Complexity and Emergence in Games(Ch. 14 & 15)

Seven Schemas

• Schema: Conceptual framework concentrating on one aspect of game design

• Schemas:– Games as Emergent Systems– Games as Systems of Uncertainty– Games as Information Theory Systems– Games as Systems of Information– Games as Cybernetic Systems– Games as Game Theory Systems– Games as Systems of Conflict

Have You Ever Been Surprised in a Game?

• Was it scripted?

• Was it a result of Game Design?

• Could a game developer be surprised from his own game?

Systems and Complexity

• Reminder:– What is a system?– Why can game be viewed as systems?

• System’s Complexity: measure of number of ways in which parts interact within a system:– Elevator example: simple algorithm used to control one elevator,

when used to control multiple elevators it fails

• Four categories of system’s complexity:– Fixed– Periodic– Complex– Chaotic

(this is NOT computational complexity)

Complexity and Meaningful Play

• Are these two related?– What happens if there is no interaction between play

elements? • Example : Grid game

– Is it meaningful?– Lets add complexity: relations between play elements

• Does it achieves meaningful play?

Ways parts interact within a system

Discernable and integrated actions

Emergence

• Behavior of the overall system is greater than its parts

• Example: simple operational rules yet unpredictable results are attained

• Obvious example: complex operational rules

• However: complex rules doesn’t make game harder. Example?

• Chess: last century versus current century• Backgammon machine learning example• Warcraft• Bluffing

–Chess vs Go

Classes of Object Interactions• Coupled: objects are linked or affect with one another

recursively– Non-gaming Example: ant colony– Gaming example?

• Context-dependent: changes are not the same over time– Non-gaming example: behaviors of the colony under

attack versus harvesting– Gaming example?

• Emergence in a system occurs when interactions are coupled and context-dependent

• To achieve emergent behavior in a game: Tuning (or iterative design) is needed

However: Be careful!

• Example of bad “emergence” in games?

• Countering that bad “emergence” can lead to trouble for game developers

• Which again reinforces the idea of iterative design

Exploit 1, exploit 2, exploit 3

Let us plan for Wednesday

• Bring laptop/ipad/… to run your game• Lets discuss Locations• All students are encouraged to try their classmates’

games– If you are not showing the game at any point during

the session, play someone else’s and give them feedback

• In addition, students who are not creating game need hand to me a filled form at the end of class

Uncertainty and Games (Ch. 15)

Uncertainty

• If a game outcome is certain can it exhibit meaningful play?

• Two kinds of uncertainty:– Macro-level (overall game)– Micro-level (individual player’s actions)

Uncertainty and Categories of Games According to AI

Perfect information

Imperfect information

Deterministic Chance

Yes

Yes Yes

Yes

For which of the following categories, label with “Yes” those for which games can have uncertainty

Lesson: you don’t have to “rolling a dice” to achieve uncertainty in a game

Feeling of Randomness

• We can even achieve a feeling of randomness in a deterministic perfect information game– Example?

• Danger: designing a chaotic game– Example?

Probability in Games

• Probability: a mathematical formalization of uncertainty

• Examples of probabilities in games:

• In a game like Chutes and Ladders, players do not make decisions (probabilities – a random number generator is deciding-), why is it “fun”?

chance to hit amount of damage dealt

Next shape in Tetris Initial location in a multiplayer RTS game Loot in an MMO …

Probability

• Example. Suppose that you are in a TV show and you have already earned 1’000.000 so far. Now, the host propose you a gamble: he will flip a coin if the coin comes up heads you will earn 3’000.000. But if it comes up tails you will loose the 1’000.000. What do you decide?

