CAP 203 - Computer Animation III

Chapter 10 - Some Elements are Game Mechanics

Objectives:

This lesson discusses material from chapter 10 of The Art of Game Design. Objectives important to this lesson:

  1. Space
  2. Objects, Attributes, States
  3. Actions
  4. Rules
  5. Skill
  6. Chance
Concepts:

Chapter 10 discusses six kinds of mechanics in games. The first is Space. Most games take place in a space defined in the game. It is helpful to a game designer to think of the space as either discrete or continuous. The author uses typical board games as examples of discrete space. For example, on a chess board, any point in space within a square is as good as any other point in space in the same square. In a first person shooter, however, the game will probably use continuous space. Where a character is standing or running in a continuous space will have an effect on the shots the character fires at an opponent, whether moving or stationary. There are no discrete squares in a game like that. Inches of difference in location make a difference in what happens.

The author uses a pool table as an example of continuous space. Small differences in location make big differences in how the game is played. Also, it is arguable whether a pool table should be represented as a two dimensional space or a three dimensional space. Most people will play pool in two dimensions, but a really good player can loft a ball over another ball. Take it a little farther: you play pool with more than balls and a table. The players and their cue sticks are also important pieces. Consider that, and you can see that pool is a three dimensional game.

It is also important to think about connections between spaces in a game. Think about the chess board again. It is obvious how the squares are connected, right? It is less obvious that some squares are connected in different ways if the pieces can move in different ways.

  • A pawn moves only forward, but it attacks only diagonally.
  • Bishops only move on unobstructed diagonals.
  • Rooks only move on unobstructed rows and columns (ranks and files).
  • Knights move in L-shaped paths, regardless of obstruction, as long as the final square is open or holds an opposing piece. For them, squares are connected in ways that they are not connected for any other piece. In this respect, a connection between spaces represents movement that could take place.

In terms of tic tac toe, connected spaces represent the possible structures of three in a row that the players could potentially achieve. A game needs a definition of space according to how it is used in that game.

Spaces in a game can also be nested, like rooms in buildings. Space can also be virtual, in that it does not even exist in the game. Trivia games are like this. The author suggests that twenty questions does not use physical space, but it can be considered to use three virtual spaces:

  • the questioner's space - where the questioner plans questions and ponders answers
  • the answerer's space - where the answerer holds the answer and constructs responses to questions
  • the game space - where the questions are posed and answers are given

Sound too formal? Well, think about those spaces in the context of a game with more formality, like Jeopardy®. The players have physical space, and so does the moderator. The clues appear in a space as well, but are any of those spaces necessary? Once we grant the logical space they exist in, that is sufficient to play. The designer of the TV show made spatial improvements. Without them the game would fit better on radio.

Lens 21, the Lens of Functional Space, asks us to think about the spaces used in a game.

  • Is the space discrete or continuous?
  • How many dimensions are used?
  • What are the boundaries?
  • Are there sub-spaces (nested spaces)?
  • How are the spaces connected?
  • Is there more than one useful way to model the space?

Games are described a bit like databases in the next section. Games contain objects, which is another way of saying games have things in them, and that we track information about them.

In chess, the pieces are examples of objects. Objects have attributes and attributes have states (values). A chess piece might have an attribute like "movement", and its state might be "free" or "blocked". Some pieces will have attributes that other pieces do not. Queens, Rooks, and Bishops might have attributes we could call "direction" and "distance", whose states would be related and have multiple values (Which ways can they move, and how far each way?). Those states will also change as the game is played. This is what Mr. Schell is talking about when he says we might diagram the states of each attribute and the events in the game that would trigger or cause changes in state.

