Luck, Skill, and Hidden
Information
Lessons from the World of Paper Games
K. Robert Gutschera
Senior Game Designer
The Amazing Society
[email protected]
GDC Canada
May 2009
Joint work with Richard Garfield and Skaff Elias
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
Luck and skill aren’t opposites; they’re
orthogonal.
low skill
high skill
low luck
tic-tac-toe
chess
high luck
slots
poker
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:
wins
60% vs.
A
wins
60% vs.
B
wins
60% vs.
C
wins
60% vs.
What does the length of this chain
measure?
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?
[email protected]