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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 :)

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.

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.

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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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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 Quote: 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).

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.

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.