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The fallacy of "easy" - Page 2

Blogs > SiskosGoatee
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endy
Profile Blog Joined May 2009
Switzerland8970 Posts
Last Edited: 2014-07-08 15:00:07
July 08 2014 14:59 GMT
#21
Can't believe it took so much text, even if I agree with what you are saying, more specifically the first paragraph. The whole problem lies in the definition of "easy". Both statements can describe an "easy race":
Mechanically easy race =/= race easy to win with

ॐ
Big J
Profile Joined March 2011
Austria16289 Posts
Last Edited: 2014-07-08 15:18:37
July 08 2014 15:18 GMT
#22
On July 08 2014 23:59 endy wrote:
Can't believe it took so much text, even if I agree with what you are saying, more specifically the first paragraph. The whole problem lies in the definition of "easy". Both statements can describe an "easy race":
Show nested quote +
Mechanically easy race =/= race easy to win with



That's not his argument at all as far as I understand.
His point is that there is no mechanically easier race to begin with (in a balanced game), because you can always do something more.

So the only reason for "A being universally easier than B" can be that A is plainly better. Because no matter how good B plays, if A plays equally good, he should be able to match what B does and have human resources left over to do more than that.
Rococo
Profile Joined May 2011
United States331 Posts
Last Edited: 2014-07-08 15:41:31
July 08 2014 15:37 GMT
#23
Yes, the skill ceiling is effectively infinite in most complex multiplayer games. What you're ignoring is that an infinite range exists between 1 and 2 just the same as it does 1 and 100. Skill ceiling can exist within a varying scale in terms of reward, which is always balanced against the impact of decisions that are mechanically capped (build order, timings, unit comp).

What makes things complicated is the unknown unknowns in terms of what could be possible strategically but hasn't been discovered yet because player's aren't skill enough, but in terms of the known aspects of the game you can absolutely observe differences in the degree to which mechanical skill levels yield game advantages even though perfect computer-like play wouldn't be possible for anyone.
biology]major
Profile Blog Joined April 2010
United States2253 Posts
Last Edited: 2014-07-08 17:37:38
July 08 2014 17:23 GMT
#24
in SC2 given limited information defending is harder than attacking, period. Races that have more attack options and allins, ie zerg and protoss, vs terran in the early mid game make it so terran can just die. Terran can't really win in early mid game just because of limited options, every game has to be taken to 3 base + and general pressure throughout the game. This actually makes it so that terran is harder to play in the early mid game, while it is equal in mid to late game. Since the allins in sc2 are quite powerful, and you can just die instantly to some random build order which is much harder to defend against than to execute, terran gets the short end of the stick.

edit: evidenced by the poor representation of terran in any of the upper leagues.
Question.?
SiskosGoatee
Profile Blog Joined May 2012
Albania1482 Posts
July 08 2014 18:52 GMT
#25
On July 09 2014 02:23 biology]major wrote:
in SC2 given limited information defending is harder than attacking, period. Races that have more attack options and allins, ie zerg and protoss, vs terran in the early mid game make it so terran can just die. Terran can't really win in early mid game just because of limited options, every game has to be taken to 3 base + and general pressure throughout the game. This actually makes it so that terran is harder to play in the early mid game, while it is equal in mid to late game. Since the allins in sc2 are quite powerful, and you can just die instantly to some random build order which is much harder to defend against than to execute, terran gets the short end of the stick.

edit: evidenced by the poor representation of terran in any of the upper leagues.
Rarely have I seen someone do such an excellent job of making it blatantly clear to reply without having read a fucking word of the OP.
WCS Apartheid cometh, all hail the casual audience, death to merit and hard work.
biology]major
Profile Blog Joined April 2010
United States2253 Posts
Last Edited: 2014-07-08 19:59:15
July 08 2014 18:55 GMT
#26
On July 09 2014 03:52 SiskosGoatee wrote:
Show nested quote +
On July 09 2014 02:23 biology]major wrote:
in SC2 given limited information defending is harder than attacking, period. Races that have more attack options and allins, ie zerg and protoss, vs terran in the early mid game make it so terran can just die. Terran can't really win in early mid game just because of limited options, every game has to be taken to 3 base + and general pressure throughout the game. This actually makes it so that terran is harder to play in the early mid game, while it is equal in mid to late game. Since the allins in sc2 are quite powerful, and you can just die instantly to some random build order which is much harder to defend against than to execute, terran gets the short end of the stick.

edit: evidenced by the poor representation of terran in any of the upper leagues.
Rarely have I seen someone do such an excellent job of making it blatantly clear to reply without having read a fucking word of the OP.


i will admit I didn't read past the first paragraph, only because I am super busy atm, so my apologies. I just wanted to share my thoughts on the subject matter.

ok so after reading all of it, I feel the OP has simplified difficulty of a race solely into APM.

