Like I said, game theory is well established by people that win Nobel prizes and have PH’Ds in the subject...and you think that THEY are wrong about what games are and aren’t?

You think wiki cares enough about gw2 to list it in the wiki article? You think that game theory doesn’t apply to complex systems, when it applies to evolutionary biology, Which is one of the most complex systems known to exist?

Here’s a YouTube video that shows that RPS is the heart of almost all games today

@lodjur.1284 said:
Something taking time isn't a trade off if all that time can be spent before the current fight.

WvW is not about 1v1 duels, so yes, time is a trade off. You fight some fights with a weak bonus or no bonus until you win enough so your bonus becomes viable/decent.

By that logic any amount of time you spend outside of WvW is a tradeoff and actively harmful...

Well in duels stacking sigils are actually not allowed.

Well after clearing 1 camp they outpace force/bursting.

Also, other than Bloodlust most stacking sigils are not even that strong. We have things like Sigil of Cleansing clearing 3 condis every 9s and Sigil of Energy giving 1 free dodge every 9s.

Corruption is equally strong

And even bloodlust is not seen that often. Several people pick other strong options. It is not like all roamers are running bloodlust.

It's seen on a majority of builds in roaming/smallscale (and zerging too when people have actual build there) >

Like I said, game theory is well established by people that win Nobel prizes and have PH’Ds in the subject...and you think that THEY are wrong about what games are and aren’t?

Has any of these people classified RPS as a game?

You think wiki cares enough about gw2 to list it in the wiki article? You think that game theory doesn’t apply to complex systems, when it applies to evolutionary biology, Which is one of the most complex systems known to exist?

I never said game theory didn't, I said RPS doesn't apply to complex systems.

But if you honestly believe that RPS applies to evolutionary biology then ye.....

Here’s a YouTube video that shows that RPS is the heart of almost all games today

Random YouTube video that I will never watch cause videos are the worst form of information.

Ögonen omges av vita och svarta penseldrag som gör att de ser större ut än vad de egentligen är. Baksidan av lodjurets öron kantas av svart päls som slutar i den karaktäristiska tofsen högst upp på örat. Lodjurets svans är kortare än de flesta andra kattdjurs.

1: Would not lose stacks on switching maps (such a silly implementation from the beginning). Really annoying to build up 25 stacks then have to move to a different borderland/EBG to help defend and poof -- there goes your stack.
2: Would build stacks as long as you have it equipped on one of your weapon sets. Swapping to the actual weapon is a pain.

1: Would not lose stacks on switching maps (such a silly implementation from the beginning). Really annoying to build up 25 stacks then have to move to a different borderland/EBG to help defend and poof -- there goes your stack.
2: Would build stacks as long as you have it equipped on one of your weapon sets. Swapping to the actual weapon is a pain.

That solution would at least fix the worst problem with the stacking sigils which is how they're mandatory and annoying. Now at least they wouldn't be annoying anymore. I am all for it

Ögonen omges av vita och svarta penseldrag som gör att de ser större ut än vad de egentligen är. Baksidan av lodjurets öron kantas av svart päls som slutar i den karaktäristiska tofsen högst upp på örat. Lodjurets svans är kortare än de flesta andra kattdjurs.

@lodjur.1284 said:
Has any of these people classified RPS as a game?

Game theory was developed in the 1950's...before computer games...and RPS has existed for nearly 2000 years, as it was one of the first games ever created...

Quote from the RPS Article:
"Rock paper scissors is a hand game usually played between two people... (It is ) a simultaneous, zero-sum game, (and) has only two possible outcomes: a draw, or a win for one player and a loss for the other."

Quote from the Game Theory Article:
"Modern game theory began with the idea of mixed-strategy equilibria in two-person zero-sum games and its proof by John von Neumann."

Quote from Von Neumann Article:
"Von Neumann founded the field of game theory as a mathematical discipline.[97] Von Neumann proved his minimax theorem in 1928. This theorem establishes that in zero-sum games with perfect information (i.e. in which players know at each time all moves that have taken place so far), there exists a pair of strategies for both players that allows each to minimize his maximum losses, hence the name minimax. When examining every possible strategy, a player must consider all the possible responses of his adversary. The player then plays out the strategy that will result in the minimization of his maximum loss.[98] Such strategies, which minimize the maximum loss for each player, are called optimal....Von Neumann improved and extended the minimax theorem to include games involving imperfect information and games with more than two players, publishing this result in his 1944 Theory of Games and Economic Behavior."

You owe your VOCABULARY in modern gaming to physicists/mathematican like Von Neumann. Min-max, metagame, optimal... these words come from his contributions to game theory, and it's not a coincidence we use these words in our vocabulary when playing games like gw2. So yes, Von Neumann, if he were still alive, probably would consider RPS as a game, since it is a ZERO SUM GAME by definition, if that wasn't the first game he actually looked at when he went and wrote his thesis on game theory.

You say you think of yourself as a math-guy who's calculated the efficiencies of stacking sigils yada yada yada... and yet you show little regard to people in the field who've actually laid the ground work for you to even do maths in this game in the first place? Blows my mind.

Oh and to address this:

But if you honestly believe that RPS applies to evolutionary biology then ye.....

Quote from the Game Theory Article: "...Game theory was developed extensively in the 1950s by many scholars. It was explicitly applied to biology in the 1970s"
Yea Game theory and even by proxy RPS, applies to biology... It has it's own page too if you want to read that also https://en.wikipedia.org/wiki/Evolutionary_game_theory

it also happens to have it's own dedicated section to RPS... Quote from Evolutionary game theory article: Unstable games, cyclic patterns Rock paper scissors
"An evolutionary game that turns out to be a children's game is rock paper scissors...Rock paper scissors incorporated into an evolutionary game has been used for modelling natural processes in the study of ecology.[41] Using experimental economics methods, scientists have used RPS game to test human social evolutionary dynamical behaviors in laboratory. The social cyclic behaviors, predicted by evolutionary game theory, have been observed in various laboratory experiments.[42][43]"

@lodjur.1284 said:
Has any of these people classified RPS as a game?

Game theory was developed in the 1950's...before computer games...and RPS has existed for nearly 2000 years, as it was one of the first games ever created...

Quote from the RPS Article:
"Rock paper scissors is a hand game usually played between two people... (It is ) a simultaneous, zero-sum game, (and) has only two possible outcomes: a draw, or a win for one player and a loss for the other."

Quote from the Game Theory Article:
"Modern game theory began with the idea of mixed-strategy equilibria in two-person zero-sum games and its proof by John von Neumann."

Quote from Von Neumann Article:
"Von Neumann founded the field of game theory as a mathematical discipline.[97] Von Neumann proved his minimax theorem in 1928. This theorem establishes that in zero-sum games with perfect information (i.e. in which players know at each time all moves that have taken place so far), there exists a pair of strategies for both players that allows each to minimize his maximum losses, hence the name minimax. When examining every possible strategy, a player must consider all the possible responses of his adversary. The player then plays out the strategy that will result in the minimization of his maximum loss.[98] Such strategies, which minimize the maximum loss for each player, are called optimal....Von Neumann improved and extended the minimax theorem to include games involving imperfect information and games with more than two players, publishing this result in his 1944 Theory of Games and Economic Behavior."

You owe your VOCABULARY in modern gaming to physicists/mathematican like Von Neumann. Min-max, metagame, optimal... these words come from his contributions to game theory, and it's not a coincidence we use these words in our vocabulary when playing games like gw2. So yes, Von Neumann, if he were still alive, probably would consider RPS as a game, since it is a ZERO SUM GAME by definition, if that wasn't the first game he actually looked at when he went and wrote his thesis on game theory.

Who coined various terms isn't really relevant to any of the matters at hand.

Here's an interesting piece of information, not all zero-sum games are actually games, but I am sure you knew that.

"In game theory and economic theory, a zero-sum game is a mathematical representation of a situation in which each participant's gain or loss of utility is exactly balanced by the losses or gains of the utility of the other participants."

Followed by an example of a zero-sum game that isn't a game

"Thus, cutting a cake, where taking a larger piece reduces the amount of cake available for others as much as it increases the amount available for that taker, is a zero-sum game if all participants value each unit of cake equally (see marginal utility)..

