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Russ_Nightshade

Rock, Paper, Scissors: Running with Paper

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A primary theory in military unit design is a concept that mimics the famous childhood game of rock, paper, scissors. The concept is simple; design one unit, that’s good against a second but week against a third. This is just horrible advice, and unfortunately it’s probably the most heard advice when it comes to game design, especially to strategy games. In reality, I don’t know why they continue to preach this advice, nobody uses it, seriously. Think for a moment, about an epic strategy game. There is probably close to 20 units. So, if unit A is good against B, and unit B is good against C, and unit C is good against D, etc. Well, tell me, when Unit A and Unit G fight, who wins? You can come up with a few basic theories to try and explain this; perhaps the unit that comes first is better, making Unit A good against B-T. If you have it loop, to Unit T is good against A. Ok, so Unit A is good Against B-J, but B is good against unit C-K, so which unit is best against Unit F, Is it E? You can quickly see how complicated this becomes, and even if you spent a few months working out all the small details, any change during the testing process would just implode the whole system. Even if you got it perfect, there are still many holes in the system. Firstly, the system almost guarantees that all units are presumably equal. Your gut might say, well hell, isn’t that a good thing? It is a good thing for the balance guy, but for the game, probably not. If we think about most games, we’ll remember that they almost all contain units that are much more powerful than other units. The most pronounced would be Warcraft 3, where your hero is stronger than any other single unit, and most would argue the hero is almost your avatar, and is hands down the best unit you have. We don’t want to eliminate fun units, but half of what makes a unit fun is it’s superiority over other units, which couldn’t happen in the rock, paper, scissors concept. We should also take a look on how this might work with a game with 3 different races, like starcraft. Most people will jump at the chance to argue this point with the marines, zerglings and zealots argument. I don’t know what blizzard would say, but me personally, I think of those three units more like rock, rock, rock then paper, rock, scissors. Although, lets for a moment try to argue that they are. Still, a game is made up of more than 3 units… so you’d have to add another tier. Like the dragoon, firebat and hydralisk, but then how does this order work? Would it be the same way as before, no, it couldn’t. That would mean that one race is good against a 2nd race, but week against a 3rd, and that’s not true in starcraft. So maybe you could reverse what race they were good for. If unit set 1's order was Terran > Zerg > Protoss, then maybe unit set 2's order would be Protoss > Zerg > Terran. Although, this also isn’t true, because this system would make every-other unit good against a race, so against 1 race you would really only use half of your forces. This obviously isn’t right either; everybody uses a wide majority of their units, regardless of their opponent’s race. So even with 3 race games, it’s far too complex to even begin to work. For my final argument, I’d like to take a minute to think about decisions. If indeed you do try to make a military based on rock, paper, scissors, then there is always a “dominate strategy”. Your strategy is now; to just build the counter to whatever your enemy is building. So if he builds a shit load of rocks, then you build a shit load of paper, then he’ll build a shit load of scissors etc. This is the same type of paradox we see with theory crafting in games, that indeed knowing the mathematical dominate strategy to a situation makes the decisions themselves far less pleasing. There have been some vary famous designers who have suggested this as a design tool, but am I crazy for calling, bullshit? What's your opinions?

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For my final argument, I'd like to take a minute to think about decisions. If indeed you do try to make a military based on rock, paper, scissors, then there is always a "dominate strategy". Your strategy is now; to just build the counter to whatever your enemy is building...


A new game, Ruse, capitalizes on this very principle. Check out the preview sometime. I for one can't wait to give that type of strategy game a try as it is something new.

Quote:
There have been some vary famous designers who have suggested this as a design tool, but am I crazy for calling, bullshit? What's your opinions?


I think it's a good design tool in understanding things on a macro level, but as you have pointed out, this design is way too simple to be the sole model a game is designed around. The problem I have with it is that it looks at things in terms of an absolute. Rock always beats scissors, scissors always beats paper, paper always beats rock. In the real world, nothing is that absolute. Under certain situations, water can't put out fire and fire can burn on water.

That of course might be too complex for a game, but a Rock-Paper-Scissors model is more for making sure you have a balance in place. You don't ever want one unit that can simply beat any other unit no matter what. For example, one zealot will always beat 1 zergling no matter how many times you run that combat simulation. However, 10 zerglings can always kill one zealot.

