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