Also we've established a pattern here, not only do you try to speak for me now you try to speak on behalf of your personal hero "Von Neumann". That's ironic given that you're accusing me of being disrespectful.

You say you think of yourself as a math-guy who's calculated the efficiencies of stacking sigils yada yada yada... and yet you show little regard to people in the field who've actually laid the ground work for you to even do maths in this game in the first place? Blows my mind.

Nope that's still just you claiming I said a bunch of kitten I didn't.

Why must you try to speak for me? First off whether I hold any regard for someone or not is utterly irrelevant. Secondly I have not in anyway expressed my thoughts on the matter.

Also the math that shows that corruption > better than corruption isn't exactly the kinda math that needs any groundwork.

Oh and to address this:

But if you honestly believe that RPS applies to evolutionary biology then ye.....

Quote from the Game Theory Article: "...Game theory was developed extensively in the 1950s by many scholars. It was explicitly applied to biology in the 1970s"
Yea Game theory and even by proxy RPS, applies to biology... It has it's own page too if you want to read that also https://en.wikipedia.org/wiki/Evolutionary_game_theory

I never said game theory didn't. I said RPS didn't, it's getting increasingly frustrating to have you attribute claims to me that I have never made. Refute what I say not what you imagine/wish I said. Also things just don't apply by proxy.

it also happens to have it's own dedicated section to RPS... Quote from Evolutionary game theory article: Unstable games, cyclic patterns Rock paper scissors
"An evolutionary game that turns out to be a children's game is rock paper scissors...Rock paper scissors incorporated into an evolutionary game has been used for modelling natural processes in the study of ecology.[41] Using experimental economics methods, scientists have used RPS game to test human social evolutionary dynamical behaviors in laboratory. The social cyclic behaviors, predicted by evolutionary game theory, have been observed in various laboratory experiments.[42][43]"

Fair enough, it can be used to describe a type of situations in a simple way. Thankfully I am a big enough person to admit when I am wrong. But still not gonna accept you trying to put words into my mouth when I've said nothing of the kind.

Ögonen omges av vita och svarta penseldrag som gör att de ser större ut än vad de egentligen är. Baksidan av lodjurets öron kantas av svart päls som slutar i den karaktäristiska tofsen högst upp på örat. Lodjurets svans är kortare än de flesta andra kattdjurs.

@lodjur.1284 said:
Fair enough, it can be used to describe a type of situations in a simple way. Thankfully I am a big enough person to admit when I am wrong. But still not gonna accept you trying to put words into my mouth when I've said nothing of the kind.

You still can't accept that fact that you were wrong...but you being wrong is not at all what bugs me about every post you've made so far. It's that your comment(s) clearly illustrates disregard for ACTUAL mathematics, and misuse of information without actually researching it. Remember the initial point here was that diversity always decreases as you remove choices, and i said that this WAS NOT an opinion...and you constantly tried to argue against that using your own personal biases/conclusions rather than doing the research. Posts like yours, is how misinformation develops and THAT is what really bothers me.

Here's an interesting piece of information, not all zero-sum games are actually games, but I am sure you knew that.

incorrect again. You CAN make cutting a cake into a game too... in fact you can make a game out of practically any situation, the only requirement is that it must have rational agents as participants to make decisions, and it doesn't even have to be zero-sum either. But, ALL zero-sum games are games. Again this isn't for debate this is FACTS backed by decades of research in the field with people who get payed 10x your paycheck and my paycheck to research exactly these things.

And, again, this is your opinion showing and not actually doing the research, or even attempting to understand the subject area that games like gw2 are built upon. This is why you aren't a developer and if you were, i can predict with 99% certainty you'd throw the game into complete clown-fiesta. If you really actually wanted to make a suggestion based on data and analysis, then you'd at least do everyone the courtesy of watching that linked video, and reading up on game theory. Introductory game balance 101 right there just for you...trying to make it easier for you...but if you want to remain willfully ignorant? i can't control that, that's on you.

Edit: Last thing, Von Neuman isn't my "personal hero," he is one of the defining mathematicians/physicists of the century, and he is on the same pedestal as mathematicians like Alan Turing and Issac Newton, and physicists like Einstein, R. Feynman. To think that they don't know what they were talking about is tantamount to saying the Earth is flat.

@lodjur.1284 said:
Fair enough, it can be used to describe a type of situations in a simple way. Thankfully I am a big enough person to admit when I am wrong. But still not gonna accept you trying to put words into my mouth when I've said nothing of the kind.

You still can't accept that fact that you were wrong...but you being wrong is not at all what bugs me about every post you've made so far. It's that your comment(s) clearly illustrates disregard for ACTUAL mathematics, and misuse of information without actually researching it. Remember the initial point here was that diversity always decreases as you remove choices, and i said that this WAS NOT an opinion...and you constantly tried to argue against that using your own personal biases/conclusions rather than doing the research. Posts like yours, is how misinformation develops and THAT is what really bothers me.

I just did, I said "I was wrong about this", that's literally accepting the fact that I was wrong about something. You saying it isn't says more about you than it does about me.

None of your posts actually contains any mathematics so I am not really disregarding it

It is not an opinion, it is actually a fact that removing choices can increase diversity. There is proof of this.

"Remember the initial point here was that diversity always decreases as you remove choices, and i said that this WAS NOT an opinion"

Your claim is that "Diversity always decrease as your remove choices". For this statement to not be proven false there can't have been a single instance of diversity increasing in a game after an option has been removed. This is an incredibly bold claim, especially as there's no proof for it.

Now sadly we can't really use guild wars 2 for this as there's very little data on the metagame historically in guild wars 2. So we'd have to resort to looking at other games to disprove this, but since it's a general statement it doesn't actually matter what game the proof comes from.

I can try to find data from some other game (I even have one in mind) that proves this if you want me to find it, but as that would be incredibly ot and would most likely be a game you haven't played making any discussion of the "proof" kinda weird I am not sure how much that would help.

Here's an interesting piece of information, not all zero-sum games are actually games, but I am sure you knew that.

incorrect again. You CAN make cutting a cake into a game too... in fact you can make a game out of practically any situation, the only requirement is that it must have rational agents as participants to make decisions, and it doesn't even have to be zero-sum either. But, ALL zero-sum games are games. Again this isn't for debate this is FACTS backed by decades of research in the field with people who get payed 10x your paycheck and my paycheck to research exactly these things.

You could ofc have a game centered around the cutting of a cake, but that's not the situation being described (or in general what cutting a cake is).

Actually that's not the wikipedia definition of a game. I linked that one earlier.

What you wrote is the definition of the kind of situation that game theory is the study of. These two things aren't always the exact same thing (even if they often are). Otherwise you'd have to say that there's some amount of ambiguity to the term "game" which is a reasonable stance to take, but hardly the one you've been pushing.

I never said all games have to be zero-sum, I said all zero-sum games aren't games. You're making false claims about what I've said again.

Again with the personal insults and throwing random numbers around about my paycheck. This is incredibly ironic given a few quotes from you such as:

"Posts like yours, is how misinformation develops and THAT is what really bothers me."
"you constantly tried to argue against that using your own personal biases/conclusions rather than doing the research"
"This is why you aren't a developer and if you were, i can predict with 99% certainty you'd throw the game into complete clown-fiesta"

Do you see the irony? You're saying that my post spreads misinformation while throwing things you have absolutely no basis for out there as facts.

And, again, this is your opinion showing and not actually doing the research, or even attempting to understand the subject area that games like gw2 are built upon. This is why you aren't a developer and if you were, i can predict with 99% certainty you'd throw the game into complete clown-fiesta. If you really actually wanted to make a suggestion based on data and analysis, then you'd at least do everyone the courtesy of watching that linked video, and reading up on game theory. Introductory game balance 101 right there just for you...trying to make it easier for you...but if you want to remain willfully ignorant? i can't control that, that's on you.

GW2 doesn't really share many similarities with RPS actually. That there is some amount of game theory behind the construction of gw2 I've never denied, but that the core of it would be a 3 option coinflip I will definitively dispute.

Well you actually have no clue whether I am a developer or not, this is just you making a guess.

