How do you make a game fair:

Game balancing is what it boils down too and you have got the basis of the topic and its fundamentals correct, however there are 2 forms of balancing in a player vs player and a computer vs player environment and I believe this has been slightly overlooked even by our omnipresent MattB.

PcM/PvC/PvE – (Monster/Computer/Enemy) Player vs AI
In order to make a game more fun a lot of people who write games employ rebalancing tactics for difficulty, some games ie. online games have one difficulty others have a fixed scale which alters a game dynamic in some cases meaning that a players scissors will have a chance beating a computer players rock on the easiest mode, this allows a player to learn through the game and even though it is easy pick up the game basics, some people like in newer versions of command and conquer have the option to automatically alter the AI level to make the battle more even.

PvP/2 Player/Multiplayer – Player vs Player
In this environment things tend to be a lot more balanced this adds to the “fun” aspect, when they work together each character type/class/unit/race etc has their own strengths and weaknesses, but in this environment the emphasis is to base the result as much on player skill as possible often meaning anything can beat anything it is down to how good the player is.

RTS
ie. Command and Conquer: Red alert 3
PvE: In this scenario as mentioned above you have different difficulty levels and the strengths come out with troop combinations the weaknesses with a single troop type, after many revisions they finally got this right with RA3 and you can see clearly a well balanced game troops can dig in and become more able to take out tanks, on the easier settings armour/firerate is also reduced for the enemy AI as are a few other things to give the player a clear advantage, later on in the harder settings not only does the player have a disadvantage as 1v1 the computers units are stronger they build faster and the computer knows the best formations and battle strategies.

PvP: The computer player here doesn’t matter the players use their own battle tactics and 1v1 their units are as strong as each other, so it comes down to good old battle tactics and formations.

FPS
ie. Quake 3 Arena
PVE: This is fairly simple to work out, AI is “dulled” down making it slower less accurate it hits less you take less damage per hit on the easier modes and as you progress it gets harder and harder sometimes if you take a single hit in some games you are dead and have to start again in the hardest mode.

PvP: Each character has no advantage/disadvantage over any other it is purely down to skill except on games like Team Fortress/BF1942/COD etc however each of these classes are well balanced enough that played correctly they are still equal in terms of power but they still have different roles as this is a team play environment.

RPG
ie. World of warcraft
PVP: You get the idea you have different classes each tactic has a different approach to play Tank/ DPS/ Boomer/ Healer/ Buffer/ Debuffer/ Combination classes. This allows for team play vs the computer or in the case of single player it allows for different battle stratergies.

PvE: There are 2 approaches to this, in heavy PvP RPG games like CABAL Online each class is balanced differently in PvP than they are in PvE this helps to ensure no matter what the class their skills and damage work differently against other players often employing different skills faster skills to beat other players with other effects such as knockdown/knock back/stun this helps make sure that any player can take on any player no matter their class but in a PvE situation they have to work as a team.

You can apply all of what I wrote in the above to any situation that is PvP and PvE no matter the genre Racing, Sports, Fighting, etc. the balancing that is used is what will be the most fun for the environment.

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So in summary it boils down to 3 different balancing aspects:

Difficulty – Single player environment the difficulty can be scaled so a players scissors can beat a rock etc. (Any single player game)

Class balancing – This is in team play where working together helps overcome difficult objectives making up for each others weakness. (Team fortress, PvE World of warcraft (Dungeons/bosses etc), Counter strike, etc.)

PvP Rebalance - In order to make player vs player more fun the game is balanced removing handicaps, on games where it is the most effectively they become extremely popular fast. (Quake 3 arena, Unreal death match mode, CABAL Online, etc.)

Sometimes balancing isn’t done quite right and it will take a couple of generations of the game learning by the creators on how to balance it, (Eg. Command and Conquer) and sometimes the balancing makes them perfect after a couple of patches (StarCraft), at the end of the day it isn’t graphics/style/originality etc that make a game a legend its how fun it is and balancing plays a major role in that.

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