In any game balance is a big deal. X cannot be too much greater than Y or else you have an issue on your hands. If the balance issue is a competitive one there can be many, many ways to fix it.
The easiest way to achieve balance and the one I see my gaming friends bring up as a common solution is a simple rock paper scissor weakness chart. However, there are lot of flaws in a rock paper scissor dynamic. The main drawback being that it limits players' available choices and strategies. Hard weakness system automatically creates a general dominant strategy of having to counter as much as possible with the occasional deviance from the norm either bombing horribly or having minor success. Another direct result of this type of balancing is a direct skill drop. It doesn't really matter how good you are at a game if someone can counter you perfectly and win anyways. A good example of this can be found in fighting games. Some fighters have moves in their kit that make them better or worse against other fighters. However it's not as though one type of character does more damage to another, they simply have the tools to work around that specific fighter better. The other guy can still win he just has to be tricky and smart and out play his opponent. As such it creates a sense of a skill gap rather than making you feel as though you simply picked the wrong character. It takes player intelligence to win an uphill battle.
I find that, "If you expand a rock paper scissor cycle to more than three options it would definitely work," is a very common counter argument which is both true and untrue. When split into, say, five parts the same arguments apply as above. There will be still a Popular Pick versus Counter to the Popular Pick general strategy being played out almost every time, but it can be expanded enough to work. In fact it's the basis for Pokémon. Pokémon are assigned types and the types have specific weaknesses or strength. Only Pokémon takes that idea and chucks it up Mount Everest. Currently there are 17 types with several weaknesses/resistances. A Pokémon can be up to two different types at the same time, the short comings of the types either being cancelled out or multiplied. Not to mention that often times Pokémon will carry moves which are effective against their own weaknesses. It's like Rock-paper-scissors-dog-cat-mouse-elephant-human if the human could bring along a dog to defend himself from paper.
So maybe you could balance your game through a rock-paper-scissors mechanic if you put enough time into it. But a slapdash system could lead to a limited and unhappy player base with only one dominant strategy. You're probably better off putting some extra effort in.
-Baxter Cranch
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