Transcript Games Defined - DePaul University

Information 2
Robin Burke
GAM 224
Spring 2004
Outline
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Admin
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Uncertainty
Information theory
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"Rules" paper
Signal and noise
Cybernetics
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Feedback loops
Admin
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Due today
 Design Milestone #2
• your group should have picked a game
• you will be working to extract the core
mechanic
"Rules" paper
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Due 5/2
 Analysis paper #1: "Rules"
 You should be playing your game and taking notes
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Important points
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thesis
• "great game" is not a thesis
• This is a thesis
•
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"Inertial navigation, fixed firing direction and accurate collision detection in
Asteroids create an environment in which ship orientation is highly coupled,
generating emergent forms of gameplay."
documentation
• game itself, book, lectures
• other sources if used
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Note
 you cannot use lab machines to do word processing
 laptops are OK
"Rules" paper 2
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Schemas
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Emergence
Uncertainty
Information Theory
Information Systems
Cybernetics
Game Theory
Conflict
Do not use them as an outline
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select one or two that are relevant to your
game
"Rules" paper 3
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Turn in
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hardcopy in class 5/2
Late policy
½ grade per day
 submit by email
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Uncertainty
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Many games are probabilistic
roll the dice
 shuffle the cards
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Some games are not
Chess
 Checkers
 Dots and Boxes
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Certainty vs uncertainty
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Certainty
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Some games operate this way
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the condition when the outcome of an action
is known completely in advance.
Chess
Dots and Boxes
But even then
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uncertainty about who will win
otherwise what is the point?
Probability
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Probability is the study of chance
outcomes
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originated in the study of games
Basic idea
a random variable
 a quantity whose value is unknown
until it is "sampled"
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Random variable 2
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We characterize a random variable
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not by its value
but by its "distribution"
the set of all values that it might take
and the percentage of times that it will take
on that value
distribution sums to 1
• since there must be some outcome
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Probability
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the fraction of times that an outcome occurs
Single Die
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Random variable
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# of spots on the side facing up
Distribution
1...6
 each value 1/6 of the time
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Idealization
Single die
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Random variable
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odd or even number of dots
Distribution
odd or even
 50%
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Distributions are not always uniform
Two dice
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Random variable
 sum of the two die values
Distribution
 2, 12 = 1/36
 3, 11 = 1/18
 4, 10, = 1/12
 5, 9 = 1/9
 6, 8 = 5/36
 7 = 1/6
Non-uniform
 not the same as picking a random # between 2-12
 dice games use this fact
Computing probabilities
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Simplest to count outcomes
Dice poker
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roll five die
keep best k, roll 5-k
becomes your "hand"
Suppose you roll two 1s
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what are the outcomes when your roll the
other 3 again to improve your hand?
Outcomes
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Each possible combination of
outcomes of 3 rolls
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6 x 6 x 6 = 216 possible outcomes
6, 6, 6
Questions
Probability of 3 of kind
or better?
 Probability of 4 of a
kind or better?
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6, 6, 1
Die #2
Die #3
1, 1, 1
Die #1
Intuition for Games
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Asking somebody
to do the same uncertain task over
increases the overall chance of
success
 to succeed on several uncertain tasks
in a row decreases (a lot) the overall
chance of success
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Role of Chance
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Chance can enter into the game in various
ways
Chance generation of resources
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Chance of success of an action
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dealing cards for a game of Bridge
rolling dice for a turn in Backgammon
an attack on an RPG opponent may have a
probability of succeeding
Chance degree of success
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the attack may do a variable degree of
damage
Role of Chance 2
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Chance changes the players' choices
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player must consider what is likely to happen
• rather than knowing what will happen
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Chance allows the designer more latitude
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the game can be made harder or easier by
adjusting probabilities
Chance preserves outcome uncertainty
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with reduced strategic input
example: Thunderstorm
Random Number
Generation
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Easy in physical games
 rely on physical shuffling or perturbation
 basic uncertainty built into the environment
• "entropy"
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Not at all simple for the computer
 no uncertainty in computer operations
 must rely on algorithms that produce "unpredictable"
sequences of numbers
• an even and uncorrelated probability distribution
sometime variation in user input is used to inject noise
into the algorithm
Randomness also very important for encryption
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Psychology
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People are lousy probabilistic reasoners
Reasoning errors
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We overvalue low probability events of high
risk or reward
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Most people would say that the odds of
rolling a 1 with two die = 1/6 + 1/6 = 1/3
Example: Otherwise rational people buy
lottery tickets
We assume success is more likely after
repeated failure
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Example: "Gotta keep betting. I'm due."
Psychology 2
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Why is this?
Evolutionary theories
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Pure chance events are actually fairly rare outside of games
• Usually there is some human action involved
• There are ways to avoid being struck by lightning
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We tend to look for causation in everything
• Evolutionarily useful habit of trying to make sense of the world
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Result
• superstition
• "lucky hat", etc.
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We are adapted to treat our observations as a local sample
of the whole environment
• but in a media age, that is not valid
• How many stories in the newspaper about lottery losers?
Psychology 3
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Fallacies may impact game design
Players may take risky long-shots
more often than expected
 Players may expect bad luck to be
reversed
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Information theory
From Wednesday
 Information can be
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public
 private
 unknown (to players)
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Information Theory
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There is a relationship between uncertainty
and information
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Information can reduce our uncertainty
Example
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The cards dealt to a player in "Gin Rummy"
are private knowledge
But as players pick up certain discarded
cards from the pile
It becomes possible to infer what they are
holding
Information Theory 2
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Classical Information Theory
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Shannon
Information as a quantity
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how information can a given communication
channel convey?