Then we get to some random percentage number about how a hypothetical game that I would be a developer would be a "clown-fiesta", I am curious how did you get to 99%?

Videos are a terrible source of information on this type of topics.

You can't easily quote them, not like text

They're extremely time inefficient compared to text

You generally need sound

If you write (and link) an article detailing what's said in the video I will probably read it.

I hope you can see the problems with labeling everyone who doesn't agree with you "willfully ignorant"

Also claiming someone is uneducated on a subject is generally a very poor argument, especially when you actually have no clue how informed I am on the topic.

Edit: Last thing, Von Neuman isn't my "personal hero," he is one of the defining mathematicians/physicists of the century, and he is on the same pedestal as mathematicians like Alan Turing and Issac Newton, and physicists like Einstein, R. Feynman. To think that they don't know what they were talking about is tantamount to saying the Earth is flat.

You keep saying that I've said he doesn't know what he is talking about, but I have never said that, I only said trivia about him is irrelevant to the discussion at hand.

But he clearly is your personal hero, you jump to his "defense" even when there was absolutely nothing bad said about him. I never said he was wrong (or that he was right) about anything, in fact I haven't actually said anything about him except for two things

You seem to be a very big fan (ie he is your personal hero)

You try to speak for him

Neither of these statements are false, my personal thoughts on him is irrelevant.

There's no need to get so emotional, in general getting emotional and throwing insults isn't conductive to a good discussion or to making logical decisions. Try to keep the name calling to a minimum and try not to speak for anyone, it really helps move this forward in a civilized and productive manner.

Ögonen omges av vita och svarta penseldrag som gör att de ser större ut än vad de egentligen är. Baksidan av lodjurets öron kantas av svart päls som slutar i den karaktäristiska tofsen högst upp på örat. Lodjurets svans är kortare än de flesta andra kattdjurs.

Your claim is that "Diversity always decrease as your remove choices". For this statement to not be proven false there can't have been a single instance of diversity increasing in a game after an option has been removed. This is an incredibly bold claim, especially as there's no proof for it.

Now sadly we can't really use guild wars 2 for this as there's very little data on the metagame historically in guild wars 2. So we'd have to resort to looking at other games to disprove this, but since it's a general statement it doesn't actually matter what game the proof comes from.

I can try to find data from some other game (I even have one in mind) that proves this if you want me to find it, but as that would be incredibly ot and would most likely be a game you haven't played making any discussion of the "proof" kinda weird I am not sure how much that would help.

I've already proved my point using RPS, which you so blatantly disregarded, due to your lack of knowledge on "games" ... but, here. I'll help you out, by helping you PROVE your conjecture.

You have 3 choices, that follow 2 Axioms.

1) There are 3 choices: X,Y, and Z
2) X is better than Y, and Y is better than Z.

This is now, where you have to prove, that removing one of these choices will yield more diversity. You can give any arbitrary description of this particular game or specific details about it's constituents, so long as you follow the 2 axioms. What you're up against in your proof, is that you have a total of 3 choices in the current diversity pool. You need to show that you can have at least 3 choices in whatever changes you make to this system in order to prove me wrong....so now go head.

Your claim is that "Diversity always decrease as your remove choices". For this statement to not be proven false there can't have been a single instance of diversity increasing in a game after an option has been removed. This is an incredibly bold claim, especially as there's no proof for it.

Now sadly we can't really use guild wars 2 for this as there's very little data on the metagame historically in guild wars 2. So we'd have to resort to looking at other games to disprove this, but since it's a general statement it doesn't actually matter what game the proof comes from.

I can try to find data from some other game (I even have one in mind) that proves this if you want me to find it, but as that would be incredibly ot and would most likely be a game you haven't played making any discussion of the "proof" kinda weird I am not sure how much that would help.

I've already proved it using RPS, which you so blatantly disregarded, due to your lack of knowledge on "games" ... but, here. I'll help you out, by helping you PROVE your theory.

You have 3 choices, that follow 2 Axioms.

1) There are 3 choices: X,Y, and Z
2) X is better than Y, and Y is better than Z.

This is now, where you have to prove, that removing one of these choices will yield more diversity. You can give any arbitrary description of this particular game or specific details about it's constituents, so long as you follow the 2 axioms. What you're up against in your proof, is that you have a total of 3 choices in the current diversity pool. You need to show that you can have at least 3 choices in whatever changes you make to this system in order to prove me wrong....so now go head.

Actually the only thing you've proven is that in RPS removing one of the pieces is a bad idea, which I don't think anyone has disputed.

What you haven't done is prove that for a complex game with a very large number of options (like guild wars 2 for example) removing an option can't increase diversity.

There's no reason my diversity pool only needs to have 3 options, GW2 doesn't only have 3 options, gw2 has somewhere between 70-100 sigils (now ofc not all of them are good, there's a ton of sigils that are a meme like sigil of luck, centaur slaying or w/e).

You can't just extrapolate that way, it doesn't work.

So until we can agree on this simple fact I am not gonna put any effort into a proof since you're just gonna dismiss it on the premise that it doesn't meet your constraints that make absolutely no sense given the situation (which is talking about diversity in a game with many choices, not one with only 3 choices)

Ögonen omges av vita och svarta penseldrag som gör att de ser större ut än vad de egentligen är. Baksidan av lodjurets öron kantas av svart päls som slutar i den karaktäristiska tofsen högst upp på örat. Lodjurets svans är kortare än de flesta andra kattdjurs.

@lodjur.1284 said:
So until we can agree on this simple fact I am not gonna put any effort into a proof since you're just gonna dismiss it on the premise that it doesn't meet your constraints that make absolutely no sense given the situation (which is talking about diversity in a game with many choices, not one with only 3 choices)

lol, typical i should have expected as much.
This is what you are saying in a nutshell:
"I can't prove my point because it will only work on a more complex game." followed by "Gw2 is too complex so i can't prove my point."

BTW, extrapolation is doing exactly what i am trying to get you to do. You take the consequences of what happens on a smaller scale and EXTRAPOLATE that to a larger scale....because the two are fundamentally the same thing...that's how extrapolation works. Analyzing the consequences of a game with 3 choices, yield the same consequences of a game with a hundred or a million choices.

So i'm gonna help you AGAIN. Let's take those axioms and change em'...JUST FOR YOU (so you can quit being a baby about it), so that there are a lot more choices. Once again, here are the axioms:

You have 26 choices, that follow 3 Axioms.

1) There are 26 choices: A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z.
2) In one mode of this game, the following choices are ranked from best to worst in MODE 1
A > B > C > D > E > F > G > H > I > J >K >L > M > N > O > P > Q > R > S >T >U > V > W > X > Y > Z
3) In another mode of this game, the following choices are ranked from best to worst in MODE 2
Z > Y > X > W > V > U > T > S > R > Q >P >O> N > M> L > K > J > I> H > G > F > E > D > C > B > A

Now is that complex enough for you? I've given you two separate modes, each with it's own unique viability value. Again, You can give any arbitrary description of this particular game or specific details about it's constituents, so long as you follow the 3 axioms. What you're up against in this proof, is that you have a total of 26 choices in the current diversity pool (for each mode). You need to show that you can have no less than 26 choices when you remove a choice from this system in order to prove me wrong.

@lodjur.1284 said:
So until we can agree on this simple fact I am not gonna put any effort into a proof since you're just gonna dismiss it on the premise that it doesn't meet your constraints that make absolutely no sense given the situation (which is talking about diversity in a game with many choices, not one with only 3 choices)

lol, typical i should have expected as much.
This is what you are saying in a nutshell:
"I can't prove my point because it will only work on a more complex game." followed by "Gw2 is too complex so i can't prove my point."

BTW, extrapolation is doing exactly what i am trying to get you to do. You take the consequences of what happens on a smaller scale and EXTRAPOLATE that to a larger scale....because the two are fundamentally the same thing...that's how extrapolation works. Analyzing the consequences of a game with 3 choices, yield the same consequences of a game with a hundred or a million choices.

I never said that I can't prove my point cause gw2 is too complex, I said there's no data on metagame changes.