" I'm just saying that the concept of not being overpowered, but being easy does not make sense. If a race is easy it is more powerful. On the assumption that the game is balanced (I am not saying that assumption is true) every race is as easy as every other race."

So I disagree with this point.

So let's create a scenario where there are 2 races. One race is designed in such a way to always be attacking, and the other is designed in such a way to always be defending. My argument is that the race that is designed to attack all the time has it "easier" because it forces the other player to react in terms of long term strategy and in the moment army movement, while at the same time obtaining more information than the other player. They are both using all of their APM to 100%, but the decisions being made by the offensive player are easier to make simply because he has more information. This is why when we see a 6/7 gate blink all in, it seems so easy for one side and so difficult for the other, not only is the build incredibly powerful, but the defending player has to scout properly, then he has to set up his defense, and then he has to execute it.

Now I think it is possible for both of these 2 races to be balanced, meaning the defending player can win 50% of the time. However you can also use my own logic against me and say that the attacking player will inherently win more. Who knows
Question.?
ninazerg
Profile Blog Joined October 2009
United States7291 Posts
July 08 2014 22:20 GMT
#27
On July 08 2014 22:54 Nebuchad wrote:
Let's create a new race, Zerg2. Zerg2 has autocast on queens, and creep puts alerts on the minimap when it detects enemy forces. However, Zerg2's units deal less damage than zerg units.

Zerg2 is easier to play than zerg. You won't be making a ton of macro mistakes, and you won't be caught off guard as easily. Less APM and less attention are required. Now, if I decide that the reduced damage is 95% of the damage zerg units deal, Zerg2 will be favored in zvz2. If I decide it's 20% of the damage zerg units deal, you won't ever win with it.


Wow, I should switch to Zerg2, it seems really strong.
"If two pregnant women get into a fist fight, it's like a mecha-battle between two unborn babies." - Fyodor Dostoevsky
L_Master
Profile Blog Joined April 2009
United States8017 Posts
July 08 2014 22:30 GMT
#28
On July 08 2014 18:25 puppykiller wrote:
So the speed that I have progressed at my offrace protoss in BW is vastly faster than the speed I progressed at my offrace zerg. This is because protoss is a lot easier. Does this mean that zerg is a worse race? No it just means at lower levels protoss is a lot easier and a lot stronger.


No, that does not necessarily follow. I'm not sure how you got to the bolded claim. It could be many other factors, i.e. perhaps protoss play is just more intuitive to you, or fits your natural play-style better.

While the bolded claim could be true, I'm not sure how you reached that claim and eliminated the others.
EffOrt and Soulkey Hwaiting!
ZERG_RUSSIAN
Profile Blog Joined November 2008
10417 Posts
July 09 2014 01:13 GMT
#29
This is dumb. Let's just think of a blatant counter-example.

A tricycle is easier to ride than a motorcycle. A motorcycle takes a lot more skill and knowledge to operate. A motorcycle will basically never lose to a tricycle in a race. The tricycle is easier, the motorcycle is harder to operate. In spite of this, the motorcycle is stronger.

Any questions?
I'm on GOLD CHAIN
SiskosGoatee
Profile Blog Joined May 2012
Albania1482 Posts
Last Edited: 2014-07-09 02:21:11
July 09 2014 02:17 GMT
#30
On July 09 2014 03:55 biology]major wrote:
Show nested quote +
On July 09 2014 03:52 SiskosGoatee wrote:
On July 09 2014 02:23 biology]major wrote:
in SC2 given limited information defending is harder than attacking, period. Races that have more attack options and allins, ie zerg and protoss, vs terran in the early mid game make it so terran can just die. Terran can't really win in early mid game just because of limited options, every game has to be taken to 3 base + and general pressure throughout the game. This actually makes it so that terran is harder to play in the early mid game, while it is equal in mid to late game. Since the allins in sc2 are quite powerful, and you can just die instantly to some random build order which is much harder to defend against than to execute, terran gets the short end of the stick.

edit: evidenced by the poor representation of terran in any of the upper leagues.
Rarely have I seen someone do such an excellent job of making it blatantly clear to reply without having read a fucking word of the OP.


i will admit I didn't read past the first paragraph, only because I am super busy atm, so my apologies. I just wanted to share my thoughts on the subject matter.

ok so after reading all of it, I feel the OP has simplified difficulty of a race solely into APM.

