balance - rensselaer polytechnic institute (rpi)destem/gamemech/9.pdf• the simplest way to ensure...

Balance2/25/16

Twelve Types of Game Balance

#1 Fairness

Symmetry

• The simplest way to ensure perfect balance is by exact symmetry

• Not only symmetrical in weapons, maneuvers, hit points etc., but symmetrical in level (i.e. no player starts with a better position)

• Although fair, it is often uninteresting

Symmetry

• Symmetric maps would look unrealistic, and is a too obvious solution to equalize the odds

• Better to have a level which is functionally symmetrical, but not obviously

• Have players be flanked by different geographical barriers, needing different units to proceed.

• The most difficult (but best!) solution is to give each player different choices, but giving them the same chance to succeed

Symmetry• If players are able to choose their starting

positions, then you don’t want any position on the map to have an overwhelming advantage

• Most general solution in this scenario is to avoid making the initial setup important

• E.g. there’s resources everywhere!

Why Go Asymmetric?

• To simulate a real-world situation

• To give players another way to explore the playscape

• Personalization

• To level the playing field

• To create interesting situations

Plane Speed Maneuverability Firepower

Piranha Medium Medium Medium

Revenger High High Low

Sopwith Camel Low Low Medium

Plane Speed Maneuverability Firepower Totals

Piranha Medium (2) Medium (2) Medium (2) 6

Revenger High (3) High (3) Low (1) 7

Sopwith Camel Low (1) Low (1) Medium (2) 4




Sopwith Camel Low (1) Low (1) Medium (4) 6




Sopwith Camel Low (1) Low (1) High (6) 8

Intransitive Relationships

• transitive, adj. - being or relating to a relation with the property that if the relation holds between a first element and a second and between the second element and a third, it holds between the first and third elements

• intransitive, adj. – not transitive (boom!)

Intransitive Game Mechanics

• Consider a fighter game with three main attacks. Forward kick, stomp, and leg sweep

• Leg sweep beats forward kick • Forward kick beats stomp • Stomp beats leg sweep

Intransitive Game Mechanics

• Against an AI that chooses randomly, you can equal its score by continually executing one move (e.g. leg sweeps). You will win, lose, and draw 1/3 of the time

• A human opponent would recognize this behavior, and adapt by using more stomps, which would force me to use more forward kicks, etc.

The Interaction Matrix Leg Sweep Forward Kick Stomp

Leg Sweep 0 +1 -1

Forward Kick -1 0 +1

Stomp +1 -1 0

• Shows payoff for playing a maneuver vs. your opponent’s maneuver

• Game is zero-sum

Odd-Number Intransitive Relationships

Samurai Shugenja Ashigaru Archer Ninja

Samurai 0 +1 +1 -1 -1

Shugenja -1 0 +1 +1 -1

Ashigaru -1 -1 0 +1 +1

Archer +1 -1 -1 0 +1

Ninja +1 +1 -1 -1 0

Or…Samurai

Shugenja

AshigaruArcher

Ninja

Even-number Intransitive Relationships

Archer Warrior Barbarian Sorcerer

Archer 0 +1 -1 0

Warrior -1 0 +1 +1

Barbarian +1 -1 0 -1

Sorcerer 0 -1 +1 0

Some players find this asymmetry appealing, since the player doesn’t merely have to learn a cyclical pattern of win-lose

relationships

Or…Archers

Sorcerers

Barbarian Warrior

=

The Interaction Matrix Leg Sweep Forward Kick Stomp

Leg Sweep 0 +1 -1


Stomp +1 -1 0

• Shows payoff for playing a maneuver vs. your opponent’s maneuver

• Game is zero-sum

What if the Costs were Different?

• Suppose a stomp costs 3 points, a forward kick costs 2 points, and a leg sweep costs 1 point

• Also suppose that by beating your opponent, you gain 5 points, and you lose 5 points if you are defeated

• The net payoff matrix now becomes…

Net Payoff Matrix Leg Sweep Forward Kick StompLeg Sweep 0 +6 -3Forward Kick -6 0 +6Stomp +3 -6 0

Thus, if I choose leg sweep and you choose stomp, you spend 3 points and I spend 1 point, meaning the

difference is +2 points in my favor. But because stomp beats leg sweep, I lose 5 points, netting me -3

Finding the Ratio of Use

• We’ll call the net payoff for using each move Lp, Fp, Sp. We’ll call the respective frequencies Lf, Ff, Sf. Thus, the net payoff for using the leg sweep is:

• Lp = (0 x Lf) + (6 x Ff) + (-3 x Sf) • These values are taken from the net payoff

matrix Leg Sweep Forward Kick Stomp

Leg Sweep 0 +6 -3


Stomp +3 -6 0

The EquationsLp = 6Ff - 3Sf

Fp = 6Sf - 6Lf

Sp = 3Lf - 6Ff

Since it’s zero sum:

