Using Randomness: Both Sides of the Coin

1. Using Randomness:Both Sides of the Coin Dave Mark – Intrinsic Algorithm LLCBrian Schwab – Blizzard

2. Dave Mark • President & Lead Designer of Intrinsic Algorithm LLC • Independent Game Studio • AI Consulting Company • Author of Behavioral Mathematics for Game AI • Contributed to: • AI Game Programming Wisdom 4 • Game Programming Gems 8

3. Eye of the Beholder 0.4%

4. Eye of the Beholder 0.4%

5. Eye of the Beholder

6. Eye of the Beholder • People are conditioned to see patterns • Inflate their importance • Easier to recall • Chunking • Packaging info into memorable chunks • “The magical number 7, plus or minus 2” • George A. Miller, Princeton, 1956

7. Eye of the Beholder • People can identify shorter patterns or groupings. • Forget to consider the entire context

8. Opportunity != Outcome • The long-term odds (or % chance) of an event happening can be a poor predictor of short term results. • People suck at remembering that. • People suck at calculating that. • It can be used for good or eeevviiilllll!

9. Opportunity != Outcome “But I had 3… and he only had 1!” Sid Meier

10. Opportunity != Outcome 7-game series (e.g. baseball, basketball) Team A has a 55% chance of winning each game Team B will win series40% of the time Team A has 66.6% chance of winning each game Team B will still win series 20% of the time

11. That’s a lot of games… • Statistically significant – i.e. weaker team wins < 5% of the time • Stronger team has 66.7% advantage • Best 12 out of 23 • Stronger team has 55% advantage • Best of 135 out of 269!

12. Law of Large Numbers As the number of trials increases, the outcome approaches the theoretically expected value.

13. When Is it “Large Enough”? To achieve a 90% chance of getting within ± n%. (Think polls)

14. Law of… small numbers? • Kahneman & Tversky • Judgment and decision-making • Behavioral economy • Sarcastic reference to misconception that a small sample accurately reflects underlying probabilities.

15. Gambler’s Fallacy • Idea that the odds of an independent event with fixed probability changing based on recent occurrences. • “Catching up.” • “His luck will run out sooner or later.” • “He’s due!”

16. We all do it… 6 22  4 19 14 00 22 20 24 13 35 31 8 30 29 17 4 25 31 11 17 24 10 35

17. What do People Perceive?

18. Determinism that Looks Random • 3 Sine waves • Different frequencies • Different magnitudes • For each value of x • Sum y values • Normalize

19. Complexity Obscures Patterns • People can only keep track of a limited number of factors • As factors increase, complexity increases • People can no longer keep track of relationships • Deterministic result looks “random”

20. Complexity Obscures Patterns

21. Complexity Obscures Patterns

22. Hidden Factors Look Random • People can only take into account what they perceive • If input factors are hidden, people ascribe it to randomness

23. Brownian Motion • Robert Brown – 1827 • Under a microscope – pollen grains moved in “jittery” manner • Ascribed it to pollen being alive • Heat-based molecular vibration bumping the grains

24. Brownian Motion ? ? ?

25. Brownian Motion ? ? ? Fake it!

26. Further Reading

27. So what can we do with this? • Random sequences that look rigged… • Unseen deterministic factors that look random… • Intentional randomness to fake complex determinism…

28. Two Ways to Use It • Fuzzying Things Up • Weighted Randoms

29. Fuzzying Things Up

30. Fuzzying Things Up • Start with a defined anchor point • Add “parametric noise” (i.e. ± n)

31. Fun with Distributions • 1 die = flat ± • 2 die = triangular distribution • 3+ die = bell curve • More die → squished curve • Fun tricks • Skewing dist. (e.g. 4 die, drop the lowest) • Combining different types of dice

32. Single Die Anchor • Adds variation • Quick to process • Single random call • Easy to visualize • Easy to tweak range

33. 2 Dice Anchor • Triangular distribution • Mostly clustered towards center • Fairly quick to process • Two random calls • Easy to visualize • Easy to tweak range

34. 1 die vs. 2 dice

35. 3+ Dice • Normal distribution • Gaussian distribution • Bell curve • Very clustered towards center • Very expressive • Slower to process • n random calls • Harder to tweak

36. 3+ Dice

37. Increase the Number of Dice

38. 3 dice vs. 5 dice

39. 3 dice vs. 5 dice

40. Where to Use Randomness • Perception • Decision • Action

41. Where to Use Randomness • Perception • Decision • Action

42. Randomizing Perception • Range • I can see 30’ ± 5’ = [25-35’] • Accuracy • I have an 80% chance of seeing you ± 10% • Frequency • Check senses every n ticks where n is 500-2000 ms

43. Where to Use Randomness • Perception • Decision • Action

44. Where to Use Randomness • Perception • Decision • Action

45. Randomizing Actions • Delay before acting • Speed of acting • Acceleration into act

46. Clap when you see the light…

47. Human Response Times • Average is ≈250ms • Not everyone clapped at 250ms • Distributed over a range • Everyone clapping at 250ms would be odd

48. Human Response Times

49. Deliberative Decisions Take Time

50. Deliberative Decisions Take Time Action Deliberation Action