" I'm just saying that the concept of not being overpowered, but being easy does not make sense. If a race is easy it is more powerful. On the assumption that the game is balanced (I am not saying that assumption is true) every race is as easy as every other race."

So I disagree with this point.

So let's create a scenario where there are 2 races. One race is designed in such a way to always be attacking, and the other is designed in such a way to always be defending. My argument is that the race that is designed to attack all the time has it "easier" because it forces the other player to react in terms of long term strategy and in the moment army movement, while at the same time obtaining more information than the other player. They are both using all of their APM to 100%, but the decisions being made by the offensive player are easier to make simply because he has more information. This is why when we see a 6/7 gate blink all in, it seems so easy for one side and so difficult for the other, not only is the build incredibly powerful, but the defending player has to scout properly, then he has to set up his defense, and then he has to execute it.

Now I think it is possible for both of these 2 races to be balanced, meaning the defending player can win 50% of the time. However you can also use my own logic against me and say that the attacking player will inherently win more. Who knows
I really don't see how you justify that when two players have a similar skill level. And it's super difficult for one player, that the winrate will be 50%, that just doesn't make sense.

Like I said, the only way you can salvage this idea is with the IdrA argument of "Yeah, but Protoss players are just dumb!" the excuse of "The players of my race just happen to all be better.", the existence of players of all races who at the very highest level have learnt to master their offraces to be almost as good as their main disputes this idea very much.

On July 09 2014 10:13 ZERG_RUSSIAN wrote:
This is dumb. Let's just think of a blatant counter-example.

A tricycle is easier to ride than a motorcycle. A motorcycle takes a lot more skill and knowledge to operate. A motorcycle will basically never lose to a tricycle in a race. The tricycle is easier, the motorcycle is harder to operate. In spite of this, the motorcycle is stronger.

Any questions?
Tricycle has a skill ceiling that's quickly reached, the entire argument explains why it relies on the assumption that the skill ceiling is infinite.

There comes a point when a tricycle just will not go any faster. The entire point of this article is that it relies on the fact that for all practical purposes there will never be a point where you don't play any better in StarCraft.

A tricycle just won't go faster than a motorcycle. The entire point is that in StarCraft you can beat anyone with any race as long as you're good enough. For every player who is super good, you can theoretically invent a player who is good enough to beat him or her with any race.
WCS Apartheid cometh, all hail the casual audience, death to merit and hard work.
Kashll
Profile Blog Joined May 2008
United States1117 Posts
Last Edited: 2014-07-09 03:47:10
July 09 2014 03:32 GMT
#31
I can only conclude that you do not understand math, or the concept of a "skill/results" graph. (And yes that's even granting you your often (always?) unrealistic precondition of an infinite skill ceiling).

Here is a mathematical example that follows how people intend to use this language and satisfies your precondition:

Let's define a function F, and a function G (for two different races) that maps skill to results.

For Race A, f(x) = x + 5
For Race B, g(x) = x

Note that both race A and race B have an infinite skill ceiling.
Note that for all n in the set of real numbers, f(n) > g(n)

Mathematically this defines a strong example of the concept that Race A is easier to play than Race B
"After silence, that which comes nearest to expressing the inexpressible is music." - Aldous Huxley
L_Master
Profile Blog Joined April 2009
United States8017 Posts
July 09 2014 03:41 GMT
#32
On July 09 2014 10:13 ZERG_RUSSIAN wrote:
This is dumb. Let's just think of a blatant counter-example.

A tricycle is easier to ride than a motorcycle. A motorcycle takes a lot more skill and knowledge to operate. A motorcycle will basically never lose to a tricycle in a race. The tricycle is easier, the motorcycle is harder to operate. In spite of this, the motorcycle is stronger.

Any questions?


If this is serious...
EffOrt and Soulkey Hwaiting!
Kashll
Profile Blog Joined May 2008
United States1117 Posts
Last Edited: 2014-07-09 03:56:06
July 09 2014 03:54 GMT
#33
On July 09 2014 12:32 Kashll wrote:
I can only conclude that you do not understand math, or the concept of a "skill/results" graph. (And yes that's even granting you your often (always?) unrealistic precondition of an infinite skill ceiling).

