23 March 2011

[Literature] Game Balance ch4 - Cards, Dice, and Other Randomness

My notes from course 4 of the Game Balance class of Summer 2010, by Ian Schreiber.

Monte Carlo simulation = good way to approximate stats when the maths are too hard.

Dices are used for independent game events: each dice roll is independent of the previous roll. XdY = throw X items that have Y sides at the same time (ex: 1d6 = one 6-sided dice). For custom dices, eg a 6-sided dice with 1-1-1-2-2-3 on the sides: p(1)>p(2)>p(3).
More dice = less random (= smaller std deviation)> Example: p(7) for 1d10 is 1/10, but it is 10/32 for 5d2.

Cards are used for dependent game events: some events may not happen again if they have happened a certain number of times Revealing information as the game goes does not change the odds in previous player choices, but it changes the odds of non-player variables. Famous related problems: Monty Hall's 3 doors or families with at least one boy.

21 March 2011

[Literature] Game Balance ch3 - Transitive Mechanics and Cost Curves

My notes from course 3 of the Game Balance class of Summer 2010, by Ian Schreiber.

An intransitive game is like Rock-Paper-Scissors, where everything is better than something else and there is no single “best” move. In contrast, in transitive games, some elements are just flat out better than others, and we balance that by giving them different costs.

The cost is expressed in terms of game resource(s) (eg money, wood, existing units, items, technology, skills, ...) but can also consist of temporal restrictions (eg single-use constraint on a particular item, or a bonus being limited in time). A player wil pay a cost if she can see benefits to her situation (eg better stats, bonus skill). The goal for the game designer is to reach benefits = cost. In other words, if the weapon is overpowered, then either decrease its power (or any benefit) or increase its price (or any cost). Overpowered <=> undercosted.

A cost curve is a game balance technique designed to put everything in terms of the resource cost. In some games, you can choose to make an increasing, linear or decreasing curve, all of them might be balanced, but they have different effects on the gameplay. In Magic: the Gathering you get one Mana per turn. If you were the designer and you made a cost curve that was increasing, so that each additional point of mana gives you more benefit than the last, you’ll have a game where late-game cards are really powerful and early-game cards are pretty weak, so you’ll have a game that is heavily weighted towards late-game play. If the cost curve is decreasing, it puts more of a focus on the early game. The curve depends on the game duration you expect.

How to build or reverse-engineer a cost curve?

  1. Start with objects that have only one little effect: is their effect cost linear, exponential or log?
  2. then, combine effects; does having +2atk AND +5def in the same item more expensive than having them separately?
  3. then, look at limited or random effects
  4. then, keep in mind the metagame (ex: all goblins in the battlefield get a bonus => full goblin deck gets OP)

"Reverse-engineering" the transitive costs and benefits from an existing game means solving (mostly) linear equations. Ex: 2HP+1atk=5po and 3HP+2atk=10po => Xpo/HP and Ypo/atk. There might be inconsistencies/exceptions for elements "manually" balanced. Creating from scratch a cost curve = intuition + playtesting, then maths with later additions to the game. Guidelines to create a cost-curve:

  • A limited benefit is always worth something.
  • If an item gives the player the choice between benefit X or benefit Y, then the cost of this item is more than the cost of X + the cost of Y. Choice has a price.
  • Too weak is better than too powerful.

There is an "escalation of power" problem for CCG or MMO (mudflation), or any game which elements are persistent. When some elements are slightly overpowered, players find them after a while and these items become the standard. For the next expansion, the cost curve has to raise to adapt to these OP items, and the new set of items is balanced in this new higher curve. It forces players to buy things at each update, but it should not be too obvious, otherwise players will see it and leave the game. => Do it VERY slowly.

17 March 2011

[Literature] Game Balance ch2 - Numerical Relationships

My notes from course 2 of the Game Balance class of Summer 2010, by Ian Schreiber.

Numbers only have meaning in relation to each other. A few kinds of numerical relationships:

  • identical (1:2:3:4)
  • linear (2:4:6:8)
  • exponential (2:4:8:16)
  • triangular (1:3:6:10)

It is much easier to balance a system when you can put everything in terms of a single central resource. For example in CRPG such as Final Fantasy, everything can be put in terms of HP (gold is used to buy stuff to reduce dmg, hence increasing HP). In 2D platformers, the loss condition is lives (sometimes, it is score), and everything is tied to it.