The balance is that you can counter a more powerful unit with more weaker units and that's what is most important. If it was setup to where 1000 zerglings could never kill a zealot, then you know you have a problem. Likewise, you don't want to have a setup where one player can simply build the max amount of most powerful units and be gaurnteed to win either.

I've actually seen such imbalances in MMORPGs where let's say 30 low levels could never kill a high level no matter what due to the lower levels not being able to generate enough damage against higher level gear. However, on a new race that was introduced to the game, those same 30 low levels could almost be guaranteed to be able to always kill any high level if they were working together and had the right skills.

So, I think the model is good to get an idea of how you want to balance out units in terms of which units are superior to others. However, a good designer should not base their designs solely on the model alone without thinking about the other issues that are important to balance. The model is a good easy checklist to use to see if you have obvious design flaws by allowing you to ask which unit can be built to counter this one? If you find no unit exists, then you know you have a problem.

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I think a mixture of the two should be in order.

Let me present an example which uses the other extreme:

GalCiv II is probably my favourite strategy game, but an element it falls short in is that absolutely no strategy is required when actually doing battle.

If you concentrate all your mental energy on going down the right research tree, and beating everyone else when it comes to manufacturing, you can then build a horde of the same gigantic powerful unit designed simply to overwhelm the enemy. When I come to this point, I don't even think, I just organize my fleets haphazardly and tell them where to go. Preparation is where all the strategy is required, after that fighting battles is a no-brainer.

Surely, an element of tactical strategy should be present.

I personally like how Hearts of Iron II does it. Please bear with me, as it's been a while since I played the game, and what I'm going to present is a general idea.

Each unit has three types of attack (Rock, Paper, Scissors, but everyone has a value in each).

Some units can be hurt by some of those attacks, others are invulnerable to some, or well protected against them. Some units can only do 2/3 of the attacks, or even 1/3.

So for example, an infantryman is pretty good at attacking other infantrymen, but pretty crappy when it comes to tanks, and airplanes. Tanks have a hard time hitting infantrymen, but their strength lies in their mobility and shock factor, making them pretty invaluable with motorized infantry. Tanks also can't hit airplanes. Bombers can only hit things on the ground, but they have a hard time hitting infantry and are mostly useful against airbases and infrastructure. Interceptors can only hit other planes etc. etc.

I think you'll find that this actually comes close to emulating real combat, and, from personal experience, it's a lot of fun.

I don't think rock should always beat scissors, but it should stand a better chance.

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Original post by Russ_Nightshade
There have been some vary famous designers who have suggested this as a design tool, but am I crazy for calling, bullshit? What's your opinions?


I hope not, because if you are, I must be some kind of frothing, raving loon. [grin]

As Drew_Benton says, the concept of RPS can be a useful thing to keep in mind, but from a zoomed out, macro level. But I've never liked it as a basis for designing individual units, nor am I a big fan of strict hard counters in general.

The main reason is, quite simply, basing a strategy game heavily on hard counters unnecessarily restricts the scope of the player's strategic choices to "What shall I build?". Other considerations such as positioning, use of cover, deception etc. end up playing second fiddle to spamming the right unit to beat your opponent's army.

I like the idea of situational counters; these potentially give rise to much more interesting, dynamic gameplay. Tanks might able to destroy infantry en-masse out in the open, where their superior range, mobility and firepower easily outclasses the infantry. But perhaps in more dense terrain, such as forests or cities, where the tank's mobility and range are less of an advantage, the infantry can get close enough to the tank to drop grenades down the hatch. Now, when faced with tanks, your reactions are not restricted to just building Tank Destroyers to defeat them; there exist some more interesting possibilities, such as luring your opponent into situation where your existing infantry can beat them.

[Edited by - Sandman on May 3, 2009 1:01:30 PM]

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I agree that it works nicely at a macro level. Think Medieval 2: Total War. Swords are strong against spears but weak against cavalry, cavalry is strong against swords but weak against spears, spears are weak against swords but strong against cavalry. Simple rock-paper-scissors model, right? But then you add fatigue, morale, flanking, attack from behind, ambushing, terrain type, terrain slope, and you end up with a pretty damn interesting game that, at its core, is still rock-paper-scissors.

This is also the answer to unit complexity mentioned by Russ in the second paragraph. You may have 150 units in the game, but chances are they all belong to one of 3-5 types.