Here is a mathematical example that follows how people intend to use this language and satisfies your precondition:

Let's define a function F, and a function G (for two different races) that maps skill to results.

For Race A, f(x) = x + 5
For Race B, g(x) = x

Note that both race A and race B have an infinite skill ceiling.
Note that for all n in the set of real numbers, f(n) > g(n)

Mathematically this defines a strong example of the concept that Race A is easier to play than Race B


Now the astute reader may notice that this example does not correspond to the first quote in the original post, namely "Race X is not the most powerful, but it is the easiest."

I attend to address this point with another brief example, but first I would like to ask the reader, "Do you understand the concept(s) explained in my previously quoted post?" If not I would urge the reader to read the post again as well as brush up on their basic math concepts until they reach a level of conceptual understanding, as this is a necessary foundation for what is to follow.

Again we will define two functions, F and G, (for two different races) that maps skill to results.

For Race A: f(x) = x + 10

For Race B
g(x) =
{
x + 5 ; x < 1,337
x + 15 ; x >= 1,337
}

Note that both race A and race B have an infinite skill ceiling.
Note that for all n such that n < 1,337, f(n) > g(n)
Note that for all n such that n >= 1,337 f(n) < g(n)

Mathematically this defines a strong example of the concept that Race A is easier to play than race B, but less powerful.
"After silence, that which comes nearest to expressing the inexpressible is music." - Aldous Huxley
ZERG_RUSSIAN
Profile Blog Joined November 2008
10417 Posts
July 09 2014 05:13 GMT
#34
On July 09 2014 12:41 L_Master wrote:
Show nested quote +
On July 09 2014 10:13 ZERG_RUSSIAN wrote:
This is dumb. Let's just think of a blatant counter-example.

A tricycle is easier to ride than a motorcycle. A motorcycle takes a lot more skill and knowledge to operate. A motorcycle will basically never lose to a tricycle in a race. The tricycle is easier, the motorcycle is harder to operate. In spite of this, the motorcycle is stronger.

Any questions?


If this is serious...

Is there a flaw in the example or is OP's argument just disproven very easily?

P.S. Hi Kashll
I'm on GOLD CHAIN
ZERG_RUSSIAN
Profile Blog Joined November 2008
10417 Posts
Last Edited: 2014-07-09 05:41:07
July 09 2014 05:35 GMT
#35
On July 09 2014 11:17 SiskosGoatee wrote:
Show nested quote +
On July 09 2014 10:13 ZERG_RUSSIAN wrote:
This is dumb. Let's just think of a blatant counter-example.

A tricycle is easier to ride than a motorcycle. A motorcycle takes a lot more skill and knowledge to operate. A motorcycle will basically never lose to a tricycle in a race. The tricycle is easier, the motorcycle is harder to operate. In spite of this, the motorcycle is stronger.

Any questions?
Tricycle has a skill ceiling that's quickly reached, the entire argument explains why it relies on the assumption that the skill ceiling is infinite.

There comes a point when a tricycle just will not go any faster. The entire point of this article is that it relies on the fact that for all practical purposes there will never be a point where you don't play any better in StarCraft.

A tricycle just won't go faster than a motorcycle. The entire point is that in StarCraft you can beat anyone with any race as long as you're good enough. For every player who is super good, you can theoretically invent a player who is good enough to beat him or her with any race.

If I was riding the tricycle and someone with insufficient knowledge of how to operate a motorcycle was riding the motorcycle, I would win. It's an exaggeration but the point still stands. The most powerful bike is not the easiest bike, and vice-versa.

There comes a point where the motorcycle will not go any faster, just as there comes a point where the tricycle will not go any faster. Both the motorcycle and the tricycle have a finite skill ceiling, just as a human playing Starcraft is limited by the speed of their body and the input format and other factors. Skill ceiling cannot be "infinite" by the input device and the laws of physics.

And I don't see how you came to the conclusion that for every player there can theoretically be a better player who can beat them with any race. What if one race is simply stronger than the others? I'm inclined to think that this is the case, unless Blizzard made a 100% perfectly balanced 3 race game. Shit, even chess isn't balanced. At some point I'm 100% certain that skill improvements will not change the outcome of a given race vs race matchup on a given map.

Obviously there has to be a limitation to the "skill ceiling" of a race because of the laws of physics on the input. Moreover, even if a player was capable of executing perfect micro/macro on every unit/building in the game, a ceiling would still exist, limited by the movement rate/attack speed/build speed of the units.