• compare radio vs telegraph, for example
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must abstract away from the meaning of the
information
• only the signifier is communicated
• the signified is up to the receiver
Information Theory 3
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Information as a quantity
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If you are listening on a channel for a yes or no answer
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many more bits need to be conveyed
Because there are more ways that people can look
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only one bit needs to be conveyed
If you need a depiction of an individual's appearance
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measured in bits
binary choices
young / old
race
eye color / shape
hair color / type
height
dress
A message must be chosen from the vocabulary of signifier options
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book: "information is a measure of one's freedom of choice when selecting a
message"
Information Theory 4
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This is the connection between
information and uncertainty
the more uncertainty about something
 the more possible messages there are
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Noise
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Noise interrupts a communication channel
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by changing bits in the original message
increases the probability that the wrong
message will be received
Redundancy
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standard solution for noise
• more bits than required, or
• multi-channel
Example 1
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Gin Rummy
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Unknown
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What cards are in Player X's hand?
Many possible answers
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Once I look at my 10 cards
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15 billion (15,820,024,220)
about 34 bits of information
1.5 billion (1,471,442,973)
about 30 bits
Signal
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I have two Kings
Player X picks up a discarded King of Hearts
Discards a Queen of Hearts
There are two possible states
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Player X now has one King <- certain
Player X now has two Kings <- very likely
Possible hands
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118 million (118,030,185)
about 27 bits
factor of 10 reduction in the uncertainty
3 bits of information in the message
Example 1 cont'd
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Gin Rummy
 balances privacy of the cards
 with messages
• discarding cards
• picking up known discards
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The choice of a discard becomes meaningful
 because the player knows it will be interpreted as a
message
When it isn't your turn
 the game play is still important because the
messages are being conveyed
 interpreting these messages is part of the skill of the
player
• trivial to a computer, but not for us
Example 2
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Legend of Zelda: Minish Cap
Monsters are not all vulnerable to the same
types of weapons
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Encounter a new monster
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10 different weapons
(we'll ignore combinations of weapons)
which weapon to use?
4 bits of unknown information
We could try every weapon
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but we could get killed
Example 2, cont'd
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Messages
 the monster iconography contains messages
• rocks and metal won't be damaged by the sword
• flying things are vulnerable to the "Gust Jar"
• etc.
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the game design varies the pictorial representations
of monsters
• knowing that these messages are being conveyed
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learning to interpret these messages
• is part of the task of the player
• once mastered, these conventions make the player
more capable
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Often sound and appearance combine
 a redundant channel for the information
Game Analysis Issues
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Be cognizant of the status of different types
of information in the game
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public
private
unknown
Analyze the types of messages by which
information is communicated to the user
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How does the player learn to interpret these
messages?
Information Flow
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Systems have objects that interact
Information is a quantity that objects in
a system may exchange
 Weiner developed cybernetics to
explain this type of system
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Cybernetics is an attempt to unify the
study of engineered and natural
systems
Cybernetic Systems
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Cybernetics is about control
 How is the behavior of a system controlled?
Control implies that there are parameters that should
be maintained
 Example: temperature
• human body
• car engine
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Control implies information
 Temperature messages
• "too high"
• "too low"
• "OK"
Feedback Loops
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Basic loop
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A cybernetic system needs a sensor that
detects its state
The information detected by the sensor is
then compared against the desired value
If the value is not correct, the system adjusts
its state
the sensor detects this new state, etc.
The system maintains stability by
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feeding the information about its state back
to the process producing the state
Two Types of Feedback
Loops
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Negative Feedback Loop
 "inhibition"
 As the state changes, the loop acts to move it in the
direction of its previous state
 Example
• thermostat
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Positive Feedback Loop
 "excitation"
 As the state changes, the loop acts to move it in the
direction that it is moving
 Example
• automobile turbocharger
• home team advantage
Feedback Loops in Games
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From book
game state
scoring function
game mechanical bias
controller
Example
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game state
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scoring function
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player's health
controller
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state of a fighting game
near-KO
bias
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increase chance of critical (high damage) hit
on opponent
Effects?
Example 2
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game state
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scoring function
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the number of pieces taken
controller
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state of the chessboard
for each piece taken
bias
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add a pawn to the taker's side in any position
Effects?
Multiple Loops
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Games may have multiple feedback loops in operation
Examples
 chess
• once a player obtains a significant piece advantage, the
opponent is likely to lose more pieces
• positive feedback loop
• a player who is behind can play for a stalemate
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Warcraft II
• players with more resources can build more units and
capture more resources
• positive feedback
• a strong defensive position may require a very large
numerical advantage to defeat
• limit to how many attackers can attack at once
• negative feedback
In General
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Negative feedback
increases system stability
 makes the game last longer
 magnifies late successes
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Positive feedback
destablizes the system
 makes the game shorter
 magnifies early success
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Game Design Issues
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Know what feedback is going on in
your system
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analyze how game mechanisms
combine to produce feedback
Feedback may be undesirable
negative feedback may make a
successful player feel punished
 positive feedback may magnify ability
differences between players
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Wednesday
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Game Design Activity