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22 minutes ago, JusticeRetroHunter.7684 said:

 

I can show you what I mean in the form of a picture, using the same example above.

 

https://i.imgur.com/gd8ZZob.png

In this image, I took one of the paths to the end of a tree (marked red), each line representing a simple addition of the values in the box. I tell you now, that the highest number in this tree game is 45...and now you are asked to verify my answer.

 

The complexity of this problem is just the the total computation size of the game...the number of boxes, and the operations taken between each box. 

 

If you were one person, you have to travel down all the paths to verify that my answer is either true or false. Your algorithm in this case is slow (a brute force algorithm) that takes you at least 11 steps and at most 28 steps.

 

If you had 7 people with you to go down the other paths, then you can verify the answer I gave in a much shorter number of steps (4 of them). This is why increasing the number of people acts as an algorithm, because it solves the problem faster. This is the notion for what computational time is and how it changes from algorithm to algorithm.

 

The problem itself is the tree (which has a definite complexity size). The algorithm here is the number of people traveling on a different path of the tree...When you think about evolution in terms of biology, these other people on the path of this tree are the other animals in the animal kingdom...they verify with each other what the "highest number is" by eating each other, competing for resources, and reproducing. The animals that survive are the "highest number" until they get verified by something else

Hmm.. i am sorry but i still dont see where the problem is to use evolution algorithm to find the optimal state.  The idea of EA is optimization and finding optimal state. 

May i ask you are you familiar with EA and how they optimize/find best solution for specific problem?

 

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5 hours ago, razaelll.8324 said:

I was thinking about that after out last discussion namely: the process of finding the best/optimal builds can be modeled as an evolution process. At least to me the more i think of it more it looks like an evolution process than a complexity computation one.

That was what I was trying to explain, but there is a little more to it. It is a process defined on sets of builds. So unlike processes you would encounter in physical phenomena (say currently my cup of tea is at 30 degrees Celsius at 10 seconds from now on, it will be something slightly below, with some randomness in it and I have neat formula to calculate how I expect it to evolve), it is prone to exhibit some problematic behavior (also it has some good behavior because people are doing what is in their best interest given their understanding of the game, but that is a separate issue) that makes complexity of the problem overinflated and at least in my opinion inappropriate to use. (the very crude extension to the tea temperature would be that my tea would simultaneously be 25 and 10 degrees at 10 seconds, since it need not be a single value)  When you think about a physical evolution, there is at least a very loose notion of "time derivative", how your process evolves with respect to time. Now, as you might remember, a notion of derivative requires continuity. Suppose you are currently at x, and expect to evolve to y, if you instead were a tiny bit from x, you would expect to be near y. However, when you are thinking about set valued objects, the notion of continuity also needs to have sets shrinking expanding. Say currently everyone is playing prot holo for some reason, and there is only one counter (I am not pushing any reasons why there is only one, that people can argue separately), so the next evolution in the meta would be that build. But suppose we changed something tiny on the prot holo say we removed one amulet or sigil, now there are 5 counters (again no assumptions on why the player base plays those as counters), which may or may not include the original counter we had in mind. This rapid, discontinuous expanding of the set is a failure of a notion called hemi-continuity. This failure automatically makes your problem very complex regardless of the rest of the real situation, and whatever you assume about player behavior, which makes using complexity not suitable in my opinion. And this kind of complexity usually does not pose a problem for human beings for simple enough tasks, or even complicated ones given enough practice, even though they may have a plethora of cognitive limitations that you would usually assume away. I tried to give examples before, R,P,S is a very complex game by this notion, yet kids play it, supply equals demand is a very simple concept , it is a well known NP hard problem yet markets even with bad business decisions seem to operate and even have some sort of stability. You can try to analyze these situations with a solution concept you have in mind where you would impose some assumptions on behavior(what players want, what they know how they react etc) that should in principle make your life easier yet doesn't get around the inflated complexity. 

Edited by Kolzar.9567
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Just now, razaelll.8324 said:

Hmm.. i am sorry but i still dont see where the problem is to use evolution algorithm to find the optimal state.  The idea of EA is optimization and finding optimal state. 
 