• We know a degree of belief

• Probability theory allows the analysis of decisions based on the degree of belief

Probability

• Suppose that I flip a “fair” coin:

what is the probability that it will come heads: 0.5

• Suppose that I flip a “totally unfair” coin (always come heads):

what is the probability that it will come heads: 1

• Assigns a number between 0 and 1 to events• The closer an event is to 1, the more likely we believe it

will occur• The closer an event is to 0, the less likely we believe it

will occur

Probability Distribution

• The events E1, E2, …, Ek must meet the following conditions:• One always occur• No two can occur at the same time

• The probabilities p1, …, pk are numbers associated with these events, such that 0 pi 1 and p1 + … + pk = 1

A probability distribution assigns probabilities to events such that the two properties above holds

Example (Probability Distribution)

• In the example:• E1 = “holding a $5 ticket”• E2 = “holding a $10 ticket”• E3 = “holding a $100 ticket”• E4 = “holding a losing ticket”

• The probabilities are:• p1 = .09• p2 = .009• p3 = .001• p4 = .9

• Note that the probabilities add to 1

• Could we add E5 = “holding a winning ticket”? No! because E5 occurs at the same time as E1, E2 and E3

Example:• 1000 tickets are sold at a value of $1 each• 100 are selected. The first 90 win $5, the next 9 win

$10, and the last will win $100

Probability in Games (II)

• Let us build a probability distribution for the following game situations (so we have to list the events and their probabilities):

• We can use probabilities to building “smart” NPCs:

chance to hit: statistics Next shape in Tetris Initial location in a multiplayer RTS game Loot in an RPG

Should NPC attack another NPC/avatar? “AI” has control of 5 NPC and has to pick one to

fight the NPC/avatar, which one should it choose?

Expected Utility (I)

• We are given a probability distribution:

The events E1, E2, …, Ek

The probabilities p1, …, pk associated with these events

We have the value of those events: U(E1), U(E2), …, U(Ek)• The Expected Utility (EU):

EU = p1 * U(E1) + … + pk * U(Ek) • Examples:

EU for the fair coin and I bet $10 EU for the lottery example

Expected Utility: Example• Coming back to the example:

• Answer to that depends on:– the probability of winning $0 or $ 3’000.000– How much money you currently have– Expected utility: a measure of how much I would gain

from taking an action

Suppose that you are in a TV show and you have already earned 1’000.000 so far. Now, the host propose you a gamble: he will flip a coin if the coin comes up heads you will earn 3’000.000. But if it comes up tails you will loose the 1’000.000. What do you decide?

Expected Utility in Games

• Let us design the following game situation by thinking about the expected utility:

• We can use expected utilities to building even “smarter” NPCs:

Player will fight “big bad monster”. What is a potential probability distribution modeling this and what would be potential value for the player?

Should “AI” attack the player?

Warnings about Probabilities (1)

• A random function assigns to k events: E1, E2, …, Ek, the same probability: 1/k (called “uniform distribution”)Example: rolling a dice has 6 events (one for each face)

with probability of each occurring been 1/6

• Problem: Computers cannot make a perfectly random function It is “random” in the sense that you cannot predict the

outcome in advanceBut it is not a uniform distributionThis is due to the fact that computers are intrinsically

deterministicBut error is too small to matter

Warnings about Probabilities (2)

• People do not always follow the rules of probability:

Experiment with people

Choice was given between A and B and then between C and D:

A: 80% chance of $4000B: 100% chance of $3000

C: 20% chance of $4000D: 25% chance of $3000

Warnings about Probabilities (2)

• Majority choose B over A and C over DThis turns out to be mathematically inconsistent with the

expected utility:

U(3000) > 0.8U(4000) and 0.2U(4000) > 0.25U(3000) There are no possible values for U(4000) and

U(3000) that will satisfy these two inequalities

• Book discusses other miss-conceptions

Final Thought• Probability is not required to get a feeling of randomness

in games

• But well laid-out element of chance will result in meaningful choices– Or build “smart” NPCs that will enhance game value

• Example: Player needs to decide whether to attack a monster or not based

This decision is based on expected utility A “feeling” of how success will it be Sometimes players can get quite formal

How worth would it be if successful Careful use of macro- and micro-level uncertainty can

result in “epic” game experience