That's a false premise actually, in some cases one can extrapolate a small system to a larger system, but that requires the systems to otherwise be identical, which isn't the case. RPS is an extremely simple system where every choice is exactly equally good and it's quantifiable, you can't easily quantify how good the most of the various sigils in gw2 are compared to each other. Only ones like bursting vs corruption, bloodlust vs force vs demon slaying, benevolance vs transference etc.

So i'm gonna help you AGAIN. Let's take those axioms and change em'...JUST FOR YOU (so you can quit being a baby about it), so that there are a lot more choices. Once again, here are the axioms:

You have 26 choices, that follow 3 Axioms.

1) There are 26 choices: A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z.
2) In one mode of this game, the following choices are ranked from best to worst in MODE 1
A > B > C > D > E > F > G > H > I > J >K >L > M > N > O > P > Q > R > S >T >U > V > W > X > Y > Z
3) In another mode of this game, the following choices are ranked from best to worst in MODE 2
Z > Y > X > W > V > U > T > S > R > Q >P >O> N > M> L > K > J > I> H > G > F > E > D > C > B > A

Now is that complex enough for you? I've given you two separate modes, each with it's own unique viability value. Again, You can give any arbitrary description of this particular game or specific details about it's constituents, so long as you follow the 3 axioms. What you're up against in this proof, is that you have a total of 26 choices in the current diversity pool (for each mode). You need to show that you can have no less than 26 choices when you remove a choice from this system in order to prove me wrong.

The system might be larger but it is still simple, it's still just a list of letters. Size =/= complexity

You're still setting up a scenario that doesn't resemble anything, that's just a list of letters essentially. Obviously if you have choices that are clearly ranked from best>worst removing an option changes absolutely nothing. You have only 1 choice in all of these modes, I could remove 25 of the letters and nothing would change. When there's a clear best choice, then there's no other choice, you should know this since you love game theory so much.

Setting up a scenario explicitly to make proving something impossible generally not how proofs happen.

A more correct example would be something along the lines of

A > B = C = D = E = F > G = H = I = J >K >L > M

Now clearly removing A from this list means that BCDEF are all now viable picks, meaning theres 5 options instead of just 1.

Now thankfully GW2 and other complex games ideally has a large number of choices where there's no clear "best" choice, what is the best in gw2 depends on the current meta, your group comp, what your goal is etc etc.

The choices that can be argued to be correct are usually different enough from each other that they're hard to make direct comparisons between.

Anyway your favorite activity in the world is RPS, so let's take an example of RPS

originally it has
P>R>S>P>etc
each option gives you 1/3rd of a chance of winning, essentially it doesn't matter what word you say, but there's 3 words you can say that are all equally "good" to say.

Lets add G to RPS
G beats R and P and S
Now we added 1 option, yet every single time both participants will pick G, because everything else is "worse". We added an option and diversity went down.
Then we remove the option and diversity goes up again and all 3 alternatives are once again 1/3rd chance of winning (as opposed to 100% of the time a draw)

Now RPS is a terrible example really because it has absolutely no similarities to any complex game, but it's your favorite thing so I figured I'd include it to make you happy.

Now onto an actual (complex) game. I am gonna assume you at least know what Magic: The Gathering is, otherwise it's a card game with roughly 15000 cards. The game has various formats, the one I am bringing up is called "Modern", that limits the cardpool by a few thousands cards.

Anyway this format usually has no clear "best deck" and the highest % of the meta a deck usually gets to is between 5-10%, meaning that there's 10-15 common decks (with minor variations) and then a couple dozen less common decks to face.

During early 2016 a single type of deck had a 40-50% metashare and the the majoriy of the rest of the field was decks made specifically to beat it (but who clearly failed at it), the period was called "Eldrazi Winter" due to how dominant it was.

In april 2016 they banned a card from the most dominant deck and the meta went back to the most popular decks having 5-10% of the meta. I can find a source if you really like, but i doubt that's what you're gonna argue.

There we go, real world example of a situation where removing an option from a complex system increased diversity. Something happening is a proof that it can happen.

Removing stacking sigils is obviously much less dramatic as the meta doesn't revolve around them (as they're just a small part of a build), but it would mean that there's 3-5 options I am considering for that sigil slot on all builds where I previously had a stacking sigil (which was most of them, where the stacking sigil usually wasn't even something that I'd ever consider swapping out). Hence removing them would increase diversity in this particular area.

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@lodjur.1284 said:
You're still setting up a scenario that doesn't resemble anything, that's just a list of letters essentially. Obviously if you have choices that are clearly ranked from best>worst removing an option changes absolutely nothing. You have only 1 choice in all of these modes, I could remove 25 of the letters and nothing would change. When there's a clear best choice, then there's no other choice, you should know this since you love game theory so much.

A more correct example would be something along the lines of

A > B = C = D = E = F > G = H = I = J >K >L > M

Now clearly removing A from this list means that BCDEF are all now viable picks, meaning theres 5 options instead of just 1.

See you've went and changed one of the axioms...but that's okay, ill explain why your "more correct example" is actually just my proof from earlier.

Let's say i was a developer, and i had managed to get the game into the following state:
A>B=C=D=E=F=G=H=I=J=K=L=M=N=O=P=Q=R=S=T=U=V=W=X=Y=Z

The first assumption you are making about this system is that B...Z are all the same, which implies that they aren't different which is realistically impossible. If sigil B is a +400 power sigil, then C must also be a +400 power sigil. Already you are seeing the issue with that right? In order for them all to be equal, they must all be the same, and if they are all the same then they really aren't choices now are they? The moment you introduce any differences between the sigils, for one mode or the other, one sigil will be better than another in some form or fashion, and that's why the previous axiom of A>B>C>D... and so on is a more accurate portrayal of a system with choices, even if the details of that system are arbitrary. Like i said in the first comment on this thread, it is impossible to equally balance distinctly different choices for this reason alone.

Now the actual fun part, is that you believe that you have only one choice which is A. This is already a false assumption because there are 26 total choices....but let's just say that you were right...that A means the diversity pool goes to 1, and that by removing it you have the diversity pool increase back to 25. So now you have 25 choices instead of 26 like you had originally. Instead of just REMOVING A which gives you 1 less choice in the diversity pool, you could have just changed A to be EQUAL to B,C,D etc... and you could have maintained 26 total choices.

Like i said, and what you still aren't able to prove it that, you will NEVER get more than 26 choices by removing one of them...it is MATHEMATICALLY impossible. and even in the situation where you have 1 clear best choice, you could have just CHANGED THE SIGIL to compete with the other sigils, or change the other sigils to compete with it by basically making all the signs into equal signs. This was MY proof from one of my earlier comments.

Anyway your favorite activity in the world is RPS, so let's take an example of RPS

originally it has
P>R>S>P>etc
each option gives you 1/3rd of a chance of winning, essentially it doesn't matter what word you say, but there's 3 words you can say that are all equally "good" to say.

Lets add G to RPS
G beats R and P and S
Now we added 1 option, yet every single time both participants will pick G, because everything else is "worse". We added an option and diversity went down.
Then we remove the option and diversity goes up again and all 3 alternatives are once again 1/3rd chance of winning (as opposed to 100% of the time a draw)

Once you add G, the diversity pool (the choices you now have) is 4, not 3. No matter how good of a choice G is, the diversity pool goes up to 4. Removing G reduces it to 3, which is net loss from 4.

What you could have done instead is just change G to defeat R, and make P defeat G. That way you can keep your new diversity pool of 4...

Anyway, i suppose that's where you are having fundamental mis-understanding...that because something is oppressive means that total diversity pool goes down. This isn't exactly wrong. You can have localized drops in diversity...but in sum-total, you are reducing diversity as a whole by removing elements from it. Like i said your proof has to beat my proof, which is that you need to get your diversity pool up to 4 in this particular case, which still you haven't been able to do, so i'm still waiting for that.

Now onto an actual (complex) game. I am gonna assume you at least know what Magic: The Gathering is, otherwise it's a card game with roughly 15000 cards. The game has various formats, the one I am bringing up is called "Modern", that limits the cardpool by a few thousands cards.

Anyway this format usually has no clear "best deck" and the highest % of the meta a deck usually gets to is between 5-10%, meaning that there's 10-15 common decks (with minor variations) and then a couple dozen less common decks to face.