 

There's no problem using evolution 😄 This is exactly what evolution is for...it's one of the most efficient processes to find an answer to a hard problem.

 

Like i said earlier we agree, there's just confusion on what "a problem" is. By problem I mean "a question." evolution is a way to answer a problem, if not the best way to solve most problems.

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39 minutes ago, Kolzar.9567 said:

That was what I was trying to explain, but there is a little more to it. It is a process defined on sets of builds. So unlike processes you would encounter in physical phenomena (say currently my cup of tea is at 30 degrees Celsius at 10 seconds from now on, it will be something slightly below, with some randomness in it and I have neat formula to calculate how I expect it to evolve), it is prone to exhibit some problematic behavior (also it has some good behavior because people are doing what is in their best interest given their understanding of the game, but that is a separate issue) that makes complexity of the problem overinflated and at least in my opinion inappropriate to use. (the very crude extension to the tea temperature would be that my tea would simultaneously be 25 and 10 degrees at 10 seconds, since it need not be a single value)  When you think about a physical evolution, there is at least a very loose notion of "time derivative", how your process evolves with respect to time. Now, as you might remember, a notion of derivative requires continuity. If you change your input a tiny bit, your output in the next step of the evolution is not too far. However, when you are thinking about set valued objects, the notion of continuity also needs to have sets shrinking expanding. Say currently everyone is playing prot holo for some reason, and there is only one counter (I am not pushing any reasons why there is only one, that people can argue separately), so the next evolution in the meta would be that build. But suppose we changed something tiny on the prot holo say we removed one amulet or sigil, now there are 5 counters (again no assumptions on why the player base plays those as counters), which may or may not include the original counter we had in mind. This rapid, discontinuous expanding of the set is a failure of a notion called hemi-continuity. This failure automatically makes your problem very complex regardless of the rest of the real situation, and whatever you assume about player behavior, which makes using complexity not suitable in my opinion. And this kind of complexity usually does not pose a problem for human beings for simple enough tasks, or even complicated ones given enough practice, even though they may have a plethora of cognitive limitations that you would usually assume away. I tried to give examples before, R,P,S is a very complex game by this notion, yet kids play it, supply equals demand is a very simple concept , it is a well known NP hard problem yet markets even with bad business decisions seem to operate and even have some sort of stability. You can try to analyze these situations with a solution concept you have in mind where you would impose some assumptions on behavior(what players want, what they know how they react etc) that should in principle make your life easier yet doesn't get around the inflated complexity. 

 

Right this is where we basically left off before the discussion diverged.

 

Our shared opinion is that the game is an NP Hard problem, approximately solvable by an evolutionary process into a Polynomial time problem. My proposition is that the game of gw2 should be a harder problem, so that it can't be solved in polynomial time.

 

In gw2 lingo, instead of a meta being found in a couple of days via an evolution process , it should take months, or years via an evolutionary process.

Edited by JusticeRetroHunter.7684
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11 minutes ago, JusticeRetroHunter.7684 said:

 

Right this is where we basically left off before the discussion diverged.

 

Our shared opinion is that the game is an NP Hard problem, approximately solvable by an evolutionary process into a Polynomial time problem. My proposition is that the game of gw2 should be a harder problem, so that it can't be solved in polynomial time.

Actually, I am not attempting to classify the game in terms of any complexity as I am deliberately trying to avoid making assumptions about why and how people play the game. All I am saying is regardless what you assume about why people play the game, the very nature of how a meta evolves, a set of builds changing into another set of builds resulting from some sort of attempted optimization by players is very complex by classifications such as NP, P etc, just because it is some sort of fixed point on a correspondence. Such complexity is present in very simple examples as well, such as repeated plays of RPS just because of the nature of the problem (and how it interacts with the formal definition of complexity) and the usual notion of more complex=hard for people too and it will take soo much time is lost.  At least in my opinion, the complexity class of say RPS, or GW2 is not representative of either the difficulty of the game or the diversity of actions/builds that are viable in the game. (Again I am not saying the game itself is difficult or not, just using complexity as a measure at least in my opinion is not very appropriate)  And since I disagreed with you on this part, I tried to offer some alternatives of a notion of diversity which I think are better suited, again these may or may not be appropriate but the whole point was to at least even find a notion of diversity that people can to some extent agree on, so that you can discuss how to increase/decrease it.

