Balance - Rensselaer Polytechnic Institute (RPI)destem/gamemech/9.pdf• The simplest way to ensure...
Transcript of Balance - Rensselaer Polytechnic Institute (RPI)destem/gamemech/9.pdf• The simplest way to ensure...
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Balance2/25/16
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Twelve Types of Game Balance
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#1 Fairness
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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
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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
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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!
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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
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Plane Speed Maneuverability Firepower
Piranha Medium Medium Medium
Revenger High High Low
Sopwith Camel Low Low Medium
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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
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Plane Speed Maneuverability Firepower Totals
Piranha Medium (2) Medium (2) Medium (4) 8
Revenger High (3) High (3) Low (2) 8
Sopwith Camel Low (1) Low (1) Medium (4) 6
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Plane Speed Maneuverability Firepower Totals
Piranha Medium (2) Medium (2) Medium (4) 8
Revenger High (3) High (3) Low (2) 8
Sopwith Camel Low (1) Low (1) High (6) 8
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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!)
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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
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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.
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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
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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
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Or…Samurai
Shugenja
AshigaruArcher
Ninja
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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
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Or…Archers
Sorcerers
Barbarian Warrior
=
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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
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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…
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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
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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
Forward Kick -6 0 +6
Stomp +3 -6 0
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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
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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
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Win Rate
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Win Rate
Tier Lists
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Play FrequencyWin Rate
Tier Lists
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Play Rates Win Rates
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“C.Viper beats Akuma in 60% of fair, high-skill games”
Character strength?
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Terran Protoss Zerg
Terran 50% 59% 56%
Protoss 41% 50% 47%
Zerg 44% 53% 50%
36%
34%
30%
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https://github.com/blinkity/metagame
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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%.
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• 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
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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
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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
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Balance Graphs
A
B
no feedback
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Unfair/Unbalanced
A
B
if equal skill, player B has unfair advantage
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Stalemate
A
B
not enough positive feedback
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Balanced, but Too Short
A
B
too much positive feedback
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Monopoly
worst of both worlds
A
B
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Wild Swings in Lead
A
B
powerful negative feedback
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Ideal*
A
B
power struggle goes back and forth, but better player wins
*mostly
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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?
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#2: Challenge vs. Success
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Game Progression (time / difficulty)
Play
er S
kill
too boring
too frustrating
juuuuust right
Flow
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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
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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?
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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!
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#3: Meaningful Choices
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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?
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Definition of “Puzzle”
A puzzle is a (miniature) game with a dominant strategy
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How Many Choices?• Too many is as bad as not enough • Choices > Desires
• overwhelming • Choices < Desires
• frustrating • Choices == Desires
• Freedom! Fulfillment!
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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
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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?