Sometimes, information about objects in a game is public to all players. In other games, some information is public, and some is known to one player or a group of players. Information may be revealed to one or more players as the game goes on, as in Battleship or Clue®. Mr. Schell relates a story about his grandmother that helps us understand an element that exists only in electronic games: his grandmother chose not to play an electronic card game because she believed that the game knew what her cards were. She had a point. The game itself had to "know" about her cards, because it told her what the cards were. What the player must believe, in order to enjoy the game, is that the virtual player in the machine (her opponent) was not given this information by the game. This may make you feel differently about video poker or blackjack in a real casino. We take the honesty of the game and its programmer on faith. How would we know if the game were actually revealing information to the virtual opponent?

Mr. Schell makes a list of kinds of information about the state of objects in games, based on who is allowed or able to know it:

  • completely public - all information is available to everyone, as in chess and checkers
  • shared among multiple players - in Clue®, for example, you might reveal information to one other player, but not to the rest
  • private to a single player - in standard poker, your cards are your business and no one else's until you show them to the other players
  • private to the game - in Fallout 3®, every time you try to hack a computer system, a new password is generated for that system; the game knows the answer, but you must guess it or reason it out.
  • random information - like shuffling a physical deck of cards; the state of the objects (their location in the shuffled deck) is unknown to the players and to the game as well, although in an electronic version, the game would have to know this information as it is generated

Lens 22, the Lens of Dynamic State asks us to examine this database aspect of our game:

  • What are the game's objects?
  • What are the attributes of the objects?
  • What are the possible states (values) of the attributes?
  • What triggers a change in state of an attribute?
  • Who knows what information states at a given moment?
  • Can the game be improved by changing who knows what information states?

If objects are the nouns of our game (page 136) then actions are the verbs (page 140). Mr. Schell defines the things players can do in a game as the operative actions. These actions can be viewed in terms of why the player does them, what strategy the player is applying to the game. When he associates a purpose with an action in this way, Mr. Schell calls it a resultant action.

A resultant action relates to a player's intentions. Playing without intention is like placing marks randomly on a tic tac toe board. It is legal, but it is unlikely to be successful or fun. We are going for fun. So, it seems obvious that the game must engage the player's mind for resultant actions to exist in it. This leads to the observation that we should tailor the game to produce emergent actions, actions that are interesting resultant actions because of their effects on the game. They are called emergent because the rules do not require them, but they are allowed within the game and players discover that they are interesting, beneficial, or otherwise enjoyable.

Mr. Schell offers a short list of tweaks that can add to the list of emergent actions in your game:

  • add more verbs - adding more operative actions to a game increases the probability of emergent actions being discovered. The ratio of resultant actions to operative actions can give you a measure of the effectiveness of adding the new actions: add actions that create resultant actions, remove needless actions that do not add resultant actions
  • verbs that can be used on many objects - the author points out that being able to shoot an NPC (non-player character) is interesting, but being able to get results from shooting various other objects in a game makes the game and the gun more interesting (What happens when you shoot a car? How about a wall? How about a fire extinguisher?)
  • goals that can be met several ways - this allows a player without specific objects to find a way to meet a goal with objects they have, which increases discovery and replay options
  • many subjects - this introduces a new term; a subject is a playing piece in a game. In terms of adventure games, a subject would be a character. More subjects leads to more kinds of interaction, which leads to more emergent play. This is why playing a game with one character is quite different from playing it with a group of characters.
  • side effects that change constraints - changing the restrictions on players, changing the game space, changing the actions that can be taken, all have an effect on the emergent play that becomes possible after the change.

This takes us to lens 23, the Lens of Emergence:

  • How many verbs are in the game? What are they?
  • How many objects can each verb be used with?
  • How many ways can a goal be achieved?
  • How many subjects does a player control?
  • How do constraints change in the game?

 

Lens 24, the Lens of Action is also related to this discussion:

  • What are a player's operative actions?
  • What are the resultant actions?
  • What resultant actions do I want in the game? How can I add them to the game?
  • Is the ratio of resultant actions to operative actions acceptable?
  • What do players want to do in the game that they cannot do? How do we fix that?

Assignment #8:

  1. Form groups for a project assignment if you have not already done so.
  2. Examine a game of your choice, using the Lenses discussed above.
  3. Turn in a proposal for improving the game using the Lenses above.