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43 minutes ago, Kolzar.9567 said:

Actually, I am not attempting to classify the game in terms of any complexity as I am deliberately trying to avoid making assumptions about why and how people play the game. All I am saying is regardless what you assume about why people play the game, the very nature of how a meta evolves, a set of builds changing into another set of builds resulting from some sort of attempted optimization by players is very complex by classifications such as NP, P etc, just because it is some sort of fixed point on a correspondence. Such complexity is present in very simple examples as well, such as repeated plays of RPS just because of the nature of the problem (and how it interacts with the formal definition of complexity) and the usual notion of more complex=hard for people too and it will take soo much time is lost. 

Ya i realized this when you brought it up pages ago. But complexity isn't about why people play the game or their personal approach to it, it's about the definite size of the complexity space of the game, and the agents are free to use whatever personal algorithm to figure it out (and regardless the system follows a macroscale evolution "algorithm"). For example you can have an Einstein monke that calculates skills based on an exact 1:1 comparison for all of them, and in another instance you can have an ESL monke who's got a good intuition for skill interaction by practicing a lot. In this way, the complexity time is variable, but if you assume that all players use whatever strategy to swim through the complexity of the game, on average the time it takes to follow macroscale evolution scales with the complexity size of the system.

 

To push the point here, The complexity space, is definite as it has a definitive, finite size. What is variable is the complexity time, and you change the scaling of complexity time by just increasing the fixed complexity space, so that already fast algorithm's, like macroscale evolution processes take a longer period of time to solve the same problem.

 

Edited by JusticeRetroHunter.7684
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1 hour ago, JusticeRetroHunter.7684 said:

 

There's no problem using evolution 😄 This is exactly what evolution is for...it's one of the most efficient processes to find an answer to a hard problem.

 

Like i said earlier we agree, there's just confusion on what "a problem" is. By problem I mean "a question." evolution is a way to answer a problem, if not the best way to solve most problems.

exactly.

Edited by razaelll.8324
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1 hour ago, Kolzar.9567 said:

That was what I was trying to explain, but there is a little more to it. It is a process defined on sets of builds. So unlike processes you would encounter in physical phenomena (say currently my cup of tea is at 30 degrees Celsius at 10 seconds from now on, it will be something slightly below, with some randomness in it and I have neat formula to calculate how I expect it to evolve), it is prone to exhibit some problematic behavior (also it has some good behavior because people are doing what is in their best interest given their understanding of the game, but that is a separate issue) that makes complexity of the problem overinflated and at least in my opinion inappropriate to use.

Exactly.

 

Quote

But suppose we changed something tiny on the prot holo say we removed one amulet or sigil, now there are 5 counters (again no assumptions on why the player base plays those as counters), which may or may not include the original counter we had in mind. This rapid, discontinuous expanding of the set is a failure of a notion called hemi-continuity. This failure automatically makes your problem very complex regardless of the rest of the real situation, and whatever you assume about player behavior, which makes using complexity not suitable in my opinion

 

Totaly agree with this.

Edited by razaelll.8324
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1 hour ago, Vancho.8750 said:

Boy is this thread derailed, lets get back on track 

They buffed holo with the superspeed change, lol , I don't understand Arenanet at all . 

 

Don't worry, this change is only significant for scrapper in PvP.

 

This was a quality of life change, meant to prevent superspeed applications from overriding each other. This rarely happens on Holo, but it was very easy to do on scrapper, especially when trying to stack quickness. You would inevitably overwrite a 12 second super speed application with a 3 second application, which was a feelsbad moment. 

 

Even for rocket boots holo, the actual impact of this change is small due to cast times. If you try to stack the super speed of Holo Leap with rocket boots, you end up wasting a second of superspeed during the rocket boots animation or during the holo leap animation. It's still more optimal to wait for a second or two. 

 

With toss Elixir U. There's no reason why you have to spam it immediately after holo leap. You could simply time it before and it would achieve the same end result. It's a placebo buff for holo. You might start seeing more Holo players running rocket boots as a result, but imo, that build was already good.

