2. GDC Canada May 2009 Joint work with Richard Garfield and Skaff Elias K. Robert Gutschera Senior Game Designer The Amazing Society krg@amazingsociety.com Luck, Skill, and Hidden Information Lessons from the World of Paper Games

3. Outline  What is Luck?  Luck vs. Skill  Sources of Luck  Pros & Cons of Luck  Hidden Information

4. Defining Luck For our purposes, luck (or randomness) in a game is uncertainty in outcome.  So all games have some luck.  Not necessarily coming from dice, cards, random number generators, etc.

5. Even Chess Has Luck  Outcome of a chess game is uncertain.  Elo measures it.  E.g. if my rating is 1800 and yours is 1870, you have a ~60% chance to win.

6. Randomly Beating Kasparov For an extreme case, consider trying to beat Kasparov by playing randomly.  Chance to win: 1 in 30^50.  Win NY lottery 7 times:  1 in (60^6)^7, about the same. A very small chance − chess has less luck than other games.

7. Example: Die-Rolling Chess Two players compete by rolling 1 die. 1-2: first player wins 3-4: second player wins 5-6: play chess All the skill of chess, but a lot more luck.

8. Luck vs. Skill low skillhigh skill low lucktic-tac-toechess high luckslotspoker Luck and skill aren’t opposites; they’re orthogonal.

9. And Yet… Surely there’s some relationship between luck and skill. What is it?

10. The Skill Chain Consider a chain of players, each beating the next 60% of the time: What does the length of this chain measure? wins 60% vs. wins 60% vs. wins 60% vs. wins 60% vs. ACB

11. The Skill Chain, II  This is just Elo!  For chess, the length is about 30.  But for die-rolling chess, it’s about 10 (harder to win 60% of the time!) Adding luck compresses the skill chain!

12. Connecting Skill and Luck  Chain seems to measure skill  (more skill => longer chain)  But in fact measures returns to skill. And so, very roughly: Returns to Skill = Skill – Luck

13. Sources of Luck  Explicit randomizers (cards, dice, RNGs)  Simultaneous choices (e.g. RPS)  Human ignorance  Combinatorial (e.g. chess)  Deliberate secrets (e.g. xword puzzles)

14. Luck: the Good  Increased range of competition  Something to blame losses on  Increased variety of gameplay  Catchup mechanism  Adds psychological interest

15. Luck: the Bad  Luck can be confusing.  People are bad at probability  Randomness can conceal feedback needed to learn a game’s strategy  People like to feel they are masters of their own fate. Historically, though, people tend to prefer games with more luck.

16. Luck: the Ugly  Experienced players may dislike luck because they think they’ll win more if the game has less.  This is both true and false.  Designers are experienced, thus prone to this trap.  Sometimes you should listen – but sometimes you shouldn’t.

17. Hidden Information Things players don’t know:  Private info – One knows, others don’t.  Special case: No players know, i.e. uncertainty, i.e. luck!

18. Luck & Hidden Information  Any source of luck is a source of HI (the “special case”).  Some kind of luck is needed to generate hidden information.  Sometimes private information generates luck (e.g. RPS). So the pros & cons of hidden information are very similar to those of luck.

19. Luck: One More Good Luck, especially private info, can control calculation by decreasing the rewards to calculation. Examples:  die rolls in minis vs. chess  random damage in an RTS  dummy in bridge (reverse e.g.)  secret victory points in German board games

20. Luck Players Will Accept  Simultaneous choices, private info tend to be accepted over explicit randomizers.  “Pre-plan luck” over “post-plan luck”.  Entrenched audiences are tough.  New platforms are an opportunity.

21. Conclusion  More luck doesn’t mean less skill!  Adding luck to a game can be a good thing.  How you add it, and who your audience is, can make all the difference. Questions? krg@amazingsociety.com