During early 2016 a single type of deck had a 40-50% metashare and the the majoriy of the rest of the field was decks made specifically to beat it (but who clearly failed at it), the period was called "Eldrazi Winter" due to how dominant it was.

In april 2016 they banned a card from the most dominant deck and the meta went back to the most popular decks having 5-10% of the meta. I can find a source if you really like, but i doubt that's what you're gonna argue.

And Magic the Gathering is a physical card game...it's not exactly easy to balance a card game where the physical cards have already been distributed out to the public. Changing effects on cards that people already own? How would you go about that exactly? Do you have card police that go into everyone's house to scribble the new effects on the cards while i'm sleeping?

In this case like above, it's because they have no choice but to ban cards as a form of control over their physically distributed card system.
In other situations where things get "Smiter's Booned" in online games, you should know that changes like these are known as the "lazy dev's" way of trying to fix a problem...instead of actually trying to balance a skill, they would rather delete it from the game and not bother actually balancing it at the cost of the diversity in the game. Why do you think people are so mad about the recent changes to 300 second passive effects? They effectively smiter's booned them instead of just giving us new abilities, or reworking existing ones.

@lodjur.1284 said:
You're still setting up a scenario that doesn't resemble anything, that's just a list of letters essentially. Obviously if you have choices that are clearly ranked from best>worst removing an option changes absolutely nothing. You have only 1 choice in all of these modes, I could remove 25 of the letters and nothing would change. When there's a clear best choice, then there's no other choice, you should know this since you love game theory so much.

A more correct example would be something along the lines of

A > B = C = D = E = F > G = H = I = J >K >L > M

Now clearly removing A from this list means that BCDEF are all now viable picks, meaning theres 5 options instead of just 1.

See you've went and changed one of the axioms...but that's okay, ill explain why your "more correct example" is actually just my proof from earlier.

Let's say i was a developer, and i had managed to get the game into the following state:
A>B=C=D=E=F=G=H=I=J=K=L=M=N=O=P=Q=R=S=T=U=V=W=X=Y=Z

The first assumption you are making about this system is that B...Z are all the same, which implies that they aren't different which is realistically impossible. If sigil B is a +400 power sigil, then C must also be a +400 power sigil. Already you are seeing the issue with that right? In order for them all to be equal, they must all be the same, and if they are all the same then they really aren't choices now are they? The moment you introduce any differences between the sigils, for one mode or the other, one sigil will be better than another in some form or fashion, and that's why the previous axiom of A>B>C>D... and so on is a more accurate portrayal of a system with choices, even if the details of that system are arbitrary. Like i said in the first comment on this thread, it is impossible to equally balance distinctly different choices for this reason alone.

Now the actual fun part, is that you believe that you have only one choice which is A. This is already a false assumption because there are 26 total choices....but let's just say that you were right...that A means the diversity pool goes to 1, and that by removing it you have the diversity pool increase back to 25. So now you have 25 choices instead of 26 like you had originally. Instead of just REMOVING A which gives you 1 less choice in the diversity pool, you could have just changed A to be EQUAL to B,C,D etc... and you could have maintained 26 total choices.

That's just the illusion of choice, options need to be reasonably balanced with each other (not perfectly balanced but at least to the point where you can't "prove" that A>B) for there to be an actual choice.

Like i said, and what you still aren't able to prove it that, you will NEVER get more than 26 choices by removing one of them...it is MATHEMATICALLY impossible. and even in the situation where you have 1 clear best choice, you could have just CHANGED THE SIGIL to compete with the other sigils, or change the other sigils to compete with it by basically making all the signs into equal signs. This was MY proof from one of my earlier comments.

You never had a proof of anything except that in an environment that can be described as RPS then removing an option reduces diversity, to which noone has said anything else.

You can't make up constraints to make things fit your imagination, that's not a proper way to go about proofs. Obviously it's possible to setup conditions that make proving anything impossible.

That you can change it compete with other sigils sigils is obvious. But the design itself is problematic, reworking it into something completely different is the same as removing it.

Anyway your favorite activity in the world is RPS, so let's take an example of RPS

originally it has
P>R>S>P>etc
each option gives you 1/3rd of a chance of winning, essentially it doesn't matter what word you say, but there's 3 words you can say that are all equally "good" to say.

Lets add G to RPS
G beats R and P and S
Now we added 1 option, yet every single time both participants will pick G, because everything else is "worse". We added an option and diversity went down.
Then we remove the option and diversity goes up again and all 3 alternatives are once again 1/3rd chance of winning (as opposed to 100% of the time a draw)

Once you add G, the diversity pool (the choices you now have) is 4, not 3. No matter how good of a choice G is, the diversity pool goes up to 4. Removing G reduces it to 3, which is net loss from 4.

Running with no sigils and naked is technically an option, yet it is always clearly incorrect. You're later on whining about how they "removed" the passive invulnerabilities/stunbreaks, by this logic they are still there.

What you could have done instead is just change G to defeat R, and make P defeat G. That way you can keep your new diversity pool of 4...

So you change completely what the piece does, keeping nothing but it's name? That's a complete rework, the original piece was deleted and you added a new one on it's place.

Anyway, i suppose that's where you are having fundamental mis-understanding...that because something is oppressive means that total diversity pool goes down. This isn't exactly wrong. You can have localized drops in diversity...but in sum-total, you are reducing diversity as a whole by removing elements from it. Like i said your proof has to beat my proof, which is that you need to get your diversity pool up to 4 in this particular case, which still you haven't been able to do, so i'm still waiting for that.

There's nothing localized about it, diversity goes down when an oppressive option is added. Sometimes you can nerf, sometimes the design is horrible and removing it is a better move.

That's not how proofs work. You don't get to dictate a bunch of random rules for proofs to fulfill, as long as it proves that diversity can increase by removing something it's a valid proof here.

Now onto an actual (complex) game. I am gonna assume you at least know what Magic: The Gathering is, otherwise it's a card game with roughly 15000 cards. The game has various formats, the one I am bringing up is called "Modern", that limits the cardpool by a few thousands cards.

Anyway this format usually has no clear "best deck" and the highest % of the meta a deck usually gets to is between 5-10%, meaning that there's 10-15 common decks (with minor variations) and then a couple dozen less common decks to face.

During early 2016 a single type of deck had a 40-50% metashare and the the majoriy of the rest of the field was decks made specifically to beat it (but who clearly failed at it), the period was called "Eldrazi Winter" due to how dominant it was.

In april 2016 they banned a card from the most dominant deck and the meta went back to the most popular decks having 5-10% of the meta. I can find a source if you really like, but i doubt that's what you're gonna argue.

And Magic the Gathering is a physical card game...it's not exactly easy to balance a card game where the physical cards have already been distributed out to the public. Changing effects on cards that people already own? How would you go about that exactly? Do you have card police that go into everyone's house to scribble the new effects on the cards while i'm sleeping?

Yet it's still an example of where removing an option increased diversity in a game, something you said was "mathematically impossible"

It can be balanced in hindsight by issuing functional errata, they try to avoid it but it has happened on a few occasions.

In this case like above, it's because they have no choice but to ban cards as a form of control over their physically distributed card system.

Actually what they can and sometimes do is ban a card then later release a weaker version of it. Yet some designs are simply mistakes that can't exist in a balanced form (ie making a weaker version would either make it useless or still broken)

In other situations where things get "Smiter's Booned" in online games, you should know that changes like these are known as the "lazy dev's" way of trying to fix a problem...instead of actually trying to balance a skill, they would rather delete it from the game and not bother actually balancing it at the cost of the diversity in the game. Why do you think people are so mad about the recent changes to 300 second passive effects? They effectively smiter's booned them instead of just giving us new abilities, or reworking existing ones.

The various free invulns and stunbreaks are horrible designs.

I think changing their CD to 300 and "removing" them is a better decision than leaving them as they are.

Some designs are mistakes, trying to balance a mistake into your system isn't actually ideal. Stacking sigils I would day is a design mistake, because they work fundamentally different from every other sigil and create tedious and annoying situations, them being balanced (which would require a minor rework anyway) doesn't change that.