Various loops in CRPG

XP - encounters: more encounters gets you more XP. Your level increases, and so do your stats, which in turn lets you face more encounters. The feedback loop here is not exactly positive, because as the level increases, the number of encounters needed to level up increases (non-linearly).

Equipment - encounters: Fight monsters, get gold, use it to buy better equipment, which lets you fight better monsters for even more gold and so on. This stops being a positive feedback loop at some point because there’s a limited set of equipment you can buy, and the best stuff requires you to travel to distant towns which can’t be reached from the start.

Gold - encounters: get more gold, which lets you buy keys, which lets you progress to new areas, which gets you to more dangerous and advanced encounters for more gold. Truly positive.

In RPG, the XP system serves as a negative feedback loop: higher-level players need to kill more monsters than low-level players. The designer can know quite precisely the level of the player, which makes it easy to design adequately challenging enemies. A fast leveling at the start is useful: it hooks up the player.

15 March 2011

[Literature] Game Balance ch1 - Intro

My notes from course 1 of the Game Balance class of Summer 2010, by Ian Schreiber.

What is game balance:

  • for single player games, it is difficulty, pacing, character progression
  • for multiplayer, advantage at the beginning of the game, strategies (any strategy could be viable OR some are more viable than others (could be overpowered)) or game objects

How to balance a game:

  • intuition (from experience, not teachable),
  • playtesting (statistical analysis, rely on player skill: novices could never find a needed good strategy),
  • math (numbers are everywhere in games)

Playtest is really needed for interconnected systems, because modifications can have rippled effects.
Player skill can make a difference in exploiting an imbalance.

Some game vocabulary

  • deterministic. Deterministic + perfect information = solvable.
  • solvable: has a single, knowable “best” action to take at any given point in play, and the player can know this action (it is undesired in games if it's trivial); including humans in the loop (like in Poker) fixes the problem of solvability
  • intransitive (eg in rock paper scissors, paper > rock and rock > scissors, but paper is not > scissors)
  • symmetric (means balance at the beginning, but not between game objects or strategies)
  • metagame: can be balanced as well, and definitely affects the game balance: drafting and rarity for trading card games, analyzing opponents' strategies to win the next Poker game, capping the salary of sport players so that most clubs can afford recruiting them


When trying to fix an unbalance, ask where it really comes from
If you do not know how much an advantage a beginning side is in a RTS like Warcraft3, you can let the playtesters bid in auctions for their beginning side. Knowing how much they give makes you know how much is necessary to balance the beginning state.
Allowing players to cooperate to kill the strongest player can balance a diplomacy game, but also sometimes only make it last longer and be more annoying (players do not want to appear too strong)

12 March 2011

[Literature] A theory of Fun for Game Design

Raph Koster. 2004. A Theory of Fun for Game Design. Paraglyph Press.

Quotes taken from Koster's book. I did not try to put them together in a meaningful way, I just copy-pasted those I found most interesting.

ch3: What games are

The only real difference between games and reality is that the stakes are lower with games.
The more formally constructed your game is, the more limited it will be. Long-lasting games integrate variables from outside the magic circle.
Fun from games arises out of mastery.
With games, learning is the drug. Fun is just another word for learning.

ch4: What games teach us

Most of the game designers working professionally today are self-taught.
Games are viewed as frivolity.
Games almost always teach us tools for being the top monkey.
Most games encourage demonizing the opponent. Can we create games that instead offer us greater insight into how the modern world works?
There has not been a topologically different 2d shooter since [the first 2d shooter to have power ups and bosses and scrolling]. Unsurprisingly, the shooter genre has stagnated and lost market share.
Algorithm for innovation: find a new dimension to add to the gameplay

ch5: What games are not

One of the most self-defeating rallying cry in history: "it's just a game"
The part of games that is least understood is the formal abstract system portion of it, the mathematical part of it. Games need to develop this formal aspect of themselves in order to improve.
This is why gamers are dismissive of the ethical implications of games. They do not see "get a blowjob from a hooker then run her over", they see a power up.
Since games are generally about power, control, and those other primitive things, the stories tend to be so as well.
When games and stories are good, you can come back to them repeatedly and keep learning something new.
Getting emotional effects out of games may be the wrong approach. Perhaps a better question is whether stories can be fun in the way games can.
Different kinds of enjoyment:

