Science of Fun

1. Science of Fun

2. Ten Billion $/year from Six Thousand Slot Machines Foxwoods Casino and Resort What makes slots fun?

4. Pared-down Poker: Cutting to the Core of Command and Control. Proc. of IEEE Symposium on Computational Intelligence and Games.

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

6. Expected Utility ≡ Probability * Utility “fair slots” 1*A = P*J A = Anted J = Jackpot P = Prob.

7. 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.

8. 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.

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

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

11. Apparent Contribution from Aesthetic Utility = W - P On a crusade in search of the Holy Grail… It’s Fun!

12. 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?

13. 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’

14. Expectation (E) Win (P=Prob) Loss (Q=1-P) E = P * log P + Q * log Q

15. Entropy of an event with Prob. P is defined as: Unpredictability = Probability * Unexpectability P * -log P Entropy = (-P * log P) + (-Q * log Q)

16. Measure of Expectation (E) This E is a negative entropy

17. Violation (V) V = -E

18. Explanation (E’) E’ = - [H+ * P * log P * R+ ] + [H- * Q * log Q * R-] H+/H- = sense of humor R = Bayesian resolution

19. 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)

20. Measure of Explanation (E’) H+/H- = 2 H+/H- = 1 Σ signed/weighted entropies

21. Fun = S = “S-thetic” utility S = (G * E) + (G’ * E’) G’/G = call to adventure

22. Fun = S = “S-thetic” utility Goldilocks Function: S = G*E + G’*E’

23. Assumed by Prospect Theory Derived by EVE’s Theory

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

25. 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.

26. 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

27. 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.

28. 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.

29. 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%.

32. 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.

33. 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”

34. Psychological “Optimal Experience” Neurological “Surprise!” Personal Pg 46: “Fun is just another word for learning”.

35. Informational Shannon Theory Perceptual Bayesian Theory Behavioral Prospect Theory

36. Mathematical Psychological-Neurological Theoretical Computing Comedy Philosophical Causality and Probability

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