Obviously the perfect solution would be to actually remove them and add completely new traits in their place which I believe anet will do eventually. But yes keeping "useless" traits in the game isn't ideal. But it sure beats having these awful mistakes around. Doesn't necessarily reduce diversity though.

Also people are just mad because they lost their passive "get-out-jail-free-cards".

"instead of just giving us new abilities, or reworking existing ones."
They can't make new traits without removing old ones, they're most likely working on new ones, but neither of us knows this.

Ögonen omges av vita och svarta penseldrag som gör att de ser större ut än vad de egentligen är. Baksidan av lodjurets öron kantas av svart päls som slutar i den karaktäristiska tofsen högst upp på örat. Lodjurets svans är kortare än de flesta andra kattdjurs.

## Comments

No the wiki articles aren’t contradicting...

Like I said, game theory is well established by people that win Nobel prizes and have PH’Ds in the subject...and you think that THEY are wrong about what games are and aren’t?

You think wiki cares enough about gw2 to list it in the wiki article? You think that game theory doesn’t apply to complex systems, when it applies to evolutionary biology, Which is one of the most complex systems known to exist?

Here’s a YouTube video that shows that RPS is the heart of almost all games today

By that logic any amount of time you spend outside of WvW is a tradeoff and actively harmful...

Well in duels stacking sigils are actually not allowed.

Well after clearing 1 camp they outpace force/bursting.

Corruption is equally strong

It's seen on a majority of builds in roaming/smallscale (and zerging too when people have actual build there) >

Has any of these people classified RPS as a game?

I never said game theory didn't, I said RPS doesn't apply to complex systems.

But if you honestly believe that RPS applies to evolutionary biology then ye.....

Random YouTube video that I will never watch cause videos are the worst form of information.

Ögonen omges av vita och svarta penseldrag som gör att de ser större ut än vad de egentligen är. Baksidan av lodjurets öron kantas av svart päls som slutar i den karaktäristiska tofsen högst upp på örat. Lodjurets svans är kortare än de flesta andra kattdjurs.

I'd be happy if they:

1: Would not lose stacks on switching maps (such a silly implementation from the beginning). Really annoying to build up 25 stacks then have to move to a different borderland/EBG to help defend and poof -- there goes your stack.

2: Would build stacks as long as you have it equipped on one of your weapon sets. Swapping to the actual weapon is a pain.

That solution would at least fix the worst problem with the stacking sigils which is how they're mandatory and annoying. Now at least they wouldn't be annoying anymore. I am all for it

Ögonen omges av vita och svarta penseldrag som gör att de ser större ut än vad de egentligen är. Baksidan av lodjurets öron kantas av svart päls som slutar i den karaktäristiska tofsen högst upp på örat. Lodjurets svans är kortare än de flesta andra kattdjurs.

Game theory was developed in the 1950's...before computer games...and RPS has existed for nearly 2000 years, as it was one of the first games ever created...

Quote from the RPS Article:"Rock paper scissors is a

hand gameusually played between two people... (It is ) a simultaneous, zero-sum game, (and) has only two possible outcomes: a draw, or a win for one player and a loss for the other."Quote from the Game Theory Article:"Modern game theory began with the idea of mixed-strategy equilibria in two-person zero-sum games and its proof by

John von Neumann."Quote from Von Neumann Article:"Von Neumann founded the field of game theory as a mathematical discipline.[97] Von Neumann proved his minimax theorem in 1928. This theorem establishes that in zero-sum games with perfect information (i.e. in which players know at each time all moves that have taken place so far), there exists a pair of strategies for both players that allows each to minimize his maximum losses, hence the name minimax. When examining every possible strategy, a player must consider all the possible responses of his adversary. The player then plays out the strategy that will result in the minimization of his maximum loss.[98] Such strategies, which minimize the maximum loss for each player, are called optimal....Von Neumann improved and extended the minimax theorem to include games involving imperfect information and games with more than two players, publishing this result in his 1944 Theory of Games and Economic Behavior."

You owe your VOCABULARY in modern gaming to physicists/mathematican like Von Neumann. Min-max, metagame, optimal... these words come from his contributions to game theory, and it's not a coincidence we use these words in our vocabulary when playing games like gw2. So yes, Von Neumann,

if he were still alive, probably would consider RPS as a game, since it is a ZERO SUM GAME by definition, if that wasn't the first game he actually looked at when he went and wrote his thesis on game theory.You say you think of yourself as a math-guy who's calculated the efficiencies of stacking sigils

yada yada yada... and yet you show little regard to people in the field who've actually laid the ground work for you to even do maths in this game in the first place? Blows my mind.Oh and to address this:

Quote from the Game Theory Article: "...Game theory was developed extensively in the 1950s by many scholars. It was explicitly applied to biology in the 1970s"

Yea Game theory and even by proxy RPS, applies to biology... It has it's own page too if you want to read that also https://en.wikipedia.org/wiki/Evolutionary_game_theory

it also happens to have it's own dedicated section to RPS... Quote from Evolutionary game theory article:

Unstable games, cyclic patternsRock paper scissors"An evolutionary game that turns out to be a children's game is rock paper scissors...Rock paper scissors incorporated into an evolutionary game has been used for modelling natural processes in the study of ecology.[41] Using experimental economics methods, scientists have used RPS game to test human social evolutionary dynamical behaviors in laboratory. The social cyclic behaviors, predicted by evolutionary game theory, have been observed in various laboratory experiments.[42][43]"

Who coined various terms isn't really relevant to any of the matters at hand.

Here's an interesting piece of information, not all zero-sum games are actually games, but I am sure you knew that.

"In game theory and economic theory, a zero-sum game is a mathematical representation of a situation in which each participant's gain or loss of utility is exactly balanced by the losses or gains of the utility of the other participants."

Followed by an example of a zero-sum game that isn't a game

"Thus, cutting a cake, where taking a larger piece reduces the amount of cake available for others as much as it increases the amount available for that taker, is a zero-sum game if all participants value each unit of cake equally (see marginal utility)..

https://en.m.wikipedia.org/wiki/Zero-sum_game

But idk maybe you consider cutting a cake a game?

Also we've established a pattern here, not only do you try to speak for me now you try to speak on behalf of your personal hero "Von Neumann". That's ironic given that you're accusing me of being disrespectful.

Nope that's still just you claiming I said a bunch of kitten I didn't.

Why must you try to speak for me? First off whether I hold any regard for someone or not is utterly irrelevant. Secondly I have not in anyway expressed my thoughts on the matter.

Also the math that shows that corruption > better than corruption isn't exactly the kinda math that needs any groundwork.

I never said game theory didn't. I said RPS didn't, it's getting increasingly frustrating to have you attribute claims to me that I have never made. Refute what I say not what you imagine/wish I said. Also things just don't apply by proxy.

Fair enough, it can be used to describe a type of situations in a simple way. Thankfully I am a big enough person to admit when I am wrong. But still not gonna accept you trying to put words into my mouth when I've said nothing of the kind.

Ögonen omges av vita och svarta penseldrag som gör att de ser större ut än vad de egentligen är. Baksidan av lodjurets öron kantas av svart päls som slutar i den karaktäristiska tofsen högst upp på örat. Lodjurets svans är kortare än de flesta andra kattdjurs.

You still can't accept that fact that you were wrong...but you being wrong is not at all what bugs me about every post you've made so far. It's that your comment(s) clearly illustrates disregard for ACTUAL mathematics, and misuse of information without actually researching it. Remember the initial point here was that diversity always decreases as you remove choices, and i said that this WAS NOT an opinion...and you constantly tried to argue against that using your own personal biases/conclusions rather than doing the research. Posts like yours, is how misinformation develops and THAT is what really bothers me.

incorrect again. You CAN make cutting a cake into a game too... in fact you can make a game out of practically any situation, the only requirement is that it must have rational agents as participants to make decisions, and it doesn't even have to be zero-sum either. But, ALL zero-sum games are games. Again this isn't for debate this is FACTS backed by decades of research in the field with people who get payed 10x your paycheck and my paycheck to research exactly these things.