  • fun is the act of mastering a problem mentally
  • aesthetic appreciation
  • visceral reactions are generally physical and relate to the physical mastery of a problem
  • social status maneuvers, intrinsic to our self-image and our standing in a community

Aesthetics is about recognizing patterns, not learning new ones.
Delight does not last. Recognition is not an extended process.
Fun is the feedback the brain gives us when we are absorbing patterns for learning purposes. Real fun comes from challenges that are always at the margin of our ability.
Fun is contextual. The reason why we are engaging in an activity matter a lot.

ch6: Different fun for different folks

Since brains have different strengths and weaknesses, different people will have different ideal games.
People will usually choose to play the games they are good at, that reflect their strength.

ch7: The problem with learning

Players try to find the optimal path to getting to the ultimate goal.
Exploiters are often the most expert players of a game.
Since we dislike tedium, we'll allow unpredictability, but only in the confines of predictable boxes, like games or TV shows. Unpredictability means new patterns to learn, therefore unpredictability is fun.
Those of us who want games to be fun are fighting a losing battle against the human brain because fun is a process and routine is its destination.
If there is not a quantifiable advantage to doing something [reward], the brain will discard it.
Successful games incorporate:

  • preparation [choices made before a given challenge], otherwise it's chance. Can the player prepare in different ways and still succeed?
  • a sense of space, otherwise it's trivial. Does the environment affect the challenge?
  • core mechanics
  • challenges [= content] otherwise it's too short. Can the rule set support multiple types of challenges?
  • a range of abilities (otherwise it's simplistic). Can the player bring multiple abilities to bear on the challenge? At high levels of difficulty, does the player have to bring multiple abilities?
  • abilities should require skill. Not requiring skill from a player should be considered a cardinal sin in game design.

A learning experience require:

  • variable feedback (a greater skill should lead to better reward). Are there multiple success states (ie no guaranteed result)?
  • high-level players can not get benefits from easy encounters or they will bottom feed.
  • failure must have a cost. Player should have the ability to try again (with another preparation round).

ch8: The problem with people

Particular problems and solutions appeal to particular brain types.
Games are not there to fulfill power fantasies.
[The increasing complexity of games within a genre] has led to a priesthood of those who can master the intricacies. Newcomers can not get into them - the barrier for entry is too high.
Designeritis [= being] hypersensitive to patterns in games.
Given the lack of codification and critique of what games are, game designers have instead operated under the more guild-like model of apprenticeship. They do what they have seen work.

ch9: Games in context

The following chart can be applied to any medium.

User goal Collaborative Competitive Solo
Constructive Community
Team game design
Commercial game development
Experiential Performance
Single player games
Deconstructive Teaching
Strategy guide writing
Hack and cheats
Writing this book

It's a lot easier to fail to respond to a painting than to fail to respond to a game.
The closer we get to understand the basic building blocks of games (...) the more likely we are to achieve the height of art.

ch10: The ethics of entertainment

For games to really develop as a medium, they need to further develop the ludemes, not just the dressing. By and large, however, the industry has spent its time improving the dressing [...] It's just easy relative to the true challenge.
The best test of a game's fun [is] playing the game with no graphics, no music, no sound, no story, no nothing.
Ethical questions [in games] are aimed at the dressing.
The ludemes themselves can have social values.
As a medium, we have to earn the right to be taken seriously.

ch11: Where games should go

For games to really step up to the plate, they need to provide us with insights into ourselves.
When you feed a player [with a game], right now, we only know "fun" and "boring". Mastery of the medium of games will have to imply authorial intent. The formal systems must be capable of invoking desired learning patterns.

ch12: Taking their rightful place

Games need to develop a critical vocabulary so that understanding of our field can be shared.
Games will never be mature so long as designers create them with complete answers to their own puzzles in mind.


The challenge game designers face is "how do we create games that do not have one right answer?"
[Game designers] are not geeks in the basement rolling funny-shaped dice. Games deserve respect.