Lp + Fp + Sp = 0

Since we’re looking for the equilibrium:

Lp = Fp = Sp = 0

The Equations

• Solving gives us the ratio

Lf : Ff : Sf = 2 : 1 : 2 • What this means is that for the game to reach equilibrium,

the leg sweep and stomp need to be used 40% of the time, while the forward kick is used 20% of the time

• This isn’t immediately obvious, hence the need to do the math

• If one option is expensive, often the other options are most affected

Win Rate

Win Rate

Tier Lists

Play FrequencyWin Rate

Tier Lists

Play Rates Win Rates

“C.Viper beats Akuma in 60% of fair, high-skill games”

Character strength?

Terran Protoss Zerg

Terran 50% 59% 56%

Protoss 41% 50% 47%

Zerg 44% 53% 50%

36%

34%

30%

https://github.com/blinkity/metagame

Death Knight

General Blood Boil, Blood Plague, Death Coil, Death and Decay, Frost Fever, and Soul Reaper damage has been increased by 10%. Frost Frost Strike, Howling Blast, and Obliterate damage has been increased by 10%. Unholy Festering Strike, Necrosis, and Scourge Strike damage has been increased by 10%. Talents Defile and Necrotic Plague damage has been increased by 10%.

• Positive feedback occurs when a player’s achievement changes the game state, making future achievements easier

• Benefits of positive feedback

• Discourages a stalemate

• Rewards success

Understanding Positive Feedback

Controlling Positive Feedback

• Increase Luck

• Often at the cost of strategic thinking

• Let other players collude against leader

• Diplomacy

• Only works with 3 or more players

• Define victory in non-numeric terms

• Taking a chess piece is positive feedback, but victory is not defined by number of pieces captured

Controlling Positive Feedback

• Introduce negative feedback!

• Benefits have costs associated with them

• Mario Kart - most weapons shoot forward - if you’re in the lead, everyone’s shooting at you!

• Blue shell = concentrated negative feedback!

• Make the game get harder

• Get better weapons, but monsters become more difficult

Balance Graphs

A

B

no feedback

Unfair/Unbalanced

A

B

if equal skill, player B has unfair advantage

Stalemate

A

B

not enough positive feedback

Balanced, but Too Short

A

B

too much positive feedback

Monopoly

worst of both worlds

A

B

Wild Swings in Lead

A

B

powerful negative feedback

Ideal*

A

B

power struggle goes back and forth, but better player wins

*mostly

The Questions of Fairness

• Should my game be symmetrical? Why?

• Should my game be asymmetrical? Why?

• Which is more important: that my game is a reliable measure of who has the most skill, or that it provide an interesting challenge to all players?

• If I want players of different skill levels to play together, what means will I use to make the game interesting and challenging for everyone?

#2: Challenge vs. Success

Game Progression (time / difficulty)

Play

er S

kill

too boring

too frustrating

juuuuust right

Flow

Techniques

• Increase difficulty with each success

• Let players get through easy parts fast

• Create “layers of challenge”

• Let players choose the difficulty level

• Playtest with a variety of players

The Questions of Challenge

• What are the challenges in my game?

• Are they too easy, too hard, or just right?

• Can my challenges accommodate a wide variety of skill levels?

• How does the level of challenge increase as the player succeeds?

• Is there enough variety in the challenges?

• What is the maximum level of challenge in my game?

Dynamic Game Balancing

• Seems like a good idea!

• Beware these pitfalls:

• It spoils the reality of the world

• It is exploitable

• Players improve with practice

• Go forth and provide new theory!

#3: Meaningful Choices

Questions You Want Players Asking Themselves• Where should I go?

• How should I spend my resources?

• What should I practice and try to perfect?

• What do I want my character to look like?

• Should I try to get through the game quickly or carefully?

• Should I focus on offense or defense?

• What strategy should I use in this situation?

• Which power should I choose?

• Should I play it safe, or take a big risk?

Definition of “Puzzle”

A puzzle is a (miniature) game with a dominant strategy

How Many Choices?• Too many is as bad as not enough • Choices > Desires

• overwhelming • Choices < Desires

• frustrating • Choices == Desires

• Freedom! Fulfillment!

Triangularity• a.k.a. “balanced asymmetric risk”

• common omission, leading to one of the biggest reasons that the prototype “just isn’t fun”

Player

Low risk/ low reward

High risk/ high reward

Questions of Meaningful Choice

• What choices am I asking the player to make?

• Are they meaningful? How?

• Am I giving the player the right number of choices? Would more make them feel more powerful? Would fewer make the game clearer?

• Are there any dominant strategies?

• Do I have triangularity? If not, how can I get it?

• Are the rewards commensurate with the risks?

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