The fourth mechanic element is the game's rules. Mr. Schell offers a list of eight kinds of rules from the work of David Parlett.

  1. Operational rules - what players do when they play the game
  2. Foundational rules - formal representations of the thing that happen in the game, such as descriptions of how character skill levels are increased, and by what specific amounts or ranges of amounts
  3. Behavioral rules - the social rules of playing the game; the unwritten rules of sportsmanship. Mr. Schell references a work by Steven Sniderman about rules. Apparently his name is Stephen Sniderman. A copy of the article is here.
  4. Written rules - the actual rules that are given to a player with the game, whether printed or electronic. Mr Schell makes a point that most (many?) players learn games from each other, not from the written rules.
  5. Laws - specific rules that apply when playing for money or status; may be called tournament rules because they are often created for tournament play
  6. Official rules - a combination of written rules and laws; created by players who want one set of rules for their play
  7. Advisory rules - strategy guidelines suggested by various players
  8. House rules - rules that players make up to make the game better (in their point of view); for example, some people place money in Free Parking (in Monopoly®) every time they pass go, so that a player who lands on that space can collect the money

At different times during a game, different rules may apply. This has the effect of placing the player in a sub-game when the new rules are applied.

Someone typically has to enforce rules. In a computer based game, the game program itself can do this. In other types of games, the rules may be enforced by the players or by a person whose job it is to monitor game play (like an umpire or a referee in sports).

The text goes into a sub-game of its own by stating that there is one all important rule that needs its own lens. The rule is the Object of the Game, a statement of the player's goals. Mr. Schell states that the goals of a good game have three qualities to be aware of:

  • concrete - the goals are clearly stated so that the players can understand them
  • achievable - the player needs to believe that the the goals can be met; not that this does not say that the goals can be met, only that the player must believe that they can be met. This probably explains gambling.
  • rewarding - the process of achieving the goal should be rewarding to the player, and the goal itself should be as rewarding as the player has been led to believe it will be

This takes us to lens 25, the Lens of Goals:

  • What is the ultimate goal of the game?
  • Is the goal clearly understood by players?
  • Do the players understand your series of goals (if they exist)?
  • Do the goals in your series relate to one another?
  • Are the goals concrete, achievable, and rewarding?
  • Are there long term and short term goals? Is the mixture a good balance?
  • Can players choose their goals?

Leaving the sub-game, we are given lens 26, the Lens of Rules:

  • What rules, of each of the types above, are used in my game?
  • Is the game growing laws or house rules? If so, should they be added to the written rules?
  • Does the game have different modes that use different sets of rules? Should there be more or less of these?
  • How are rules enforced, and by whom?
  • Do the rules need simplifying?

The fifth mechanic element is skill. Mr. Schell lists three types of skills, which should each be viewed as being real or virtual in the game. (page 151)

  • physical - skills typically used in sports; real skills are required in real sports, character skills are required in virtual environments
  • mental - memory, observation, puzzle solving, decision making, resource gathering and use; typically, these are real skills the player must have, even in a virtual environment
  • social - understanding opponents and teammates

A game designer should allow for a player to become better at the game, and accommodate that with greater challenge, as noted previously. It is recommended that you analyze your game, listing all the skills needed to play it, and deciding what could be added to improve it.

Lens 27, the Lens of Skill:

  • What player skills does the game require?
  • Are there categories of skill missing that we could add to the requirements?
  • What skill is used most?
  • Do these skills add to the desired experience?
  • If some players are better than others, does the game seem unfair?
  • Can players improve their skills by playing more?
  • Does the game require "the right" skill level?