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The point of rock-paper-scissors is balance and fairness.

Now, the problem is that it only works if you've got three types of responses.
Otherwise you simply can't be fair.

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In my opinion, you completely missed the point of the rock-paper-scissors idea. It is a one-dimensional metaphor that provides a single point: games should have balance. There should be no one dominant strategy -- a counter should always be available.

Star-Craft just implements a multi-variable implementation of this concept. Instead of rock-paper-scissors being identifiers, they are now vectors with [strength, defense, time-to-build, cost-to-build, speed, attack-type, flying, ...].

To play off your 'multi-unit' example, let's think about Star-Craft. If I bring a zergling and you bring an ultralisk, you are going to win. But, zerglings cost less, are much faster to produce, and are much lower on the tech-tree. Ignoring the tech-tree part, if we both start at the same time, I might be able to build 10 in the time you build an ultralisk. Now with 10 and their speed advantage, I might be able to perform hit and run attacks on your ultralisk that even that playing field.

That is multi-variable R-P-S.

So to me, R-P-S is a design metaphor that captures a core design concept in strategy games: make sure that there is always a counter. If there is always a counter, the game will always be balanced. If you and I sit down at computers to play each other, our chances to win should NOT be based on the race we choose to use, but rather the strategy we choose to employ. Much like R-P-S, it doesn't matter what we throw, just as long as we beat the other person...

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Tactical Balance vs Power Balance

Hi, I am one of the people that knows how to design for tactical balance instead of power balance (as in RPS). Tactical balance involves how to use something to defeat the enemy's course of action. Power balance involves only what to use to defeat what the enemy has.

Dynamic Situations

Sandman mentioned situational counters. This is different. This is the kind of interaction Chess and Go has where the "landscape" changes with each move of the opponent, and game is about being able to decipher the features (threats) of the landscape. A real life example is that of battleships. In a sea battle, there is no obstacle at all. Everyone just openly float. It is the formation and movement of the ships/fleet that determines which ship gets to have better shots, which ship gets to evade more shots, and which ship gets to ram into another ship (Ancient Greece).

The similar situation happens in dogfight (World War II biplanes). The biplanes of both sides are homogeneous (the entire squadron has the same biplane model). They were inevitably different in performance, but one side can beat the other depending on what they do during the fight.

These examples have nothing to do with RPS. But they have tactics. Join the crowd that represents tactics as what they are.

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There have been some vary famous designers who have suggested this as a design tool, but am I crazy for calling, bullshit? What's your opinions?

I would have to disagree with you, simply because you have not understood the Scisors/paper/Rock concept as applied to game design.

Here is why:

1)
Quote:
Think for a moment, about an epic strategy game. There is probably close to 20 units. So, if unit A is good against B, and unit B is good against C, and unit C is good against D, etc. Well, tell me, when Unit A and Unit G fight, who wins?

In SPR, every unit has a specific relationship with every other unit (win, loss, tie). So this problem in SPR does not exist. In SPQ A would have had a specific relationship with G.

These relationships are designed so as to specifically bring about a blanace and are not arbitary assignments. There is a mathimatical relationship that assures of this balance.

What you have done is apply the incorrect mathimatical relationship and got not a SPR relationship but a cyclic relationship rather than an intransitive relationship.

It is a common mistake. What you have done is assumed that you can extraplolate from a beats b beats c beats a and change it to a beats b beats c beats d beats e and so on. But what ouy have not addressed is that you need a relationship between all options.

Thismeans that for A you have to say how it interacts with b, c, d and e.

As an exampleof this:
A beats B and D
B beats C and E
C beats D and A
D beats E and B
E beats A and C

In this Each choice beats two other choices and is beaten by two other choices. Of course, this is an extremely simple set up and you can get a much more complex design here. The reason that this mistake occurs so often is that people try to use the 3 node SPR as a basis, however because there is only one configuration if a 3 node SPR, people tend to think that the constraints imposed by the 3 node SPR is endemic to all SPR systems, which it is not.

2)
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You can quickly see how complicated this becomes, and even if you spent a few months working out all the small details, any change during the testing process would just implode the whole system

Actually, because of the mathematical relationships between the nodes in a proper SPR system, this complexity is managed. IF you apply the mathematical functions to the design, any changes you make to it will have a specific set of changes that you must apply if the system is to remain balanced.

