Outline
AdminErratumDesign groups"Rules" paper
UncertaintyProbability
Information theorySignal and noise
Erratum
The rules of "8 & out" are not isomorphic to "Thunderstorm" Mr. Allen was correct
Consider all players draw no ones for seven turns each player should be 1 turn from being out but each player should have 7*(k-1) points none of them can go out next turn
Moral it is hard to find a confusing alternative to
counting
Rules paper
Due 10/10Analysis paper #1: "Rules"You should be playing your game and
taking notes Note
you cannot use lab machines to do word processing
laptops are OK
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."
No thesis = paper will not be graded Documentation
game itself, book, lectures other sources if used Missing or inadequate documentation = paper will not
be graded
Rules paper 2
Schemas Emergence Uncertainty Information Theory Information Systems Cybernetics Game Theory Conflict
Do not use more than one
Rules paper 3
Outlinessuggestions
Focusdo not catalog every rule, every game
objectidentify those items that contribute to
your argumentdepth over breadth
Rules paper 4
Turn inhardcopy in class 10/10
Turn in to turnitin.comon 10/10
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?
Strategically-interesting deterministic games are hard to design
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
Basic probability theory
Repeated trials addbut not in a simple wayprobability of a coin flip = heads?probability of heads in 3 flips?
Outcome sequences multiplyprobability of 3 flips all heads?
Relevance for Games
Many game actions are probabilistic even if their effects are deterministic player may not be able to exercise the
controls perfectly every time 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 Chance due to physical limitations
the difficulty of the hand-eye coordination needed to perform an action
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
Information can bepublic
• board position in chess
private• one's own poker hand
unknown / hidden (to players)• monsters in the next room
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 quantitymeasured in bitsbinary choices
If you are listening on a channel for a yes or no answeronly one bit needs to be conveyed
ExampleLOTR
Information Theory 4
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 5
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
Example 1 cont'd
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? How are redundant channels used to
communicate?