And for that, see Kashll's posts. This argument is dumb. Of course something can be easier yet weaker.

Let's try again: A club has an infinite skill ceiling. A gun has an infinite skill ceiling. The club is easier to operate than the gun.

Get the picture?
I'm on GOLD CHAIN
SiskosGoatee
Profile Blog Joined May 2012
Albania1482 Posts
July 09 2014 07:44 GMT
#36
On July 09 2014 12:32 Kashll wrote:
I can only conclude that you do not understand math, or the concept of a "skill/results" graph. (And yes that's even granting you your often (always?) unrealistic precondition of an infinite skill ceiling).

Here is a mathematical example that follows how people intend to use this language and satisfies your precondition:

Let's define a function F, and a function G (for two different races) that maps skill to results.

For Race A, f(x) = x + 5
For Race B, g(x) = x

Note that both race A and race B have an infinite skill ceiling.
Note that for all n in the set of real numbers, f(n) > g(n)

Mathematically this defines a strong example of the concept that Race A is easier to play than Race B
Ignoring the ridiculousness of quantifying skill so simply. Race A in this sense has better results and is thus overpowered. Thereby demonstrating my point that there is no such thing as "easier to play, yet weaker."
WCS Apartheid cometh, all hail the casual audience, death to merit and hard work.
SiskosGoatee
Profile Blog Joined May 2012
Albania1482 Posts
July 09 2014 07:54 GMT
#37
On July 09 2014 14:35 ZERG_RUSSIAN wrote:
Show nested quote +
On July 09 2014 11:17 SiskosGoatee wrote:
On July 09 2014 10:13 ZERG_RUSSIAN wrote:
This is dumb. Let's just think of a blatant counter-example.

A tricycle is easier to ride than a motorcycle. A motorcycle takes a lot more skill and knowledge to operate. A motorcycle will basically never lose to a tricycle in a race. The tricycle is easier, the motorcycle is harder to operate. In spite of this, the motorcycle is stronger.

Any questions?
Tricycle has a skill ceiling that's quickly reached, the entire argument explains why it relies on the assumption that the skill ceiling is infinite.

There comes a point when a tricycle just will not go any faster. The entire point of this article is that it relies on the fact that for all practical purposes there will never be a point where you don't play any better in StarCraft.

A tricycle just won't go faster than a motorcycle. The entire point is that in StarCraft you can beat anyone with any race as long as you're good enough. For every player who is super good, you can theoretically invent a player who is good enough to beat him or her with any race.

If I was riding the tricycle and someone with insufficient knowledge of how to operate a motorcycle was riding the motorcycle, I would win. It's an exaggeration but the point still stands. The most powerful bike is not the easiest bike, and vice-versa.
And that's immaterial to my point.

My point relies on the assumption that for every theoretical player of race X, there is a theoretical player of race Y that can beat him or her.

What you formality is: For some theoretical player of race X, there is a theoretical player of race Y that can beat him or her.

There are people who drive motorcycles so well that it is no longer humanly possible to beat them on a tricycle, many such people in fact. There is no Zerg player for which you can't invent a theoretical Terran/Protoss player that can beat him or her.

There comes a point where the motorcycle will not go any faster, just as there comes a point where the tricycle will not go any faster. Both the motorcycle and the tricycle have a finite skill ceiling, just as a human playing Starcraft is limited by the speed of their body and the input format and other factors. Skill ceiling cannot be "infinite" by the input device and the laws of physics.
It cannot be infinite in parallel games like drag racing where you do not influence your opponent. StarCraft however is not a parallel game but a game that allows you to hinder and influence your opponent. The skill ceiling will always be theoretically infinite in a game that allows this. If your opponent plays "perfect" and doesn't miss a beat with macro you can improve and disrupt your opponent's play in StarCraft such that this no longer happens. You can't do this with racing. If your opponent races the track optimally there is nothing you can do to alter that.

And I don't see how you came to the conclusion that for every player there can theoretically be a better player who can beat them with any race. What if one race is simply stronger than the others? I'm inclined to think that this is the case, unless Blizzard made a 100% perfectly balanced 3 race game. Shit, even chess isn't balanced. At some point I'm 100% certain that skill improvements will not change the outcome of a given race vs race matchup on a given map.
Even if a race is stronger, even if the game is grossly imbalanced. You can always invent this theoretical superplayer that can overcome the balance no matter how much it is favoured against him or her.

