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Information 2. Robin Burke GAM 224 Spring 2004. Outline. Admin "Rules" paper Uncertainty Information theory Signal and noise Cybernetics Feedback loops. Admin. Due today Design Milestone #2 your group should have picked a game you will be working to extract the core mechanic. - PowerPoint PPT Presentation
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Information 2
Robin Burke
GAM 224
Spring 2004
Outline
Admin"Rules" paper
Uncertainty Information theory
Signal and noise Cybernetics
Feedback loops
Admin
Due todayDesign Milestone #2
• your group should have picked a game• you will be working to extract the core
mechanic
"Rules" paper
Due 5/2 Analysis paper #1: "Rules" You should be playing your game and taking notes
Important points thesis
• "great game" is not a thesis• This is a thesis
• "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
Note you cannot use lab machines to do word processing laptops are OK
"Rules" paper 2
Schemas Emergence Uncertainty Information Theory Information Systems Cybernetics Game Theory Conflict
Do not use them as an outline select one or two that are relevant to your
game
"Rules" paper 3
Turn inhardcopy in class 5/2
Late policy½ grade per daysubmit by email
Uncertainty
Many games are probabilisticroll the diceshuffle the cards
Some games are notChessCheckersDots and Boxes
Certainty vs uncertainty
Certainty the condition when the outcome of an action
is known completely in advance. Some games operate this way
Chess Dots and Boxes
But even then uncertainty about who will win otherwise what is the point?
Probability
Probability is the study of chance outcomesoriginated in the study of games
Basic ideaa random variablea quantity whose value is unknown
until it is "sampled"
Random variable 2
We characterize a random variable 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 Probability
the fraction of times that an outcome occurs
Single Die
Random variable# of spots on the side facing up
Distribution1...6each value 1/6 of the time
Idealization
Single die
Random variableodd or even number of dots
Distributionodd or even50%
Distributions are not always uniform
Two dice
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
Simplest to count outcomes Dice poker
roll five die keep best k, roll 5-k becomes your "hand"
Suppose you roll two 1s what are the outcomes when your roll the
other 3 again to improve your hand?
Outcomes
Each possible combination of outcomes of 3 rolls6 x 6 x 6 = 216 possible outcomes
QuestionsProbability of 3 of kind
or better?Probability of 4 of a
kind or better?
Die #1
Die #2
Die #31, 1, 1
6, 6, 1
6, 6, 6
Intuition for Games
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
Role of Chance
Chance can enter into the game in various ways
Chance generation of resources dealing cards for a game of Bridge rolling dice for a turn in Backgammon
Chance of success of an action an attack on an RPG opponent may have a
probability of succeeding Chance degree of success
the attack may do a variable degree of damage
Role of Chance 2
Chance changes the players' choices player must consider what is likely to happen
• rather than knowing what will happen
Chance allows the designer more latitude the game can be made harder or easier by
adjusting probabilities Chance preserves outcome uncertainty
with reduced strategic input example: Thunderstorm
Random Number Generation Easy in physical games
rely on physical shuffling or perturbation basic uncertainty built into the environment
• "entropy" 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
Psychology
People are lousy probabilistic reasoners Reasoning errors
Most people would say that the odds of rolling a 1 with two die = 1/6 + 1/6 = 1/3
We overvalue low probability events of high risk or reward Example: Otherwise rational people buy
lottery tickets We assume success is more likely after
repeated failure Example: "Gotta keep betting. I'm due."
Psychology 2
Why is this? Evolutionary theories
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
We tend to look for causation in everything• Evolutionarily useful habit of trying to make sense of the world
Result• superstition
• "lucky hat", etc. 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
Fallacies may impact game designPlayers may take risky long-shots
more often than expectedPlayers may expect bad luck to be
reversed
Information theory
From Wednesday Information can be
publicprivateunknown (to players)
Information Theory
There is a relationship between uncertainty and information Information can reduce our uncertainty
Example 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
Classical Information Theory Shannon
Information as a quantity how information can a given communication
channel convey?• compare radio vs telegraph, for example
must abstract away from the meaning of the information
• only the signifier is communicated• the signified is up to the receiver
Information Theory 3
Information as a quantity measured in bits binary choices
If you are listening on a channel for a yes or no answer only one bit needs to be conveyed
If you need a depiction of an individual's appearance many more bits need to be conveyed
Because there are more ways that people can look young / old race eye color / shape hair color / type height dress
A message must be chosen from the vocabulary of signifier options book: "information is a measure of one's freedom of choice when selecting a
message"
Information Theory 4
This is the connection between information and uncertaintythe more uncertainty about somethingthe more possible messages there are
Noise
Noise interrupts a communication channel by changing bits in the original message increases the probability that the wrong
message will be received Redundancy
standard solution for noise• more bits than required, or• multi-channel
Example 1
Gin Rummy Unknown
• What cards are in Player X's hand?• Many possible answers
• 15 billion (15,820,024,220)• about 34 bits of information
• Once I look at my 10 cards• 1.5 billion (1,471,442,973)• about 30 bits
Signal• I have two Kings• Player X picks up a discarded King of Hearts• Discards a Queen of Hearts• There are two possible states
• Player X now has one King <- certain• Player X now has two Kings <- very likely
• Possible hands• 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
Gin Rummy balances privacy of the cards with messages
• discarding cards• picking up known discards
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
Legend of Zelda: Minish Cap Monsters are not all vulnerable to the same
types of weapons 10 different weapons (we'll ignore combinations of weapons)
Encounter a new monster which weapon to use? 4 bits of unknown information
We could try every weapon but we could get killed
Example 2, cont'd
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.
the game design varies the pictorial representations of monsters
• knowing that these messages are being conveyed learning to interpret these messages
• is part of the task of the player• once mastered, these conventions make the player
more capable Often sound and appearance combine
a redundant channel for the information
Game Analysis Issues
Be cognizant of the status of different types of information in the game public private unknown
Analyze the types of messages by which information is communicated to the user How does the player learn to interpret these
messages?
Information Flow
Systems have objects that interactInformation is a quantity that objects in
a system may exchangeWeiner developed cybernetics to
explain this type of system Cybernetics is an attempt to unify the
study of engineered and natural systems
Cybernetic Systems
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
Control implies information Temperature messages
• "too high"• "too low"• "OK"
Feedback Loops
Basic loop 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 feeding the information about its state back
to the process producing the state
Two Types of Feedback Loops Negative Feedback Loop
"inhibition" As the state changes, the loop acts to move it in the
direction of its previous state Example
• thermostat 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
From book
game state scoring function
controllergame mechanical bias
Example
game state state of a fighting game
scoring function player's health
controller near-KO
bias increase chance of critical (high damage) hit
on opponent
Effects?
Example 2
game state state of the chessboard
scoring function the number of pieces taken
controller for each piece taken
bias add a pawn to the taker's side in any position
Effects?
Multiple Loops
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 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
Negative feedbackincreases system stabilitymakes the game last longermagnifies late successes
Positive feedbackdestablizes the systemmakes the game shortermagnifies early success
Game Design Issues
Know what feedback is going on in your systemanalyze 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
Wednesday
Game Design Activity