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.

Analyzing humor (and fun) is like dissecting a frog.Few people are interested and the frog dies of it....

E.B. White

P = Prob.

Expected Utility ≡ Probability * Utility

“fair slots”1*A = P*J

A = Anted J = Jackpot

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.

The $20 Question

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.

De Martino et al. (2006). “Frames, Biases and Rational DecisionMaking in the Human Brain”. Science, Vol. 313, pp 684-687.

average

Kahneman and Tversky (1979). “Prospect Theory: An Analysis ofDecision Under Risk”. Econometrica, Vol. 47, No. 2, pp 263-291.

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

Apparent Contribution from Aesthetic Utility = W - P

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 humoris like dissecting a frog.

Few people are interested… and the frog dies of it. Comedy?

Per EVE’, Fun (S) is the sum of:

pleasure (p) from success in formingExpectations (E)

+

pleasure (p’) from success in formingExplanations (E’)

S = G*E + G’*E’

E = P * log P + Q * log Q

Expectation (E)

Loss (Q=1-P)Win (P=Prob)

Entropy of an event with Prob. P is defined as:Unpredictability = Probability * Unexpectability

P * -log P

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

Measure of Expectation (E)

This E is a negative entropy

V = -E

Violation (V)

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

Explanation (E’)

H+/H- = sense of humorR = Bayesian resolution

posterior = prior * likelihood R = ρ (Y|e) = ρ (Y) * ρ (e|Y)

Bayesian Belief (ρ is a Prob.)

e is evidence: win or lossY is hypothesis: “good luck” or “bad luck”

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

Measure of Explanation (E’)

Σ signed/weighted entropies

H+/H- = 1

H+/H- = 2

S = (G * E) + (G’ * E’)

Fun = S = “S-thetic” utility

G’/G = call to adventure

Goldilocks Function: S = G*E + G’*E’

Fun = S = “S-thetic” utility

Assumed by Prospect Theory Derived by EVE’s Theory

Twenty-one Bell Three Wheel Nickel Slot Machine (Rake = 6%).Has 8 different payoff combinations/probabilities, w/ Pagg = 13%.

Game of Skill (Punch Out)

Performance vs. Enjoyment

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

-10 -8 -6 -4 -2 0 2 4 6 8 10

Margin of Victory

Me

an

En

joy

me

nt

Relating Cognitive Models of Computer Games to User Evaluations of Entertainment.P. Piselli, Masters Thesis, WPI Department of Computer Science, 2006.

WPI Data EVE’ Model

EVE’s Fun FactorsH+/H- = sense of humorG’/G = call to adventureF = price for pleasure

EVE’s Fun FunctionsE = log PV = -log PE’ = -log P * H * R

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.

Shlomo Dubnov“Thoughts About Memex”.

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

Bach: … C D F E C G C…

Mozart: … D C G B B A …

Beethoven: …A F E C G A C…

PQ

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

If it steps, the next note is C.If it jumps, the next note is A.Beethoven’s 4 > Mozart’s 2.

4

2

P was tweaked by the human creator until the machine compositionsounded “best”, which turned out to be much like slots – a P of 13%.

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.

http://www.urmc.rochester.edu/smd/mbi/faculty/Labs/robert/Xenopeace4%20copy.jpg

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.

EVE’s Entropy: A Formal Gauge of Fun in Games. In:Advanced Intelligent Paradigms in Computer Games.

Ch 1: “Slots of Fun, Slots of Trouble: An Archaeology of Arcade Gaming”

Historical

“Rise of Aesthetics”Cultural

SociologicalCh 24: “Games as the Play of Pleasure”

Psychological“Optimal Experience”

Neurological“Surprise!”

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

PerceptualBayesian Theory

BehavioralProspect Theory

InformationalShannon Theory

TheoreticalComputing Comedy

PhilosophicalCausality and Probability

MathematicalPsychological-Neurological

www.tracsgame.com On TRACS: Dealing with a Deck of Double-sided CardsProc. IEEE Symposium on Comp. Intelligence and Games.