For instance: in the above 5 node SPR if I change it so that A only beats B but not D, then I have to make further changes in such a way as to maintain the 0 sum nature of the setup. One solution is to change it thus:

A beats B
B beats C, D and E
C beats D and A
D beats E and A
E beats C and A

These changes are dictated by the mathematical framework that defines what a SPR system is. If you do not follow these mathematical requierments, it is not a failure of SPR, but that you are not implimentuing a proper SPR in the first place.

3)
Quote:
Firstly, the system almost guarantees that all units are presumably equal. Your gut might say, well hell, isn’t that a good thing? It is a good thing for the balance guy, but for the game, probably not. If we think about most games, we’ll remember that they almost all contain units that are much more powerful than other units. The most pronounced would be Warcraft 3, where your hero is stronger than any other single unit, and most would argue the hero is almost your avatar, and is hands down the best unit you have. We don’t want to eliminate fun units, but half of what makes a unit fun is it’s superiority over other units, which couldn’t happen in the rock, paper, scissors concept.

SPR does not guarantee that all units are equal, nor does it requier it. In fact, it requiers that the units are not equal at all, because if they were eq1ual, then there would be no difference between the units and therefore could not be a SPR relationship.

What it does do is make all units valueable.

In SPR, you can have a unit that is extremely powerful, but it must hve some weakness that another unit can (but not necesarily) exploit.

Lets look at medieval warfare: In this cavalry are fast and fairly well armoured. This means that archers can be run down easily, and the armour of the cavalry will protect them against the arows.

In SPR terms Cavalry beat archers.

But cavalry have one major weakness: The horse. No matter how well trained, a horse will not charge into a mass of sharp stakes. SO if you were to get a bunch of people with long spiked stickes (pikes) and line them up and train them, then they can't be charged at by the cavalry.

Put in SPR terms Pikemen beat cavalry.

Archers, could be lighter armoured than pikemen as they would not usually be involved in melee. This means that if pikemen were to give chance, then the archers could out run them and skirmish agains them. Also, as pikemen could not be as heavily armoured as cavalry, this ment that archers arows could penertrate the armour iof the pikemen and do damage.

In SPR terms Archers beat pikemn giving us our 3 node SPR relationship.

Now, for each unit cavalry were also considdered to be worth 100 units of infantry. This is by no means equal at all, but there is a SPR relationship which means that your claim that SPR gaurantee of equality can not be true.

What it does mean is that the relationship between the units is balanced. That is: that all are valuable, not equally powered.

In the case of medieval werfare, if your enemy fielded a lot of cavalry, your pikemen would be more valuable as they could stop the enemy cavalry. But then the enemy archer would become more valuable to them as they would allow them to attack you pikemen easily.

4)
Quote:
We should also take a look on how this might work with a game with 3 different races, like starcraft. Most people will jump at the chance to argue this point with the marines, zerglings and zealots argument. I don’t know what blizzard would say, but me personally, I think of those three units more like rock, rock, rock then paper, rock, scissors. Although, lets for a moment try to argue that they are.

Actually blizard have stated that they used a SPR relationaship for their units, just not a simple one.

Again this comes down to my first point. You have misunderstood what a SPR actually is, thus when one is presented to you you don't actually recognise it as such and also can't interperet it properly.

The SPR relationship in Starcraft is not specifically between the units, but it lies between the atributes of the units.

As the starcraft SPR is quite complex, I'll start with a simpler one: Homeworld.

In the game Homeworld you have 3 classes of ships: Fighters, Corvets and Capital Ships.

In each class of ship they have a ship designed to defeat one of the classes of ship. So in Fighters, they have a Fighter killer, a Corvet killer and a Capital Killer.

If you draw this up as a diagram (arrows pointing at who beats who) you will find that it forms a 9 node SPR system.

If you do the same thing for Starcraft, you will find a similar (but not identical) diagram, and in each case it conforms to the mathematical relationship requiered to form a SPR relationship.

However, what you ahve done is to take 3 units and shown that these 3 units in isolation do not form a SPR relationship. And this is true, but it makes the mistake in thinking that SPR exist as a relatioshiop betwee any 3 units only. This is not true. SPR applies to the whole system, if you take less units than the whole system then you will not necesarily (and extremely unlikely) get a SPR system between them.