And, again, this is your opinion showing and not actually doing the research, or even attempting to understand the subject area that games like gw2 are built upon. This is why you aren't a developer and if you were, i can predict with 99% certainty you'd throw the game into complete clown-fiesta. If you really actually wanted to make a suggestion based on data and analysis, then you'd at least do everyone the courtesy of watching that linked video, and reading up on game theory. Introductory game balance 101 right there just for you...trying to make it easier for you...but if you want to remain willfully ignorant? i can't control that, that's on you.

Edit: Last thing, Von Neuman isn't my "personal hero," he is one of the defining mathematicians/physicists of the century, and he is on the same pedestal as mathematicians like Alan Turing and Issac Newton, and physicists like Einstein, R. Feynman. To think that they don't know what they were talking about is tantamount to saying the Earth is flat.

I just did, I said "I was wrong about this", that's literally accepting the fact that I was wrong about something. You saying it isn't says more about you than it does about me.

None of your posts actually contains any mathematics so I am not really disregarding it

It is not an opinion, it is actually a fact that removing choices can increase diversity. There is proof of this.

"Remember the initial point here was that diversity always decreases as you remove choices, and i said that this WAS NOT an opinion"

Your claim is that "Diversity always decrease as your remove choices". For this statement to not be proven false there can't have been a single instance of diversity increasing in a game after an option has been removed. This is an incredibly bold claim, especially as there's no proof for it.

Now sadly we can't really use guild wars 2 for this as there's very little data on the metagame historically in guild wars 2. So we'd have to resort to looking at other games to disprove this, but since it's a general statement it doesn't actually matter what game the proof comes from.

I can try to find data from some other game (I even have one in mind) that proves this if you want me to find it, but as that would be incredibly ot and would most likely be a game you haven't played making any discussion of the "proof" kinda weird I am not sure how much that would help.

You could ofc have a game centered around the cutting of a cake, but that's not the situation being described (or in general what cutting a cake is).

Actually that's not the wikipedia definition of a game. I linked that one earlier.

What you wrote is the definition of the kind of situation that game theory is the study of. These two things aren't always the exact same thing (even if they often are). Otherwise you'd have to say that there's some amount of ambiguity to the term "game" which is a reasonable stance to take, but hardly the one you've been pushing.

I never said all games have to be zero-sum, I said all zero-sum games aren't games. You're making false claims about what I've said again.

Again with the personal insults and throwing random numbers around about my paycheck. This is incredibly ironic given a few quotes from you such as:

"Posts like yours, is how misinformation develops and THAT is what really bothers me."

"you constantly tried to argue against that using your own personal biases/conclusions rather than doing the research"

"This is why you aren't a developer and if you were, i can predict with 99% certainty you'd throw the game into complete clown-fiesta"

Do you see the irony? You're saying that my post spreads misinformation while throwing things you have absolutely no basis for out there as facts.

GW2 doesn't really share many similarities with RPS actually. That there is some amount of game theory behind the construction of gw2 I've never denied, but that the core of it would be a 3 option coinflip I will definitively dispute.

Well you actually have no clue whether I am a developer or not, this is just you making a guess.

Then we get to some random percentage number about how a hypothetical game that I would be a developer would be a "clown-fiesta", I am curious how did you get to 99%?

Videos are a terrible source of information on this type of topics.

If you write (and link) an article detailing what's said in the video I will probably read it.

I hope you can see the problems with labeling everyone who doesn't agree with you "willfully ignorant"

Also claiming someone is uneducated on a subject is generally a very poor argument, especially when you actually have no clue how informed I am on the topic.

You keep saying that I've said he doesn't know what he is talking about, but I have never said that, I only said trivia about him is irrelevant to the discussion at hand.

But he clearly is your personal hero, you jump to his "defense" even when there was absolutely nothing bad said about him. I never said he was wrong (or that he was right) about anything, in fact I haven't actually said anything about him except for two things

Neither of these statements are false, my personal thoughts on him is irrelevant.

There's no need to get so emotional, in general getting emotional and throwing insults isn't conductive to a good discussion or to making logical decisions. Try to keep the name calling to a minimum and try not to speak for anyone, it really helps move this forward in a civilized and productive manner.

I've already proved my point using RPS, which you so blatantly disregarded, due to your lack of knowledge on "games" ... but, here. I'll help you out, by helping you PROVE your conjecture.

You have 3 choices, that follow 2 Axioms.

1) There are 3 choices: X,Y, and Z

2) X is better than Y, and Y is better than Z.

This is now, where you have to prove, that removing one of these choices will yield more diversity. You can give any arbitrary description of this particular game or specific details about it's constituents, so long as you follow the 2 axioms. What you're up against in your proof, is that you have a total of 3 choices in the current diversity pool. You need to show that you can have at least 3 choices in whatever changes you make to this system in order to prove me wrong....so now go head.

Actually the only thing you've proven is that in RPS removing one of the pieces is a bad idea, which I don't think anyone has disputed.

What you haven't done is prove that for a complex game with a very large number of options (like guild wars 2 for example) removing an option can't increase diversity.

There's no reason my diversity pool only needs to have 3 options, GW2 doesn't only have 3 options, gw2 has somewhere between 70-100 sigils (now ofc not all of them are good, there's a ton of sigils that are a meme like sigil of luck, centaur slaying or w/e).

You can't just extrapolate that way, it doesn't work.

So until we can agree on this simple fact I am not gonna put any effort into a proof since you're just gonna dismiss it on the premise that it doesn't meet your constraints that make absolutely no sense given the situation (which is talking about diversity in a game with many choices, not one with only 3 choices)

lol, typical i should have expected as much.

This is what you are saying in a nutshell:

"I can't prove my point because it will only work on a more complex game." followed by "Gw2 is too complex so i can't prove my point."

BTW, extrapolation is doing exactly what i am trying to get you to do. You take the consequences of what happens on a smaller scale and EXTRAPOLATE that to a larger scale....because the two are fundamentally the same thing...that's how extrapolation works. Analyzing the consequences of a game with 3 choices, yield the same consequences of a game with a hundred or a million choices.

So i'm gonna help you AGAIN. Let's take those axioms and change em'...JUST FOR YOU (so you can quit being a baby about it), so that there are a lot more choices. Once again, here are the axioms:

You have 26 choices, that follow 3 Axioms.

1) There are 26 choices: A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z.

2) In one mode of this game, the following choices are ranked from best to worst in MODE 1

A > B > C > D > E > F > G > H > I > J >K >L > M > N > O > P > Q > R > S >T >U > V > W > X > Y > Z

3) In another mode of this game, the following choices are ranked from best to worst in MODE 2

Z > Y > X > W > V > U > T > S > R > Q >P >O> N > M> L > K > J > I> H > G > F > E > D > C > B > A

Now is that complex enough for you? I've given you two separate modes, each with it's own unique viability value. Again, You can give any arbitrary description of this particular game or specific details about it's constituents, so long as you follow the 3 axioms. What you're up against in this proof, is that you have a total of 26 choices in the current diversity pool (for each mode). You need to show that you can have no less than 26 choices when you remove a choice from this system in order to prove me wrong.

Big brain move. Bring back Demon Summoning Stacking sigils so I can care about WvW again. Keep shattered aegis nerfed though.

Holy Warriors of [Kazo] following Kazo doctrine guided by, Our Lord and Commander, Zudo in the holy Trinity of Him and his two firm glutes.

I never said that I can't prove my point cause gw2 is too complex, I said there's no data on metagame changes.

That's a false premise actually, in some cases one can extrapolate a small system to a larger system, but that requires the systems to otherwise be identical, which isn't the case. RPS is an extremely simple system where every choice is exactly equally good and it's quantifiable, you can't easily quantify how good the most of the various sigils in gw2 are compared to each other. Only ones like bursting vs corruption, bloodlust vs force vs demon slaying, benevolance vs transference etc.

The system might be larger but it is still simple, it's still just a list of letters. Size =/= complexity

You're still setting up a scenario that doesn't resemble anything, that's just a list of letters essentially. Obviously if you have choices that are clearly ranked from best>worst removing an option changes absolutely nothing. You have only 1 choice in all of these modes, I could remove 25 of the letters and nothing would change. When there's a clear best choice, then there's no other choice, you should know this since you love game theory so much.

