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Science of Fun. Ten Billion $/year from Six Thousand Slot Machines. Foxwoods Casino and Resort. What makes slots fun?. Pared-down Poker: Cutting to the Core of Command and Control. Proc. of IEEE Symposium on Computational Intelligence and Games .

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slide2

Ten Billion $/year from Six Thousand Slot Machines

Foxwoods Casino and Resort

What makes slots fun?

slide4

Pared-down Poker: Cutting to the Core of Command and Control.

Proc. of IEEE Symposium on Computational Intelligence and Games.

slide5

Analyzing humor (and fun) is like dissecting a frog.

Few people are interested and the frog dies of it....

E.B. White

slide6

Expected Utility ≡ Probability * Utility

“fair slots”

1*A = P*J

A = Anted

J = Jackpot

P = Prob.

slide7

The $20 Question

You have a choice between:

(s) a sure-thing of getting $20;

(g) a gamble with 20% chance of getting $100

and 80% chance of getting nothing.

slide8

The $80 Question

You have a choice between:

(s) a sure-thing of getting $80;

(g) a gamble with 80% chance of getting $100

and 20% chance of getting nothing.

slide9

De Martino et al. (2006). “Frames, Biases and Rational Decision

Making in the Human Brain”. Science, Vol. 313, pp 684-687.

average

slide10

Kahneman and Tversky (1979). “Prospect Theory: An Analysis of

Decision Under Risk”. Econometrica, Vol. 47, No. 2, pp 263-291.

slide11

Apparent Contribution from Aesthetic Utility = W - P

On a crusade in search of the Holy Grail… It’s Fun!

slide12

The Atoms of EVE’: A Bayesian Basis for Aesthetic Analysis…

Artificial Intelligence for Engineering Design, Analysis and Manufacturing (AIEDAM)

Expectation – Violation – Explanation

Set-up – Punchline – Get-it?

Garden – Eaten – Tragedy?

Analyzing humor

is like dissecting a frog.

Few people are interested…

and the frog dies of it.

Comedy?

slide13

Per EVE’, Fun (S) is the sum of:

pleasure (p) from success in forming

Expectations (E)

+

pleasure (p’) from success in forming

Explanations (E’)

S = G*E + G’*E’

slide14

Expectation (E)

Win (P=Prob)

Loss (Q=1-P)

E = P * log P + Q * log Q

slide15

Entropy of an event with Prob. P is defined as:

Unpredictability = Probability * Unexpectability

P * -log P

Entropy = (-P * log P) + (-Q * log Q)

slide16

Measure of Expectation (E)

This E is a negative entropy

slide18

Explanation (E’)

E’ = - [H+ * P * log P * R+ ] + [H- * Q * log Q * R-]

H+/H- = sense of humor

R = Bayesian resolution

slide19

Bayesian Belief (ρ is a Prob.)

posterior = prior * likelihood

R = ρ (Y|e) = ρ (Y) * ρ (e|Y)

e is evidence: win or loss

Y is hypothesis: “good luck” or “bad luck”

For slots, posterior = 1; R=+1 (win) or -1 (loss)

slide20

Measure of Explanation (E’)

H+/H- = 2

H+/H- = 1

Σ signed/weighted entropies

slide21

Fun = S = “S-thetic” utility

S = (G * E) + (G’ * E’)

G’/G = call to adventure

slide22

Fun = S = “S-thetic” utility

Goldilocks Function: S = G*E + G’*E’

slide23

Assumed by Prospect Theory

Derived by EVE’s Theory

slide24

Twenty-one Bell Three Wheel Nickel Slot Machine (Rake = 6%).

Has 8 different payoff combinations/probabilities, w/ Pagg = 13%.

slide25

Game of Skill (Punch Out)

WPI Data

EVE’ Model

Relating Cognitive Models of Computer Games to User Evaluations of Entertainment.

P. Piselli, Masters Thesis, WPI Department of Computer Science, 2006.

slide26

EVE’s Fun Functions

E = log P

V = -log P

E’ = -log P * H * R

EVE’s Fun Factors

H+/H- = sense of humor

G’/G = call to adventure

F = price for pleasure

slide27

Shlomo Dubnov

“Thoughts About Memex”.

http://music.ucsd.edu/~sdubnov

Memex Music

Memex, the machine (Bush 1945), was a futuristic device,

For creating and recalling associations –

In the form of memory trails.

Memex, the music (Dubnov 2006), is an algorithmic composition,

Designed to create new music from old music –

By associations along probabilistic trails.

slide28

Let’s say that the current note in Memex is G - taken from Bach. To get the next note:

The machine will step forward with probability Q - or jump backward with probability P

Where jump backward is to the same note (different song) with “most similar” history.

Bach: … C D F E C G C…

Q

P

Beethoven: …A F E C GA C…

4

Mozart: … D C G B B A …

2

If it steps, the next note is C.

If it jumps, the next note is A.

Beethoven’s 4 > Mozart’s 2.

slide29

Fun (flow) function computed by EVE’ with same G’/G as for slots.

All E’ was assumed to be positive and Resolution (R) was set to Q2.

P was tweaked by the human creator until the machine composition

sounded “best”, which turned out to be much like slots – a P of 13%.

slide32

EVE’s Entropy: A Formal Gauge of Fun in Games. In:

Advanced Intelligent Paradigms in Computer Games.

SCIENCE OF FUN

Imagine a community with thousands of people sitting at machines playing games for hours. What makes it fun? Is it virtual reality? Is it engaging narrative? Is it multiplayer interaction? Actually, it’s none of the above. The community is Foxwoods and the machines are slots. I’ll bet that slots are the most popular and profitable machine game of all time – more than any modern computer game. I also think that research and development in digital media has not done much to advance a scientific understanding of fun in any game. So I cut to the chase, dissecting the aesthetic experience using mathematical analyses and psychological experiments. I look at gambling, music and artwork. I show how formal notions of Bayesian probability and Shannon entropy can explain and predict feelings of pleasure. I have some demos to make the math fun. I guarantee you have never seen fun like this before.

slide33

Historical

Ch 1: “Slots of Fun, Slots of Trouble:

An Archaeology of Arcade Gaming”

Cultural

“Rise of Aesthetics”

Sociological

Ch 24: “Games as the Play of Pleasure”

slide34

Psychological

“Optimal Experience”

Neurological

“Surprise!”

Personal

Pg 46: “Fun is just another word for learning”.

slide35

Informational

Shannon Theory

Perceptual

Bayesian Theory

Behavioral

Prospect Theory

slide36

Mathematical

Psychological-Neurological

Theoretical

Computing Comedy

Philosophical

Causality and Probability

slide37

On TRACS: Dealing with a Deck of Double-sided Cards

Proc. IEEE Symposium on Comp. Intelligence and Games.

www.tracsgame.com

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