The SPR for starcraft lies betwwen all units of all races, and this is why it is so complex, but due to the mathematical nature of the relatioships between SPR nodes this complexity can be managed far more easily than if it did not exist.

5)
Quote:
Still, a game is made up of more than 3 units… so you’d have to add another tier. Like the dragoon, firebat and hydralisk, but then how does this order work? Would it be the same way as before, no, it couldn’t. That would mean that one race is good against a 2nd race, but week against a 3rd, and that’s not true in starcraft.

Again you misunderstanding of SPR systems is the cause of this concern. Put simply: SPR is not like that so this problem does not occur.

SPR is not jsut between only 3 units but can be between any number of units, and the SPR of starcraft is not in tiers like you have proposed.

So the problem is not with SPR or starcraft but you undersntaing of the situation. The main factors in Starcraft's SPR is not between races or such, but between Air and ground based units (and armour types too). It also has influece between massed, cheap units and powerful expensive units. the amo0unt of factors that go into the SPR in starcraft is quit large and increasesw tghe complexity of it.

6)
Quote:
For my final argument, I’d like to take a minute to think about decisions. If indeed you do try to make a military based on rock, paper, scissors, then there is always a “dominate strategy”. Your strategy is now; to just build the counter to whatever your enemy is building. So if he builds a shit load of rocks, then you build a shit load of paper, then he’ll build a shit load of scissors etc. This is the same type of paradox we see with theory crafting in games, that indeed knowing the mathematical dominate strategy to a situation makes the decisions themselves far less pleasing.

Think about what you ahve written here. You say that SPR creates a dominent strategy problem but then as your example you show a situation that is clearly without a dominent strategy.

You present one strategy (build lost of rocks) and then present a counter to that strategy (build lost of paper) but then go on even further and present a counter to that (build lots of scissors). And the counter strategy to that is build lots of Rocks...

There is no dominent strategy as there is always a counter strategy to whatever counter strategy you make. This is the exact opposite of a dominent strategy situation.

What you are trying to get at is called "Equilibrium". This is the situation where you make the best possible choice but it will only give a tie. It is similar to, but not the same as a dominent strategy.

The difference is that a dominent strategy is robust and an equlibrium is not. Ina dominent strategy it does not matter what your oppoenent does, or small variations in the environment, you will not have to change your strategy, also if you oppoenent does anyhting other than the same dominent strategy you are guarenteed a victory.

In an equlibrium these tenents do not hold. Changes to your oppoennts strategy can requier changes to your own, also, environmental changes (like terrain, etc) will have a significant influence on what the equlibrium is.

Equlibrium also depends on the reletive power and costs of each choice as well. A unit that is more powerful might seem at first to be a dominent choice (and ina dominent strategy system this would be true), however, if there is a cheap counter to that unit (and in SPR there would likey be one) then this counter unit becomes more likely to see action as it would be used against the powerful one.

This shows the differenes between the results of a dominent strategy existing and an equlibrium strategy existing. A dominent strategy causes a positive feedback loop, and an equlibrium forces a negative feedback loop.

They are similar (in that they force feedback loops), but different because they force a different type of loop, and this diference in loop type has a huge significance to the outcome of the system.

Conclusion:
Due to a misunderstandign of the fundamentals of what SPR type systems entail, you have made the same mistakes as many others before you. These mistakes have led you to believe that a spr system is fundamentally flawed, but it is instead the mistaken syswtem that you created due to your misunderstanding that is flawed, and that is no suprise at all.

If you put together a watch incorrectly because you don't understand how a watch is supposed to work, would you expect it to tell the time properly? No.

So if you puttogether an SPR system incorrectly because you don't understand how a SPR system is supposed to work, would you expect it to work properly? Again No.

This is what has occurred. hopefully what I have written will help you to properly understnad how SPR systems are supposed to work, and why they actually are useful.

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Think of RPS not (just) in terms of units, but in terms of the choices available to the player.

Most RTS games have the rush/defend/expand set of options at the beginning. Defend beats rush, but will lose to an expansion game. An expansion game loses to a rush. This is an RPS cycle on a strategic level vs. a unit level.

"Loses" in this case doesn't have to mean loses 100% either, it can mean losing ground/falling behind.

There's a number of basic game "patterns" in game theory. RPS is a well-known one, as is the prisoner's dilemna. RPS just has a lot of useful qualities, such as not having any dominant strategies.

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