The purpose of balancing is giving a fair chance for all players no matter the side they pick, and no matter what kind of starting customization they choose or what kind of starting random setting they get.
One of the simplest balancing forms is giving all sides identical starting resources, and abilities. For example chess. Even then however, it matters weather you start or go second. However for non professional chess players like me the starting advantage is quite irrelevant.
Once you start adding different abilities, or different starting resources, or randomness, then the balance gets disrupted. If you take civilization series, then the starting area is random, it really plays a huge role, how you get your game going. Of course when I start to play the game, I know what I'm getting into, and the randomness is also good as it creates for different situations, making me seek out different strategies from game to game. In games like these you only care about having the fighting chance. So how is this achieved?
Suppose we were playing three player chess and one player starts with 1 rook instead of 2. Does he have a disadvantage over the other 2 players? What if he had no rooks? As the goal of the game is to defeat all other players, meaning for the both other players point of view will be that there is a weakened opponent, and a normal opponent. So when they start to build up their strategy, they will create a certain perception of both opponents, and if they perceive the situation right at all times then eventually the 2 rook advantage that 2 players have will be taken away from them. In a 3 player game, where all players depend on each other, the perception and keeping the game in balance is one of the things players have to keep their eye out if they want to succeed.
Let's take a more trastic example. Suppose that in 3 player chess 1 player starts with 1 king and 7 queens in the back lane. Now he has a stronger army compared to other players, but since all 3 players will want to win, then the other 2 players will most likely start cooperating from the very beginning until they perhaps come to a situation where the armies of all 3 are somewhat more equal. However, what if the overpowered player picked 1 of the 2 other players and started focusing him, saying that if he doesn't betray his "temporary ally", he will lose anyways. This is a situation, where picked player has no chance to win, but he gets to decide who of the other players wins. This happens because the alliance is bound to be temporary anyways, and the breaking is inevitable, since all players want to win. Propably there are some ways to play around it, but a situation like that, where you can't win but can decide who else wins is something that can happen in a 3 player game, where everyone influence other players very strongly. Like in chess, through taking pieces.
Similar is the board game "diplomacy", where you can make deals but don't have to keep them, leading to inevitable betrayal, and leading to similar situations as prisoner's dilemma. The emotions play a very strong part of the game, and by creating negative kind of emotions, many players don't like it, even though it has "balance" in it. My personal idea on the matter is that a 3 player war game - it represents 3 tyrants fighting for the overrule of the land, no honor, only deception and millitary is used... and to look it like that you can see the non-appeal of such games. Especially for the people in the democratic states, who propably don't relate to the idea of going to an all out brute force war just to be the overruling nation in the end.
So, as you can see having more than 2 players can be a balancing experience, but also a ridiculous experience, as there are lot's of ways to lose just because other players choose less rational and more emotional decisions.
In my board game Pactio, players get to pick roles, and some of them are with really unique play-styles, strengths and weaknesses. On 1 vs 1 level many of the roles are far from balanced, the strengths of some roles actually assume having multiple of players. However since the game is played with at least 3 players, the players can start balancing the game them-selves. However compared to 3 player chess, Pactio is an economic game. So the whole game revolves around growth. There are a few destructive aspects, but mostly it is about growth. Also players can do sealed deals between each other, meaning all their interaction have much more strategical meaning, since you can make deals, which you think will be fair and balanced and having a guarantee that they will be kept, therefore having the calculated effect on the game. So what happens is that once players learn to play the game, they understand that it is all about perception, if you manage to perceive players right you are able to understand what kind of deals are actually profitable, fair or bad for you. Of course the perception part can still involve emotional play, but taking into account all the play-testing I believe it has done way more good than bad to the game.
Also since there is little to no destructive element there is much more solid ground to base your actions, and players, when actually having a situation where they can decide the winner other than themselves tend to simply choose the path that gives them the higher score, creating for a better emotional feeling after the game. As this game is about becoming economically best. You might argue that from a rational perspective it doesn't matter, but from an emotional perspective you simply take it as one player traded the best and others came close being second, third etc. while in a war game 1 player crushes all others and the others lose - there is no second or third place.
To sum things up, one way of balancing a game, is to make it a over 2 player game, and give players tools to effect or interact with other players. That leads to a much more robust system, where players can balance the game by keeping stronger players in check. However note, that it can also lead to wierd situations, and my personal opinion is that, games like 3 player chess, or diplomacy can have rational situations, but the goal itself leads to lot's of emotional dilemmas rather than rational game play. Furthermore 3+ player games may be as balanced that a perfect game-play would lead to an inevitable tie for all parties, ruining the point for a war game, but being a completely acceptable outcome for an economy game. Never the less, playing such games where, players themselves balance the game teaches a lot about balance in real world, and I strongly advise it. At least for a few times.
And again, don't hesitate to comment and share your ideas on the matter.
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