 

It's a good change overall. 

 

 

 

 

Edited by Kuma.1503
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53 minutes ago, JusticeRetroHunter.7684 said:

To push the point here, The complexity space, is definite as it has a definitive, finite size. What is variable is the complexity time, and you change the scaling of complexity time by just increasing the fixed complexity space, so that already fast algorithm's, like macroscale evolution processes take a longer period of time to solve the same problem.

I am not saying complexity is ill-defined or it doesn't exist. I am just saying since this is a fixed point on some correspondence, the complexity class is not representative of how long people will actually take to reach a certain point. If you google equilibria/fixed points and complexity classes you will see that even simple settings we encounter and even solve in real life are just too hard by this classification, because algorithms usually can't take the mental shortcuts/fallacies we have.

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18 hours ago, Paradoxoglanis.1904 said:

what even is this thread

 

This thread is rare. Enjoy and immerse yourself in something rather extraordinary. One thing is for sure, they have a STEM background (Science, Technology, Engineering Math)

 

Probably masters degree level, even PhD. 

 

Probably economists, professor, engineer, etc....

 

Probably working in Wall St as investment banking analysts. 

 

I'd say this is one of the best threads ever. 

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3 minutes ago, Pimsley.3681 said:

 

This thread is rare. Enjoy and immerse yourself in something rather extraordinary. One thing is for sure, they have a STEM background (Science, Technology, Engineering Math)

 

Probably masters degree level, even PhD. 

 

Probably economists, professor, engineer, etc....

 

Probably working in Wall St as investment banking analysts. 

 

I'd say this is one of the best threads ever. 

Unfortunately most of the people get bored when science get involved, but this thread is truly awesome in my opinion, because it is constructive.

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1 minute ago, razaelll.8324 said:

Unfortunately most of the people get bored when science get involved, but this thread is truly awesome in my opinion, because it is constructive.

 

Yes! 

 

No name calling, no insults. They conveyed their side using theories and a very very very thorough explanation. In the end, they were friendly and non-toxic. 

 

Such rarity!!!

 

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8 minutes ago, Pimsley.3681 said:

 

Yes! 

 

No name calling, no insults. They conveyed their side using theories and a very very very thorough explanation. In the end, they were friendly and non-toxic. 

 

Such rarity!!!

 

There was a bit of toxicity here and there, but overall it is very constructive thread with a lot of interesting things and ideas mentioned.

 

I hope to see more threads like this.

 

Balancing a game is not an easy task and the typical nerf/buff threads many times are actually doing more bad than good for the game in my opinion, thats why this thread is interesting to me , because people are trying to find a better approach to that complex problem.

Edited by razaelll.8324
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On 6/10/2021 at 12:11 AM, JusticeRetroHunter.7684 said:

Right now as far as I've come along here with the fixed point theorems, this is @Kolzar.9567 Fixed point model :

 

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

 

the vector x is just one build, where f(x) is the vector for the "next" build. The smaller fixed point is akin to a completely homogenous game, while the larger fixed point is akin to a rock paper scissors game. 

 

Also, I am pretty sure this is not a accurate definition of fixed point. You can clearly say the number of fixed points for a function, but  the size of the fix point?

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20 hours ago, razaelll.8324 said:

This failure automatically makes your problem very complex regardless of the rest of the real situation, and whatever you assume about player behavior, which makes using complexity not suitable in my opinion

...cannot use complexity on complex issues. emmm.

2 hours ago, razaelll.8324 said:

Unfortunately most of the people get bored when science get involved, but this thread is truly awesome in my opinion, because it is constructive.

You need to know usually people use science to give a clear solution to a problem, not something like: when balancing you need to take into account the complexity of the problem; it is complicated; there is no clear answer etc. Like in this thread and in some posts.,people have asked something like ok: X build is OP, if we cannot address the numbers, then how can we make the game more balanced/enjoyable. But the answers were just meh.

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46 minutes ago, Crozame.4098 said:

...cannot use complexity on complex issues. emmm.

