You might already disagree on the description of the environment and in fact that was the reason of my first post, I disagreed with the notion of diversity that the other poster posed, we kept respectfully disagreeing and they seem to agree with some of my choices. I am making at least in my opinion some minimal assumptions of my description, the other poster does another set of them. I tried to explain to them why some of those assumptions they are making would be invalid (people behaving randomly does not generate enough continuity to think of it as a mechanical equation), they came up with their own arguments. I tried to keep the level low so that other users can also understand what I was saying and agree/disagree, maybe I missed something in my description, maybe I didn't.

 

Once a reasonable framework is established via discussion, then you can impose some behavioral(i mean this very loosely, essentially assumptions on the black box you left for preferences/knowledge/rationality, anything that will govern the path of play)  assumptions, you can say they come from economic theory, you can say they come from some other theory, people lay out their assumptions you can try to agree or refute, using observational data/logic/math whatever is at your disposal. If your behavioral assumptions are sufficiently justified, then you can try to generate solution concept, which again you can justify/refute and check using data/analysis whatever strikes your fancy. So it is fundamental to have meaningful framework to facilitate the rest of the discussions, say where did Prot holo came from. This is what you would do for real economic concepts as well, although I have given this example before, say you want to have a notion of inequality, for the time inconsistent retirement problem. Even though your economic agents objectives and knowledge may be unbeknownst to you or they are so complicated that you don't have a good notion of solution. Once you have your notion you can talk about it, try to put structural assumptions on for example form of inconsistency etc, ask other people, you know improve your understanding on the problem at hand.

 

Once again I feel like I am being led to a random gotcha instead of a meaningful discourse if that is so, again please stop asking me questions. I am readily willing to give you that you are right and I am wrong on whatever thing you believe I am wrong in.

Edited June 8, 2021 by Kolzar.9567

[Crozame.4098]

31 minutes ago, JusticeRetroHunter.7684 said:

Because in the formal definition where the lines on a graph are just functions, then the lines (functions) between elements(variables) can be thought of as a math problem. Adding +150 power to an attack is a very simple math problem. So even though an element can connect to 1000 other elements, doesn't mean that relationship is complex...the function (the relationship) is just as important if not more so then number of elements it's connected to. Soothing Power: works very much in the same way, where the function is a rather simple addition problem.

 

You can definitely argue about how complex the current mechanics are in comparison to how complex the mechanic could be, given the space of all mathematical problems. That's really all the game is really...we're all just solving little math problems, and our brain does this very easily when the math problems are easy. How hard are those problems depends on the relationships these variables have. Addition subtraction...those are easy problems. Add more variables? slightly harder problem. Richness of the function? very much a harder problem. 

But you were talking about relations between elements in some previous posts, and now you are saying simple addition would work... 

[Crozame.4098]

33 minutes ago, Kolzar.9567 said:

This is literally the way to have a meaningful discussion in a sensible framework. You might already disagree on the description of the environment and in fact that was the reason of my first post, I disagreed with the notion of diversity that the other poster posed, we kept respectfully disagreeing and they seem to agree with some of my choices. I am making at least in my opinion some minimal assumptions of my description, the other poster does another set of them. I tried to explain to them why some of those assumptions they are making would be invalid (people behaving randomly does not generate enough continuity to think of it as a mechanical equation), they came up with their own arguments. I tried to keep the level low so that other users can also understand what I was saying and agree/disagree, maybe I missed something in my description, maybe I didn't.

 

Once a reasonable framework is established via discussion, then you can impose some behavioral(i mean this very loosely, essentially assumptions on the black box you left for preferences/knowledge/rationality, anything that will govern the path of play)  assumptions, you can say they come from economic theory, you can say they come from some other theory, people lay out their assumptions you can try to agree or refute, using observational data/logic/math whatever is at your disposal. If your behavioral assumptions are sufficiently justified, then you can try to generate solution concept, which again you can justify/refute and check using data/analysis whatever strikes your fancy. So it is fundamental to have meaningful framework to facilitate the rest of the discussions, say where did Prot holo came from. This is what you would do for real economic concepts as well, although I have given this example before, say you want to have a notion of inequality, for the time inconsistent retirement problem. Even though your economic agents objectives and knowledge may be unbeknownst to you or they are so complicated that you don't have a good notion of solution. Once you have your notion you can talk about it, try to put structural assumptions on for example form of inconsistency etc, ask other people, you know improve your understanding on the problem at hand.

 

Once again I feel like I am being led to a random gotcha instead of a meaningful discourse if that is so, again please stop asking me questions. I am readily willing to give you that you are right and I am wrong on whatever thing you believe I am wrong in.

we use game theory in order to find equilibria  not just to stop at the description of the situation.