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Balance
Game design
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Balance
Dominant strategy
Balance
(In)transitive relations
(A)symmetric balance
Feedback loops
Player balance
Level design
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What is balance?
Difficulty =
• …
• Uncertainty
• …
A balanced game retains uncertainty to retain difficulty
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What is balance?
The game should be balanced to keep the game
challenging. Uncertainty should be preserved.
● Balance to retain uncertainty
Other unrelated uses of the term “balance”:
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The balance between difficulty and skill to achieve flow
A broader sense, for example: the narrative and gameplay are in balance
The balance between uncertainty and fairness
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Balance
This lecture focuses on the balance between two (or more)
competing powers
● Two human players
● One human player and one AI player
● More human/AI players
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Fairness
Balance is not the same as fairness!
Balance is about more than fairness
● Imagine a game where the rules almost always force a
draw
Fairness requires more than balance
● Imagine a game which relies for 90% on chance
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Imbalance
Balance retains uncertainty
Examples of imbalance:
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One player (type) has a structural
advantage over another
One strategy has a structural
advantage over all other strategies
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Dominant strategy
A losing player has no chance of
catching up
A better player cannot win
…
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Players
When a novice player competes against an expert, is the
game imbalanced?
● It is certain that the expert will win
● So balance also depends on the players?
Balance also depends on the player skill level
● Not always controllable by the game designer
● Later more on this
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Players Initial choices
Example:
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At the start of a game, the players choose a character class
Some classes turn out to be weak, others strong
The game seems to be imbalanced
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But what if everyone chooses strong classes?
The game is suddenly balanced?
Balance also depends on in-game choices
We focus on choices intended to give equal winning chances
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Summary
Balance between two powers
● To retain uncertainty who will win
Important criteria
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No player type/strategy has a structural
advantage
A losing player should still have a chance to catch
up, while the better player can also win
Player skill and in-game choices also affect balance
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Balance
Dominant strategy
Balance
(In)transitive relations
(A)symmetric balance
Feedback loops
Player balance
Level design
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Dominant strategy
Term from the economic field “game theory”
● A strategy which is objectively the best strategy in
this scenario
A “strategy” in this sense dictates all choices
● Like an algorithm
Drains all strategic uncertainty from the game
● Just about executing the dominant strategy
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Example
Modification of Tic Tac Toe:
● The first player determines the first move of the
opponent
There is a strategy where the first player always wins
● This strategy is a dominant strategy
● It is the worst kind of dominant strategy, it guarantees
winning
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Dominant strategy
A dominant strategy can reduce choice
● E.g. only 3 out of 8 classes are sensible to choose
Or totally remove choice
● One strategy guarantees winning
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Example
An early rush in RTS games can be a dominant strategy
● Can we design something to fix this?
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Example: turtling
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Dominant strategy
Basketball
It was possible to delay the
game until the time ran out
Few points ahead?
Keep the ball!
Not the worst kind of
dominant strategy: The
team needs an advantage
first
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Avoiding dominant strategies
Dominant strategy
● A strategy which is the best strategy,
regardless of other options
Instead, the strategy should always depend on the
strategy of the opponent
● The losing player should be able to escape the loss by
changing to a good strategy
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Balance
Dominant strategy
Balance
(In)transitive relations
(A)symmetric balance
Feedback loops
Player balance
Level design
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Transitive relation
A transitive relation is a mathematical concept
If (A,B) and (B,C) then (A,C) is also true
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Transitive relation
In game design terms:
● A, B and C are strategies/units/class/etc.
● If A beats B and B beats C, then A also beats C
Why would we ever want to choose B (or C)?
● We’ll always choose A, which is the dominant strategy
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Transitive relation
Transitive relations should be avoided
● They result in useless strategies/units
● And can result in dominant strategies
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Intransitive relation
The opposite of a transitive relation is an intransitive relation
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If A beats B and B beats C, then A does not beat C
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Intransivity
Example: Rock, paper, scissors
Literal implementation
of intransitivity
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Rock, Paper, Scissors
Does this mean rock, paper, scissors does not have a
dominant strategy?
● Each choice has an equal chance of winning
● We don’t know the opposing move
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Rock, Paper, Scissors
Intransivity can be
expanded
For example:
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Rock, Paper, Scissors
You can also take it too far…
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Intransivity
Example
● Can you spot any transivities?
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Intransivity
Example
● Can you spot any transivities?
● Cavalry and heavy infantry!
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Intransivity
Example
● Can you spot any transivities?
● Cavalry and heavy infantry!
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Intransivity
Example
● Can you spot any transivities?
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Intransivity
Example
● Can you spot any transivities?
● Sniper! (But not the tank!)
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Intransivity
Example
● Can you spot any transivities?
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Intransivity
Actually there are much more factors
● Production cost/time, movement/reload speed, …
● These are all (over)simplified into one arrow
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Intransivity
Increase in complexity can result in less transivity
● More likely that there is a scenario
where a unit is useful
● But it’s also more difficult to check
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Example
In a racing game with multiple cars to choose from
● Three types: slow, medium, fast
They form a transitive relation!
Oh no!
