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

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

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.

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.

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.

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.

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

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

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

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!

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

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)

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

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.

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.

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!

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.

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

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.

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?