Obviously there has to be a limitation to the "skill ceiling" of a race because of the laws of physics on the input. Moreover, even if a player was capable of executing perfect micro/macro on every unit/building in the game, a ceiling would still exist, limited by the movement rate/attack speed/build speed of the units.
See the point about hindrance. StarCraft is not a parallel game like marathons or darts.


Let's try again: A club has an infinite skill ceiling. A gun has an infinite skill ceiling. The club is easier to operate than the gun.

Get the picture?
And a gun is overpowered compared to a club? Your example only serves to aid to my point that easier and more powerful are the same thing.
WCS Apartheid cometh, all hail the casual audience, death to merit and hard work.
endy
Profile Blog Joined May 2009
Switzerland8970 Posts
July 09 2014 08:20 GMT
#38
On July 09 2014 16:54 SiskosGoatee wrote:
Show nested quote +
On July 09 2014 14:35 ZERG_RUSSIAN wrote:
Let's try again: A club has an infinite skill ceiling. A gun has an infinite skill ceiling. The club is easier to operate than the gun.

Get the picture?


And a gun is overpowered compared to a club? Your example only serves to aid to my point that easier and more powerful are the same thing.


No, he just showed the club is easier (to manipulate) yet the gun is more powerful. Just like the race that is the easiest to use is not necessarily the one that will get the better results.

So you will say that it's easier to kill someone with a gun, so I will point you to my post above about the definition of "easy", because clearly that's the source of disagreement here.

To ZERG_RUSSIAN, easy = easy to manipulate/use/choose applicable verb for Gun/Starcraft race/Tricycle/ ...
To you, easy = easy to win a game/kill/ whatever is the final goal.
ॐ
ZERG_RUSSIAN
Profile Blog Joined November 2008
10417 Posts
July 09 2014 08:29 GMT
#39
To the OP:

Basically I disagree with you on the idea that the game is so immaculately balanced that someone playing a race at the highest level of possible play (like, computer controls each action of each unit and building "perfectly") will always be able to be outplayed by some other player.

I think that there is a limit to how well a race can be played. Like, if neither perfect computer player makes a SINGLE mistake, one person will still win. That comes down to the inherent imbalance in races on maps.

Suggesting that there's a limitless ceiling is just silly. All players are hard limited by multiple factors including map, distance, game timings, movespeed, etc. Skill has no effect on how fast a marine spawns. Sure, Starcraft and Chess and Go and other games are reasonably balanced, but asserting that there's always a better way to play is making a LOT of baseless assumptions that are very easily disproved.
I'm on GOLD CHAIN
Big J
Profile Joined March 2011
Austria16289 Posts
July 09 2014 08:30 GMT
#40
About the examples:
- Trycycle vs Motorcycle isn't balanced, even though you may invoke that there is some theoretically unreachable skill ceiling. (shown by the existance of motorsports)

- Same goes for Kashll's example, it's not balanced as he found out himself.

- But even his modified example isn't balanced for a given n=/=1,337. So for the functions to be balanced, we need to ask about their domains. For example, if the highest reached n is 1, it is clearly imbalanced in the favor of f. If however the average n is 5, it is imbalanced towards g.
What we could however include in this model is that for any given player of these functions, anytime he plays he gets assigned a randomly chosen n from -infinity to infinity (this domain could obviously vary. We could also make it [0;2674]). This would indeed balance our game, however this is a very bad modelling of a certain level of Starcraft players.

Given a certain skill level, you'd rather play around 2.5 everygame (e.g. a progamer) or 1.0 (e.g. a silver leaguer). So regardless of the league choice we make, we would plainly have imbalance in the one or other way.

A much better way to model (a balanced) Starcraft is imo if we take functions f and g with a domain of [0;10000] like that:

T(x) = x+1 for x in [n;n+0.5]; n being a natural
T(x) = x-1 else
Z(x) = x+2 for x in [n+0.5;n+1]; n being a natural
Z(x) = x-2 else
P(x) = x+1

This is somewhat similar to Kashll's example, but given how the skill/the metagame - these kinds of things modelled by n - progresses, a player may have a natural advantage for a periode of time. For a low enough x for all players, hence x<<10000 and x ever growing (metagame, skill progression) and being "randomly" assigned from a number +/- from your skill level, this is indeed a balanced game. Not exactly at every level, but close to your level you should be able to find another level where you may not have a disadvantage.
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