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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.

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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 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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Original post by Edtharan

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.


Well, an equilibrium is better defined as a scenario where neither side can improve their results by changing their strategy, without their opponent changing theirs.

RPS has no equilibrium. If player A chooses rock, while B chooses paper, the next round can have A improve his position by choosing scissors instead. If B continues to choose paper, he will lose.

This is one of the reasons that RPS works (if the concepts are tied to minute-to-minute play, not just a single chocie at the beginning of the game). Any strategy can be defeated by adapting to it.

An example of an equilibrium might be a shootout - both sides are behind cover. If either side pops out of cover, they get shot by the other team and lose. If they both pop up, they both run away and can win. Once both teams are hiding, the game will likely stay that way forever, as neither team will want to risk being the first to pop up and lose.

This is where grenades might come in. By using grenades against a team in cover, you can defeat them without opening yourself up to attack. Of course, if someone uses grenades, it gives you an opportunity to either run away or move up and shoot them with guns - we've now gone back to an RPS design, which ends up being much more dynamic.

Good games will often have a number of RPS cycles going on at one time. An RTS might simultaneously have a unit-based RPS cycle, a expand/rush/turtle cycle going on, and an attack/capture/defend cycle going on.

One of the other interesting things is that it doesn't really matter if all of the choices are "balanced" or not, within reason. Even if playing scissors vs. paper is worth two points, compared to one point for winning with rock or paper, the game still works. It just changes the strategy a little bit. Of course, that's only true to some extent - in rock paper scissors to 10 points, if scissors is worth 10 points, that's still pretty broken :)

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I think these sorts of patterns emerge in any RTS game based on resource management, even if they are not designed with that in mind. If your infantry require a barracks and your cavalry a stable, and these two unit types do not have any specific advantage over one another, then what is the point in building both? If you count the cost of the buildings, then using just one unit type becomes a superior strategy, as well as a boring one.

If you have different units and they are not all equally powered against one another, then you have an RPS-like relation between them whether you intended for it or not.

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Any game that uses balanced unit designs will have Rock-Paper-Scissors play emerge from it.

If you have to distribute X amount of "points" across the attributes for each unit type you design, what you will have are units whom either specialize in an attribute or are right in the middle, being a jack-of-all-trades.

If you are able to "buy" more points to insert into your unit designs, what you have are higher tier units.

Quote:
Original post by Russ_Nightshade
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.

"Rock-Paper-Scissors" (or Unit Specialization I would rather call it) is the result of limited resources, to which mimic reality quite well. Sure you would love to have military units that are strong against everything, but what is the cost towards making such? That's right, it is going to be quite expensive, if not downright impossible. Nothing can be invulnerable against everything.

You can get close, however, and have superunits that are good against a wide variety of encounters - but keep in mind that the numerical amount of such "superunits" you can afford will be significantly less then the amount of common, regular, and/or specialist units that your enemy can afford en masse, which can be much more useful in certain situations than others.

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Quote:
Original post by kyoryu
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.

This is a good point. RPS does not only apply to units, but can apply to a more abstract construct, like situation, or even terrain.

Also losing does not have to be 100% like you said. However it can also mean that you don't make progress (where the winner would). Although this can be analysed as if the looser just falls behind, in practice is can have different consequences. Loosing ground could mean that you loose access to a needed resource, where as not making progress would mean you still have access to that resource.

Some other game patterns are:
Ultimatum game: Where one player can split a resource into 2 parts of any size and offer either of those parts to another player. If the second player refuses to accept that deal then neither of the players gets the resources, but if they accept they get the amount offered to them (and the first player gets the remainder).

Tragedy of the Commons: Where 2 or more players have access to a common, but limited resource. If the players use the resource then they can advance, however, the more players that use the resource the less any individual player will advance. Effective use of resources becomes an important consideration.

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Original post by kyoryu
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Original post by Edtharan

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.


Well, an equilibrium is better defined as a scenario where neither side can improve their results by changing their strategy, without their opponent changing theirs.

RPS has no equilibrium. If player A chooses rock, while B chooses paper, the next round can have A improve his position by choosing scissors instead. If B continues to choose paper, he will lose.

Your explanation of an equilibrium is better than mine (strong pain killers and complex concepts are not a good mix :/ ).

Also a single game of RPS does not ahve an equilibrium, but if you play repeated games of RPS, then you can have an equilibrium: Chose one at random. This is as good as any other strategy.

However, what is interesting is that if you are playing against a human, there are strategies that can be employed that go outside the SPR system. By using psychology you can trick another player into making less than optimal strategic choices.