You need to know usually people use science to give a clear solution to a problem, not something like: when balancing you need to take into account the complexity of the problem; it is complicated; there is no clear answer etc. Like in this thread and in some posts.,people have asked something like ok: X build is OP, if we cannot address the numbers, then how can we make the game more balanced/enjoyable. But the answers were just meh.

I think you know my stance about numbers and that i disagree with Justice on that topic , so i am not sure why you quote me

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2 hours ago, razaelll.8324 said:

I think you know my stance about numbers and that i disagree with Justice on that topic , so i am not sure why you quote me

Its the quoting system issue. I think the reason is that you quoted him about this, and I just copy pasted the relevant section. Previously, this would also quote him...

 

But yea, my intention was not arguing with you.

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On 6/11/2021 at 7:57 AM, Crozame.4098 said:

Also, I am pretty sure this is not a accurate definition of fixed point. You can clearly say the number of fixed points for a function, but  the size of the fix point?

The size of the fixed point is just the size of the loop that's made. 40 builds in a loop means "a bigger" fixed point then a game with 5 builds in a loop... Right now, we aren't assuming there's more then one fixed point, which is perfectly possible too but its just a different area of discussion that isn't involved here.

 

On 6/10/2021 at 12:53 PM, Kolzar.9567 said:

I am not saying complexity is ill-defined or it doesn't exist. I am just saying since this is a fixed point on some correspondence, the complexity class is not representative of how long people will actually take to reach a certain point. If you google equilibria/fixed points and complexity classes you will see that even simple settings we encounter and even solve in real life are just too hard by this classification, because algorithms usually can't take the mental shortcuts/fallacies we have.

 

So I spent some time looking into this, and i need to spend some more... but so far from what I gathered, this doesn't seem to have anything to do with the complexity of the games we are talking about. This topic only deals with the complexity of calculating a nash equilibrium, to any game.

 

Example, You want to make a computer program to calculate the equilibrium of some random game. These papers here are about how hard it is to make such a program basically.

 

So the comparison between the complexity of RPS and Gw2 being the same, is not valid here and this would explain why I was so confused for many pages now.

 

Just a quote from one of the papers I read (the first one that appears on google search):

 

4. Rational equilibria, Piecewise Linear Functions and the Class PPAD

Consider a 2-player finite game, with the payoffs given explicitly in terms of the two payoff matrices A1, A2 of the two players (i.e., the game is presented in normal form). Computing a specific Nash equilibrium, such as one that maximizes the payoff to one of the players, or to all the players, is NP-hard [30]. However, the search problem that asks for any Nash equilibrium is a different, ‘easier’ problem, and is unlikely to be NP-hard.

 

5. Irrational Equilibria, Nonlinear Functions, and the Class FIXP

Games with 3 or more players are quite different from 2-player games: Nash equilibria are generally irrational; knowing the support of an equilibrium does not help us much, and there may be many different such equilibria. There are many search problems as we saw in Section 3, and in particular many problems that can be cast in a fixed point framework, where the objects that we want to compute (the answers) are irrational. Of course we cannot compute them exactly in the usual Turing machine model of computation. One can consider the exact computation and the complexity of such search problems in a real model of computation [6]. In the usual (discrete) Turing model of computation and complexity, we have to state carefully and precisely what is the (finite) information about the solution that we want to compute, as the nature of the desired information can actually affect the complexity of the problem, i.e., some things may be easier to compute than others. That is, from a search problem Π with a continuous solution space, another search problem Π′ is derived with a discrete space. Several types of information are potentially of interest, leading to different problems Π′ .

 

Now...I still have to really dig deep to find what the discrepancy is on the topic. As of right now it makes no sense to me that the size of the system isn't dependent on it's complexity time. This kind of contradicts every major facet of complexity theory, which I've studied for a while now. Diversity, is an intrinsic part of complex systems, so the whole topic is related.

 

 

Edited by JusticeRetroHunter.7684
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24 minutes ago, JusticeRetroHunter.7684 said:

he size of the fixed point is just the size of the loop that's made. 40 builds in a loop means "a bigger" fixed point then a game with 5 builds in a loop... Right now, we aren't assuming there's more then one fixed point, which is perfectly possible too but its just a different area of discussion that isn't involved here.

You are talking about the length of a walk that happens to be a circle?

 

 

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