Information 2

1. Information 2 Robin Burke GAM 224 Spring 2004

2. Outline • Admin • "Rules" paper • Uncertainty • Information theory • Signal and noise • Cybernetics • Feedback loops

3. Admin • Due today • Design Milestone #2 • your group should have picked a game • you will be working to extract the core mechanic

4. "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

5. "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

6. "Rules" paper 3 • Turn in • hardcopy in class 5/2 • Late policy • ½ grade per day • submit by email

7. Uncertainty • Many games are probabilistic • roll the dice • shuffle the cards • Some games are not • Chess • Checkers • Dots and Boxes

8. 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?

9. Probability • Probability is the study of chance outcomes • originated in the study of games • Basic idea • a random variable • a quantity whose value is unknown until it is "sampled"

10. 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

11. Single Die • Random variable • # of spots on the side facing up • Distribution • 1...6 • each value 1/6 of the time • Idealization

12. Single die • Random variable • odd or even number of dots • Distribution • odd or even • 50% • Distributions are not always uniform

13. 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

14. 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?

15. Outcomes • Each possible combination of outcomes of 3 rolls • 6 x 6 x 6 = 216 possible outcomes • Questions • Probability of 3 of kindor better? • Probability of 4 of a kind or better? 6, 6, 6 6, 6, 1 Die #2 Die #3 1, 1, 1 Die #1

16. 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

17. 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

18. 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

19. 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

20. 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."

21. 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?

22. Psychology 3 • Fallacies may impact game design • Players may take risky long-shots more often than expected • Players may expect bad luck to be reversed

23. Information theory • From Wednesday • Information can be • public • private • unknown (to players)

24. 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

25. 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

26. 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"

27. Information Theory 4 • This is the connection between information and uncertainty • the more uncertainty about something • the more possible messages there are

28. 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

29. 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

30. 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

31. 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

32. 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

33. 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?

34. Information Flow • 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 • Cybernetics is an attempt to unify the study of engineered and natural systems

35. 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"

36. 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

37. 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

38. Feedback Loops in Games • From book game state scoring function game mechanical bias controller

39. 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

40. Effects?

41. 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

42. Effects?

43. 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

44. In General • Negative feedback • increases system stability • makes the game last longer • magnifies late successes • Positive feedback • destablizes the system • makes the game shorter • magnifies early success

45. Game Design Issues • Know what feedback is going on in your system • 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

46. Wednesday • Game Design Activity