Setting up a scenario explicitly to make proving something impossible generally not how proofs happen.

A more correct example would be something along the lines of

A > B = C = D = E = F > G = H = I = J >K >L > M

Now clearly removing A from this list means that BCDEF are all now viable picks, meaning theres 5 options instead of just 1.

Now thankfully GW2 and other complex games ideally has a large number of choices where there's no clear "best" choice, what is the best in gw2 depends on the current meta, your group comp, what your goal is etc etc.

The choices that can be argued to be correct are usually different enough from each other that they're hard to make direct comparisons between.

Anyway your favorite activity in the world is RPS, so let's take an example of RPS

originally it has

P>R>S>P>etc

each option gives you 1/3rd of a chance of winning, essentially it doesn't matter what word you say, but there's 3 words you can say that are all equally "good" to say.

Lets add G to RPS

G beats R and P and S

Now we added 1 option, yet every single time both participants will pick G, because everything else is "worse". We added an option and diversity went down.

Then we remove the option and diversity goes up again and all 3 alternatives are once again 1/3rd chance of winning (as opposed to 100% of the time a draw)

Now RPS is a terrible example really because it has absolutely no similarities to any complex game, but it's your favorite thing so I figured I'd include it to make you happy.

Now onto an actual (complex) game. I am gonna assume you at least know what Magic: The Gathering is, otherwise it's a card game with roughly 15000 cards. The game has various formats, the one I am bringing up is called "Modern", that limits the cardpool by a few thousands cards.

Anyway this format usually has no clear "best deck" and the highest % of the meta a deck usually gets to is between 5-10%, meaning that there's 10-15 common decks (with minor variations) and then a couple dozen less common decks to face.

During early 2016 a single type of deck had a 40-50% metashare and the the majoriy of the rest of the field was decks made specifically to beat it (but who clearly failed at it), the period was called "Eldrazi Winter" due to how dominant it was.

In april 2016 they banned a card from the most dominant deck and the meta went back to the most popular decks having 5-10% of the meta. I can find a source if you really like, but i doubt that's what you're gonna argue.

There we go, real world example of a situation where removing an option from a complex system increased diversity. Something happening is a proof that it can happen.

Removing stacking sigils is obviously much less dramatic as the meta doesn't revolve around them (as they're just a small part of a build), but it would mean that there's 3-5 options I am considering for that sigil slot on all builds where I previously had a stacking sigil (which was most of them, where the stacking sigil usually wasn't even something that I'd ever consider swapping out). Hence removing them would increase diversity in this particular area.

They'll be slightly better due to damage making skills harder to pull off but hardly op.

Shield of Wrath: Reduced the cooldown of this skill from 36 seconds to 35 seconds.

Quality balance changes^TM

See you've went and changed one of the axioms...but that's okay, ill explain why your "more correct example" is actually just my proof from earlier.

Let's say i was a developer, and i had managed to get the game into the following state:

A>B=C=D=E=F=G=H=I=J=K=L=M=N=O=P=Q=R=S=T=U=V=W=X=Y=Z

The first assumption you are making about this system is that B...Z are all the same, which implies that they aren't different which is realistically impossible. If sigil B is a +400 power sigil, then C must also be a +400 power sigil. Already you are seeing the issue with that right? In order for them all to be equal, they must all be the same, and if they are all the same then they really aren't choices now are they? The moment you introduce any differences between the sigils, for one mode or the other, one sigil will be better than another in some form or fashion, and that's why the previous axiom of A>B>C>D... and so on is a more accurate portrayal of a system with choices, even if the details of that system are arbitrary. Like i said in the first comment on this thread, it is impossible to equally balance distinctly different choices for this reason alone.

Now the actual fun part, is that you believe that you have only one choice which is A. This is already a false assumption because there are 26 total choices....but let's just say that you were right...that A means the diversity pool goes to 1, and that by removing it you have the diversity pool increase back to 25. So now you have 25 choices instead of 26 like you had originally. Instead of just REMOVING A which gives you 1 less choice in the diversity pool, you could have just changed A to be EQUAL to B,C,D etc... and you could have maintained 26 total choices.

Like i said, and what you still aren't able to prove it that, you will NEVER get more than 26 choices by removing one of them...it is MATHEMATICALLY impossible. and even in the situation where you have 1 clear best choice, you could have just CHANGED THE SIGIL to compete with the other sigils, or change the other sigils to compete with it by basically making all the signs into equal signs. This was MY proof from one of my earlier comments.

Once you add G, the diversity pool (the choices you now have) is 4, not 3. No matter how good of a choice G is, the diversity pool goes up to 4. Removing G reduces it to 3, which is net loss from 4.

What you could have done instead is just change G to defeat R, and make P defeat G. That way you can keep your new diversity pool of 4...

Anyway, i suppose that's where you are having fundamental mis-understanding...that because something is oppressive means that total diversity pool goes down. This isn't exactly wrong. You can have localized drops in diversity...but in sum-total, you are reducing diversity as a whole by removing elements from it. Like i said your proof has to beat my proof, which is that you need to get your diversity pool up to 4 in this particular case, which still you haven't been able to do, so i'm still waiting for that.

And Magic the Gathering is a physical card game...it's not exactly easy to balance a card game where the physical cards have already been distributed out to the public. Changing effects on cards that people already own? How would you go about that exactly? Do you have card police that go into everyone's house to scribble the new effects on the cards while i'm sleeping?

In this case like above, it's because they have no choice but to ban cards as a form of control over their physically distributed card system.

In other situations where things get "Smiter's Booned" in online games, you should know that changes like these are known as the "lazy dev's" way of trying to fix a problem...instead of actually trying to balance a skill, they would rather delete it from the game and not bother actually balancing it at the cost of the diversity in the game. Why do you think people are so mad about the recent changes to 300 second passive effects? They effectively smiter's booned them instead of just giving us new abilities, or reworking existing ones.

That's just the illusion of choice, options need to be reasonably balanced with each other (not perfectly balanced but at least to the point where you can't "prove" that A>B) for there to be an actual choice.

You never had a proof of anything except that in an environment that can be described as RPS then removing an option reduces diversity, to which noone has said anything else.

You can't make up constraints to make things fit your imagination, that's not a proper way to go about proofs. Obviously it's possible to setup conditions that make proving anything impossible.

That you can change it compete with other sigils sigils is obvious. But the design itself is problematic, reworking it into something completely different is the same as removing it.

Running with no sigils and naked is technically an option, yet it is always clearly incorrect. You're later on whining about how they "removed" the passive invulnerabilities/stunbreaks, by this logic they are still there.

So you change completely what the piece does, keeping nothing but it's name? That's a complete rework, the original piece was deleted and you added a new one on it's place.

There's nothing localized about it, diversity goes down when an oppressive option is added. Sometimes you can nerf, sometimes the design is horrible and removing it is a better move.

That's not how proofs work. You don't get to dictate a bunch of random rules for proofs to fulfill, as long as it proves that diversity can increase by removing something it's a valid proof here.

Yet it's still an example of where removing an option increased diversity in a game, something you said was "mathematically impossible"

It can be balanced in hindsight by issuing functional errata, they try to avoid it but it has happened on a few occasions.

Actually what they can and sometimes do is ban a card then later release a weaker version of it. Yet some designs are simply mistakes that can't exist in a balanced form (ie making a weaker version would either make it useless or still broken)

The various free invulns and stunbreaks are horrible designs.

I think changing their CD to 300 and "removing" them is a better decision than leaving them as they are.

Some designs are mistakes, trying to balance a mistake into your system isn't actually ideal. Stacking sigils I would day is a design mistake, because they work fundamentally different from every other sigil and create tedious and annoying situations, them being balanced (which would require a minor rework anyway) doesn't change that.

Obviously the perfect solution would be to actually remove them and add completely new traits in their place which I believe anet will do eventually. But yes keeping "useless" traits in the game isn't ideal. But it sure beats having these awful mistakes around. Doesn't necessarily reduce diversity though.

Also people are just mad because they lost their passive "get-out-jail-free-cards".

"instead of just giving us new abilities, or reworking existing ones."

They can't make new traits without removing old ones, they're most likely working on new ones, but neither of us knows this.