We all know that if you play Rock Rock Rock, then this appears as a pattern. If your opponent is just playing random, then you will do equally well against them as they will against you. But because your opponent sees a pattern, they might fall for the trick and play Paper. IF you have judged your opponent correctly, then you switch to scissors when you expect them to play paper and you can gain points on them.

This is called Signal faking, or bluffing.

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Original post by Tangireon
Any game that uses balanced unit designs will have Rock-Paper-Scissors play emerge from it.

No. You can have balanced games that do not employ Scissors/Paper/Rock systems. SPR is just one way of easily creating a balance.

An intransitive mechanic (SPR) is just one of many ways you can have a balance in a game. For instance: If all players start off the same and a unit can only defeat its own unit type, then there is no intransitive system but you do have a balanced game.

Also games with large amount of chance in them rarely have any SPR relationship in them because for RPS to exist there has to be a certain degree of structure to the relationships, and a game with too much randomness will disrupt any SPR system. However, SPR can still survive in a high degree of randomness, which shows the stability of the solution.

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Original post by EdtharanIf all players start off the same and a unit can only defeat its own unit type, then there is no intransitive system but you do have a balanced game.


I've been mulling over this example. It doesn't seem to apply to games in which the player has a choice over which units to build within a set number of resources, but with a little alteration we can make a version that does (I'm not sure if this is equivalent to a well known game/mechanic, but I'd be interested to know).

Lets say each player has a choice of three unit types and six (benefit of hindsight here) max units, whereby each type can only fight the same type, numbers dominate within each type (so that 4 beats 3, 3 beats 2 etc.), and the full battle is determined by an average of the three type-skirmishes. In other words, each player gives a triple (x, y, z) where x, y, and z are non-negative and x + y + z = 6, and a player wins if they have two variables ahead of their opponent. For example (2, 2, 0) is beaten by (1, 3, 2).

Ignoring all the possible draws (same as RPS, we'll just repeat if this happens), we have this intrasitive property that every option a player can pick has a counter option that beats it.

Indeed, assume player 1 chooses (X, Y, Z), where X, Y, Z >= 0 and X + Y + Z = 6. Without loss of generality assume X <= Y <= Z.

Player 2 can pick (X + 1, Y + 1, 6 - ((X + 1) + (Y + 1))).

Clearly player 2 has chosen 6 units, and clearly X + 1 and Y + 1 are positive. It remains to show that 6 - ((X + 1) + (Y + 1)) >= 0. Given X <= Y <= Z, we have Z >= 2. Hence 6 - ((X + 1) + (Y + 1)) = X + Y + Z - ((X + 1) + (Y + 1)) = Z - 2 >= 2 - 2 = 0.

Since X + 1 > X and Y + 1 > Y, player 2 wins.

This same argument works (and this is where the hindsight comes in) whenever the max unit limit is at least six. Below six; I haven't finished mulling that far (I think below 6 you can always force at least a draw). Regardless, this seems to be, once again, a Rock Paper Scissors type mechanic (only with 28 different options; not too sure how many are draws).

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This is a bit of a digression, but I am honestly against all forms of Rock-Paper Scissors balance. It can be fun, and leads to tremendously well-balanced games, but it requires the player to learn a set of arbitrary rules that really make little sense, and limits the developer to providing units with artificial stats and attack styles which are not often reflected in the game itself.

My personal design philosophy when it comes to balance is to design tactically. That is, no unit should have artificial restrictions; and every unit should have varying levels of the same sorts of statistics. Balance comes through the physical capabilities of units (ie. artillery can shoot far, but can't take out air units simply because it can't aim very fast), that are run through a physical simulation of the game world. For instance, infantry shouldn't be able to take out stone structures, simply because bullets don't have enough mass to do significant damage to stone (this should be reflected in the game engine as a literal interpretation). This way, the player has to make tactical decisions to affect gameplay which have much more to do with orientation and numbers than actual unit types. This is much more similar to the real world, and is much more intuitive.

One of the early pioneers of this type of balance was Total Annihilation.

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Original post by Edtharan
Also a single game of RPS does not ahve an equilibrium, but if you play repeated games of RPS, then you can have an equilibrium: Chose one at random. This is as good as any other strategy.


I was trying to gloss over pure strategies vs. mixed strategies...

Ultimately, I'm okay with having a mixed strategy equilibrium, because it's ridiculously hard for a human to actually maintain complete randomness. Most people fall victim to the Gambler's Fallacy to some extent. And even if they don't, they will probably suspect that their opponent does.