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Example
Three types cars form a transitive relation
To counter this, they need a different property
● For example: acceleration, handling, …
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Intransivity
Intransivity is a way to model balance in a game
Disclaimer
● Simplified representation
● Usually it is only a model
○ Not a mathematical proof of balance
○ Most games are too complex
■ Real-time (instead of turn-based)
■ Psychological factors
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Balance
Dominant strategy
Balance
(In)transitive relations
(A)symmetric balance
Feedback loops
Player balance
Level design
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(A)symmetric balance
Intransivity is a method to analyze balance
(A)symmetric balance are types of
balancing between players
● Symmetric balance
● Asymmetric balance
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Symmetric games
Same set of rules for both players
● Both players have the same opportunity to win
● But dominant strategies can occur
Easier to balance
● But can be(come) boring to play
○ Why is that?
○ The system is usually less complex, thus less
uncertainty
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Symmetric games
Examples:
● Tic Tac Toe
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What about the first turn?
● Chess
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What about the first turn?
● Rock, Paper, Scissors
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Does it have asymmetric components?
● Civilization
○
The player invests in a strategy. When two players invest in a different
strategies, is the game asymmetric?
Symmetric games usually have asymmetric aspects
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Asymmetry
Not the same set of rules for both players
Different types of asymmetry
● The players choose a type/class/race at the start
○ But have the same goal
● The players have different goals
○ And thus play (slightly) different games
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(A)Symmetry
There are usually both symmetric and asymmetric
aspects in a game
Identify both symmetric and asymmetric aspects for the
following games
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A racing game
Team Capture the Flag
Asymmetry
Asymmetry can be created by varying attributes such as speed/strength/…
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For example: Oblivion
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Each race has different attribute modifiers
Still a lot of symmetry
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Asymmetry
Asymmetry can also be created by assigning unique
properties to types/classes
● For example: Team Fortress or Overwatch
○ Every character has truly unique moves
● Also called orthogonal unit differentiation
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Asymmetry
Can you think of a 100% asymmetric game?
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Asymmetric balance
Asymmetry requires balance to retain uncertainty
Does symmetry require balance?
● Not a balance of powers, but a balance of strategies. To
prevent a dominant strategy.
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Balancing asymmetric games
Balancing asymmetry can be difficult
● Especially when complexity rises
For example: A fighting game with 12 unique characters
● There are 12*12 = 144 different combinations to
balance!
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Balancing asymmetric games
Balancing asymmetry requires testing and iteration
● A lot of testing and iteration!
Usually too complex for mathematical verification or
simulated testing
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Dominant strategies
Symmetric balance
● Can have dominant strategies
● But the other player can copy it
Asymmetric balance
● More prone to dominant strategies
● And also the worst kind of dominant strategies
○ For example when one class is stronger than the
others
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Fairness
Symmetric balance
● Usually feels fair
● Both players have the same possibilities
Asymmetric balance
● Can easily feel unfair
● Is the other player better or is the game imbalanced?
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Balance
Dominant strategy
Balance
(In)transitive relations
(A)symmetric balance
Feedback loops
Player balance
Level design
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Feedback loops
Has nothing to do with player
feedback!
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Which is about communicating
the game state
A feedback loop is a type of rule
system
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The output affects the input again
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Machinations
Machinations are interactive diagrams which formalize
abstracted game rule systems
By Joris Dormans
Visualizes rule-systems in games nicely
● For example feedback loops
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Machinations
Example machination
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Machinations
Basketball
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Represents tactics and skill as a simple chance to score
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Positive feedback loop
Positive feedback loop in basketball
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Winning team gets more players
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Positive feedback loop
Positive feedback loop in basketball
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With equally skilled teams
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Positive feedback loop
Enlarges the difference
● More likely to lead to a definitive winner
More difficult for the losing team to recover
● Reduces uncertainty
Rewards success
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Negative feedback loop
Negative feedback loop in basketball
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Losing team gets more players
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Negative feedback loop
Reduces the difference
● Encourages the losing team recover
More difficult to get a winner
● Can be problematic in games without score
○ Such as RTS games
● Increases chances of a tie or stalemate
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Different example
Gaining experience in an RPG
● What kind of feedback loop is this?
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Gaining experience in an RPG
Positive feedback loop
● Spirals quickly out of control
● The player becomes extremely powerful
Balance with a negative feedback loop
● Experience becomes more difficult to obtain
● Enemies level with you
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Examples
Identify feedback loops for a game
● Positive feedback loops
● Negative feedback loops
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Balance
Dominant strategy
Balance
(In)transitive relations
(A)symmetric balance
Feedback loops
Player balance
Level design
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Player skill
At the start we noted that balance also depends on player
skill
● Ignored so far
Important issue in many games
● Especially online multiplayer games
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Player skill
A (large) difference in player skill removes uncertainty
● The experienced player always wins
● Loss is certain for the novice player
Online communities have a lot of skill difference
● Veterans playing since the start
● Novices who have just begun
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Balancing for player skill
Separate players of different skill levels
● Match players depending on skill
○ Using some sort of ranking score
○ Can be manipulated by creating a new account
● Restricted beginner areas
○ Used in MMORPGs
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Balancing for player skill
Create powerful options for novice players
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With a large chance factor for success
Keeps players encouraged
Other example
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Button bashing in fighting games
Pitfall: Players may not try other approaches to win and won’t learn
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players should be encouraged to explore other options
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Summary
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Balancing summary
● Balance is about preserving uncertainty
○ Symmetric and asymmetric aspects influence
balance differently
● Dominant strategies should be avoided
○ Modelling transivities can help to detect them
● Feedback loops can help preserving uncertainty
● Balance for differing player skill
○ In multiplayer games
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TODO’S
Assignment 3.1 – Analysis
Deadline March 16 before 23.59
Assignment 2.3 – prototype
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Meet with your tutor today
Discuss planning!
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