The last mechanic is chance, or probability. The text talks about probability math for a dozen pages. Read the material if you are interested and unfamiliar with the subject. You will need to appreciate the laws of probability to design games that use random number generators to determine combat or other events. Mr. Schell offers us some facts about probability and some lenses to go with them:

  1. Fractions, decimals, and percents are equivalent mathematical expressions.
  2. A probability of 0 is 0%: something will not happen. A probability of 1 is 100%: something must happen. All other probabilities fall between these extremes. There is no such thing as a probability greater than 1 or less than 0.
  3. Looked For divided by Possible Outcomes equals Probability. This means: the number of ways for a particular thing to happen, divided by the number of ways anything can happen equals the probability of the first thing happening.
    Example: Humans typically have two genes for eye color. You get one from each parent. If you have a brown eyed parent, who has one brown gene and one blue gene (brown is dominant) and you have a blue eyed parent who has two blue genes (the only way to get blue eyes), what is the probability that you have blue eyes?

      blue gene blue gene
    brown gene brown-blue: brown eyes brown-blue: brown eyes
    blue gene blue-blue: blue eyes blue-blue: blue eyes

    There are four ways to get genes from these two parents. Your probability of getting blue eyes is 2 in 4, or 2/4, or .5, or 50%. What if your brown eyed parent had only brown genes? Every combination you could get from those parents (4) would result in your getting one brown gene and one blue gene, which would produce brown eyes. (4/4, or 100%)
  4. Enumerate: list every possible way for things to happen. In the example above, I listed each of the four possible outcomes, and stated what would happen in each case.
  5. If you are calculating the probability of either of two things happening (a OR b) add the probability of a to the probability of b, ONLY if a and b are mutually exclusive. In the example above, what is the probability of getting either blue or brown eyes? 100%, because you can only get blue or brown in this situation (mutually exclusive), and each has a probability of 50%.
  6. If two events are not mutually exclusive, you can multiply their probabilities to get the probability of both things happening.
  7. If you can easily calculate the probability of something happening, or of it not happening, you only have to subtract whichever you know from 100% to get the other one.
  8. Not all events have equal probabilities Consider the table Mr. Schell presents of the outcomes of throwing two six-sided dice (page161). The total can run from 2 to 12. Are all totals equally probable? There are 36 possible outcomes, and only one of them has a total of 2. Only one other event has a total of 12. This makes the odds of one of these events happening 1 in 36. Enumerating the possible events and their values makes this clear.
  9. If you can't calculate, run the system enough times to get an idea of the probability of events.
  10. If you can't figure it out, find a mathematician.

So, why do we examine probability? We want to know the real probability of an outcome before we pick an action in a game. Players want to do the same, but they will rarely calculate probability, even if they have the data to do so. Mr. Schell recommends that we consider a quantity he calls the expected value of an event. If you calculate the value for each possible outcome of an event, then take the average (mean) of those values, you get the average value of the event, the expected value. This leads to lens 28, the Lens of Expected Value:

  • What is the probability of an event?
  • What does the player think the probability of the event is?
  • What is the value of the event for the player?
  • Are the values of the possible events too rewarding or too punishing? Is the player interested in the events?

The chapter ends with a discussion of the relationship between skill and chance.

  • Estimating chance (probability) is a skill. Players who are better at doing it will be more successful in games that involve it.
  • Skills have a probability of success. He means that it is not certain that a skilled player will always triumph. Every action a player takes will have some probability of success that is less than 100%.
  • Estimating an opponent's skill is a skill. This works both ways. A good bluffer will make the opponent think the wrong thing and take the wrong action. A good player will be able to read other players more accurately, and take a right action based on that read.
  • Predicting pure chance is not a skill, it is an imagined skill. In other words, you can't predict a truly random event. Mr. Schell cites the case of a gambler believing that a lucky streak will continue, or that a bad luck streak will end because he is due to win. Both beliefs ignore probability.
  • Controlling pure chance is an imagined skill. This means that relying on superstitious behavior to control fate makes no sense. It ignores the math above.

The last lens for the chapter is lens 29, the Lens of Chance:

  • What parts of the game are random? What parts appear random, but are not?
  • Does the randomness excite or depress the players?
  • Does changing the probability of events improve the game?
  • Are the risks in the game interesting to players?
  • Do I have the right mix of chance and skill in the game?