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Original post by Thatotherguy
This is a bit of a digression, but I am honestly against all forms of Rock-Paper Scissors balance. It can be fun, and leads to tremendously well-balanced games, but it requires the player to learn a set of arbitrary rules that really make little sense, and limits the developer to providing units with artificial stats and attack styles which are not often reflected in the game itself.

My personal design philosophy when it comes to balance is to design tactically. That is, no unit should have artificial restrictions; and every unit should have varying levels of the same sorts of statistics. Balance comes through the physical capabilities of units (ie. artillery can shoot far, but can't take out air units simply because it can't aim very fast), that are run through a physical simulation of the game world. For instance, infantry shouldn't be able to take out stone structures, simply because bullets don't have enough mass to do significant damage to stone (this should be reflected in the game engine as a literal interpretation). This way, the player has to make tactical decisions to affect gameplay which have much more to do with orientation and numbers than actual unit types. This is much more similar to the real world, and is much more intuitive.

One of the early pioneers of this type of balance was Total Annihilation.


RPS doesn't have to mean that any number of unit X will always defeat any number of unit Y. As I said, it's better to think of it in terms of player choices than units. 20 "rocks" may well defeat 5 "papers". But, the choice of the other player may be to leave that area lightly defended while he expands elsewhere, or to accept the temporary loss as an acceptable cost for being able to tech up earlier. There's still an RPS mechanic at work, but it's operating at a different level.

The main point of RPS-style balance is that there is no single decision, at any point, that is clearly better than all other decisions. Again, I'd really recommend looking at RPS mechanics in terms of decisions, rather than in terms of units.

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Re: kyoryu

In your definition, how do you tell whether a tactical game has or does not have an RPS system? It seems that in your definition, the two are equivalent and you will not be able to give an example where a game that has tactics does not have RPS. It seems to me that you were saying:

"If something can be defeated, then it must be paper; whatever course of action that beats it must be scissors; and whatever course of action that it beats must be rock."

In Go, what is rock, what is scissors, what is paper?

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Original post by Wai
Re: kyoryu

In your definition, how do you tell whether a tactical game has or does not have an RPS system? It seems that in your definition, the two are equivalent and you will not be able to give an example where a game that has tactics does not have RPS. It seems to me that you were saying:

"If something can be defeated, then it must be paper; whatever course of action that beats it must be scissors; and whatever course of action that it beats must be rock."

In Go, what is rock, what is scissors, what is paper?


RPS really refers to strategies that have a cyclical relationship. There are other prototypical games as well, some of which have been mentioned here in earlier posts.

The closest thing in Go would be securing territory vs. expanding vs. attacking your enemy's territory.

Over-expansion invites attacks, while attacks can be defeated with reasonable defensive structures. But playing too defensively will result in your opponent expanding and winning.

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In your description, you were talking about the case where the players are either too defensive, too aggressive, or too ambitious. But what about the normal case where the players are not playing the game at these mental extremes when a player simply out-think the other player?


In a game like Go, a move often satisfies all three motives: it secures, it expands, and it is also attacking. Each move can be part of a larger course of action: this stone I place looks like an attack, but it is to secure my future expansion. It is often not easy to tell the intention of the opponent even though you could see all the stones on the board.

If Go is like RPS, it would be like a game where you cannot tell what sign the opponent played (thus not knowing who is winning or who has just won in the last encounter), and a sign that your opponent made 15 moves ago, that you thought was a stone was really a scissors, that beats your paper this turn.


Describing dynamics like this in terms of RPS seems misfitting. Will you consider a different set of terminology to describe them?

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Original post by Edtharan
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Original post by Tangireon
Any game that uses balanced unit designs will have Rock-Paper-Scissors play emerge from it.

No. You can have balanced games that do not employ Scissors/Paper/Rock systems. SPR is just one way of easily creating a balance.

What if I had presented the SPR in the particular game you have described (all same units) in this manner:

Unit > Unit > Unit > ... - Would this not be a form of unit specialization within your game? Since there are no other units available to counter the Unit in this particular game world, Unit then takes on the role of countering (specializing) its own kind. Lets call this the Identity Specialization? Very interesting!

It could also be as though the Unit here is composed of all three of the classical "Rock", "Paper", and "Scissors" hand signs, so that one end of the unit specializes in taking another of its own kind, much in the manner of a puzzle piece. What do you think?

