Twelve Types of Game Balance

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Ashley Griffin
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1 Balance 2/25/16

2 Twelve Types of Game Balance

3 #1 Fairness

4 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

5 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

6 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!

7 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

8 Plane Speed Maneuverability Firepower Piranha Medium Medium Medium Revenger High High Low Sopwith Camel Low Low Medium

9 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

10 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

11 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

12 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!)

13 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

14 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.

15 The Interaction Matrix Leg Sweep Forward Kick Stomp Leg Sweep Forward Kick Stomp Shows payoff for playing a maneuver vs. your opponent s maneuver Game is zero-sum

16 Odd-Number Intransitive Relationships Samurai Shugenja Ashigaru Archer Ninja Samurai Shugenja Ashigaru Archer Ninja

17 Or Samurai Ninja Shugenja Archer Ashigaru

18 Even-number Intransitive Relationships Archer Warrior Barbarian Sorcerer Archer Warrior Barbarian Sorcerer Some players find this asymmetry appealing, since the player doesn t merely have to learn a cyclical pattern of win-lose relationships

19 Or Archers = Sorcerers Barbarian Warrior

25 The Interaction Matrix Leg Sweep Forward Kick Stomp Leg Sweep Forward Kick Stomp Shows payoff for playing a maneuver vs. your opponent s maneuver Game is zero-sum

26 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

27 Net Payoff Matrix Leg Sweep Forward Kick Stomp Leg Sweep Forward Kick Stomp 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

28 Finding the Ratio of Use We ll call the net payoff for using each move L p, F p, S p. We ll call the respective frequencies L f, F f, S f. Thus, the net payoff for using the leg sweep is: L p = (0 x L f ) + (6 x F f ) + (-3 x S f ) These values are taken from the net payoff Leg Sweep Forward Kick Stomp matrix Leg Sweep Forward Kick Stomp

29 The Equations L p = 6F f - 3S f F p = 6S f - 6L f S p = 3L f - 6F f Since it s zero sum: L p + F p + S p = 0 Since we re looking for the equilibrium: L p = F p = S p = 0

30 The Equations Solving gives us the ratio L f : F f : S f = 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

32 Win Rate

33 Win Rate Tier Lists

34 Tier Lists Win Rate Play Frequency

35 Play Rates Win Rates

36 C.Viper beats Akuma in 60% of fair, highskill games Character strength?

37 Terran Protoss Zerg 36% 34% 30% Terran 50% 59% 56% Protoss 41% 50% 47% Zerg 44% 53% 50%

45 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%.

49 Understanding Positive Feedback 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

50 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

51 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

52 Balance Graphs no feedback A B

53 Unfair/Unbalanced if equal skill, player B has unfair advantage A B

54 Stalemate not enough positive feedback A B

55 Balanced, but Too Short too much positive feedback A B

56 Monopoly worst of both worlds A B

57 Wild Swings in Lead powerful negative feedback A B

58 Ideal* power struggle goes back and forth, but better player wins A B *mostly

59 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?

60 #2: Challenge vs. Success

61 Flow too boring Player Skill juuuuust right too frustrating Game Progression (time / difficulty)

62 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

63 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?

64 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!

65 #3: Meaningful Choices

66 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?

68 Definition of Puzzle A puzzle is a (miniature) game with a dominant strategy

69 How Many Choices? Too many is as bad as not enough Choices > Desires overwhelming Choices < Desires frustrating Choices == Desires Freedom! Fulfillment!

70 Triangularity a.k.a. balanced asymmetric risk common omission, leading to one of the biggest reasons that the prototype just isn t fun Low risk/ low reward High risk/ high reward Player

72 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?

Game Balance. Chris Ko and Jonathan Janosi

Game Balance. Chris Ko and Jonathan Janosi Game Balance Chris Ko and Jonathan Janosi A good game is a series of interesting choices. - Sid Meier Balancing Games 2 Major issues Fairness (PvE) Difficulty (PvP) What is a balanced game? Characteristics