GDC CanadaMay 2009

Joint work with Richard Garfield and Skaff Elias

K. Robert GutscheraSenior Game DesignerThe Amazing Society

krg@amazingsociety.com

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 wins5-6: play chessAll the skill of chess, but a lot more

luck.

Luck vs. Skill

low skill high skill

low luck tic-tac-toe chess

high luck slots poker

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?

wins60% vs.

wins60% vs.

wins60% vs.

wins60% vs.A CB

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?

krg@amazingsociety.com