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Original post by Thatotherguy
My personal design philosophy when it comes to balance is to design tactically. That is, no unit should have artificial restrictions; and every unit should have varying levels of the same sorts of statistics. Balance comes through the physical capabilities of units (ie. artillery can shoot far, but can't take out air units simply because it can't aim very fast), that are run through a physical simulation of the game world. For instance, infantry shouldn't be able to take out stone structures, simply because bullets don't have enough mass to do significant damage to stone (this should be reflected in the game engine as a literal interpretation). This way, the player has to make tactical decisions to affect gameplay which have much more to do with orientation and numbers than actual unit types. This is much more similar to the real world, and is much more intuitive.

That still sounds a bit like Rock Paper Scissors to me - you have your limitations and capabilities to which are moderated by cost, "points", or technology, though it may be more intuitive to those players who have some prior knowledge in real-world warfare (but might not be so intuitive to those who have no knowledge of real-world warfare).

[Edited by - Tangireon on May 4, 2009 10:37:25 PM]

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Original post by Wai
Re:


In your description, you were talking about the case where the players are either too defensive, too aggressive, or too ambitious. But what about the normal case where the players are not playing the game at these mental extremes when a player simply out-think the other player?


In a game like Go, a move often satisfies all three motives: it secures, it expands, and it is also attacking. Each move can be part of a larger course of action: this stone I place looks like an attack, but it is to secure my future expansion. It is often not easy to tell the intention of the opponent even though you could see all the stones on the board.

If Go is like RPS, it would be like a game where you cannot tell what sign the opponent played (thus not knowing who is winning or who has just won in the last encounter), and a sign that your opponent made 15 moves ago, that you thought was a stone was really a scissors, that beats your paper this turn.


Describing dynamics like this in terms of RPS seems misfitting. Will you consider a different set of terminology to describe them?


The RPS here is not happening on the level of the individual stone, but the overall strategy of the player. And yes, it is to be expected that not only do you not play at the extremes, but that your tactics will shift over the course of a game. This is a good thing, and is a direct result of not having an equilibrium inherent in the game design.

In game theory terms, RPS really refers to this kind of cyclical relationship between strategies. So, it's actually the correct term. That doesn't mean that each move has to be absolute in terms of having a 'counter' or that strategies can't shift.

In fact, a good RPS design will end up with players attempting to out-think each other, in terms of predicting their opponent's next move. That's actually the crux of the RPS pattern - shifting your strategy to match and predict what your opponent does. The fact that an RPS game contains no pure strategy equilbriumm is what makes this "out-thinking" possible in the first place, and RPS in this case really describes the relationship of strategies to one another.

I think you're looking at it mostly from the "x has a hard counter in y" viewpoint, at a micro- rather than macro- level.

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In the example, micro or macro, the decision does not form a cyclical dynamic.

Micro: The player plays a stone. The stone defends, attacks, and expands. All three actions are done as once. This move is not part of a cyclical interaction. It could happen that the move has no counter. Once it is placed, it forms an indestrutible structure.

Macro: The player chooses a strategy that defends, attacks, and expands. Within a group of choices that all satisfy the three intentions simultaneous, the player chooses the course of action that can secure the most territory. The player is not switching between defending, attacking, and expanding. The player is always doing all three at once. The dynamic does not fall into a sequence of counters.


In both cases the interaction is not cyclical. A move that does all three is prefered over those that does two, which is better than a move that does only one.


How do you frame Tic-Tac-Toe in terms of RPS? What about Reversi/Othello?

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Quote:
Original post by Tangireon
Quote:
Original post by Edtharan
Quote:
Original post by Tangireon
Any game that uses balanced unit designs will have Rock-Paper-Scissors play emerge from it.

No. You can have balanced games that do not employ Scissors/Paper/Rock systems. SPR is just one way of easily creating a balance.

What if I had presented the SPR in the particular game you have described (all same units) in this manner:

Unit > Unit > Unit > ... - Would this not be a form of unit specialization within your game? Since there are no other units available to counter the Unit in this particular game world, Unit then takes on the role of countering (specializing) its own kind. Lets call this the Identity Specialization? Very interesting!

It could also be as though the Unit here is composed of all three of the classical "Rock", "Paper", and "Scissors" hand signs, so that one end of the unit specializes in taking another of its own kind, much in the manner of a puzzle piece. What do you think?

You are falling into the problem of thinking that Scissors Paper Rock relates to a specific unit. SPR relates to the choices a player makes, not just units (it is just that using units as examples makes it easier to understand the consequences).

So, in the case where you have a unit with 3 parts (in your example), this is still SPR because you have to make a choice of one or the others. It is still just 1 unit, but how you use that unit is the subject of SPR.

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