Is it Percival time yet?: A preliminary analysis of Avalon gameplay

Is it Percival time yet?: A preliminary analysis of Avalon gameplay
Is it Percival time yet?: A preliminary analysis of Avalon
gameplay and strategy
Yuzuko Nakamura
Carnegie Mellon University
5000 Forbes Avenue
Pittsburgh, PA 15213
[email protected]
ABSTRACT
The Resistance: Avalon is a hidden-roles-style board game. In this
paper, we use data collected over dozens of Avalon games to make
recommendations on role sets and game sizes that maximize the
game-playing experience. We also evaluate the effect of various
strategies on good and evil’s chances of winning.
KEYWORDS
Board games, hidden-role games, game design
ACM Reference format:
Yuzuko Nakamura. 2017. Is it Percival time yet?: A preliminary analysis of
Avalon gameplay and strategy. In Proceedings of SIGBOVIK, Pittsburgh, PA
USA, April 2017 (SIGBOVIK’17), 6 pages.
DOI: 10.1145/nnnnnnn.nnnnnnn
1
INTRODUCTION
The Resistance: Avalon [1], like Mafia, is a multiplayer game centered around hidden roles. Hidden role games involve players being
randomly assigned roles that are not revealed to other players.
These games often feature two or more sides with their own win
conditions; in particular, there is frequently an evil or sabotaging
side that attempts to bluff and win people’s trust in order to win the
game, and a good (but generally information-less) side that must
correctly guess who to trust in order to win the game.
Avalon is a two-team game themed around King Arthur: the
loyal knights of King Arthur (good team) attempt to succeed three
quests (missions), and the minions of Mordred (evil team) attempt
to be placed on the missions so as to sabotage them and lead three
of them to fail. As such, the aim of evil is to be trusted by good
players and the aim of good is to determine who can be safely
trusted to be sent on a mission. In addition, all members of the evil
team know each other (with possible exceptions).
Avalon in its simplest form1 features two special roles, Merlin
and the Assassin. The addition of two other special roles, Percival
1 Avalon
may also be played without any special roles (in which case it resembles its
predecessor, The Resistance). However, the main feature of Avalon are these special
roles.
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DOI: 10.1145/nnnnnnn.nnnnnnn
and Morgana, creates more opportunities for bluffing, trust, and
strategy so we are interested in games with these four roles:
• Merlin (good): The player with this role knows all evil roles.
They must guide other good players to this knowledge.
However, Merlin must be subtle in the way they do this
due to the role of the Assassin.
• Assassin (evil): If good successfully passes three missions,
the player with this role gets to choose one good person to
assassinate (after discussing with the rest of the evil team).
If the assassinated player was Merlin, evil snatches victory
from the jaws of defeat and wins the game. As such, this
person serves as a check on Merlin’s ability to help the
good team.
• Percival (good): The player with this role knows who Merlin is. As such, they can also gain indirect information
about who to trust by quietly observing Merlin’s actions
and can appear to evil as a decoy Merlin. However, due to
the role of Morgana, Percival must first determine which
Merlin to trust.
• Morgana (evil): The player with this role appears as a second Merlin to Percival, forcing Percival to spend some time
determining who to trust, and possibly leading Percival to
sabotage the good team by trusting Morgana instead of
Merlin.
Good players who are neither Merlin nor Percival (generic good)
know nothing about any player other than themselves. Merlin and
evil players know the full evil team. Percival knows the two people
who are Merlin and Morgana, but not which is which. This selective
information is revealed to the appropriate players at the start of the
game - termed the “nighttime phase” - by asking players to close
their eyes, and then open their eyes to get information or raise their
thumb to identify themselves, as appropriate.
In this paper, we seek to evaluate how rules and game size affect
the funness of the gaming experience, and how different strategies
are more or less successful for good and evil.
2 GAME ANALYSIS
2.1 Evaluating funness
2.1.1 Ideal win ratio. One feature of Avalon is that, not only are
the good and evil teams asymmetrical (having different abilities,
information, and objectives), but they are also of asymmetric sizes
(the evil team in Mafia-style games needing to be a minority to
avoid the game being trivially easy).
SIGBOVIK’17, April 2017, Pittsburgh, PA USA
Yuzuko Nakamura
Table 1: Ideal win ratios for each possible size of Avalon
game under Supposition B (making evil wins as likely as
good wins).
Game Size
# Evil
Ideal Good Win Chance
5
6
7
8
9
10
2
2
3
3
3
4
.40
.33
.43
.38
.33
.40
Supposition A: Funness is maximized by maximizing uncertainty.
In other words, we want the probability of winning to be 1/2 regardless which team one is on. This means overall win chance of
good and evil must be balanced to be 1/2 for an ideal game-playing
experience.
Supposition B: Funness is maximized by making each person’s
wins equally likely to be earned while on the good team as while
on the evil team. Equivalently, across all games, the good and evil
teams both produce roughly the same number of winners. Under
this supposition:
Pr (i is good | i wins) = Pr (i is evil | i wins) =
1
2
(1)
Or...
Pr (i is good ∩ i wins) Pr (i is evil ∩ i wins)
=
(2)
Pr (i wins)
Pr (i wins)
Assuming player i doesn’t affect the win probability of their
team, this is the same as:
Pr (i is good) · Pr (good wins) = Pr (i is evil) · Pr (evil wins) (3)
If pдood is the win probability for good, and G is the chance of
being good (i.e. the number of good roles over the total game size),
then this equation is:
G · pдood = (1 − G) · (1 − pдood )
(4)
G · pдood = 1 − G − pдood + G · pдood
(5)
pдood = 1 − G
(6)
In other words, under this supposition of equalizing the portion
of good and evil wins, the ideal win ratio for win is 1 − G, or the
chance of being evil.
The number of evil players changes depending on the total number of players. Table 1 summarizes the ideal win chances under this
second supposition.
2.1.2 Game duration. Another important component of fun is
the length of a board game session. We hypothesize that length of
game goes up as the number of players in the game increases due
to more discussion. We also are interested in comparing the typical
game length to the 30 minutes claimed on the box.
2.2
Strategy
2.2.1 Percival claims. The rules in the instruction manual are
not clear on whether players are allowed to claim to be Percival.
However, the role of Percival is similar to the role of generic good
– and unlike Merlin or the evil roles – in that claiming the role
can potentially help the claimant’s team (whether good or evil).
Therefore, we allow players to publicly claim to be Percival.
A true Percival claim (Percival claiming Percival) can increase
trust among good members but can possibly make Merlin assassination easier for the evil team. We are interested in whether claiming
to be Percival, and the timing of such claims, tends to help good or
evil.
2.2.2 The first mission fail. Evil players have the choice whether
to throw in a fail card or a success card for missions that they go
on. A sole evil player on the first mission may decide to pass the
mission to avoid detection / suspicion for being on a failing team.
However, an early mission fail can make the evil team’s task of
failing three missions total easier.
We are interested in whether first mission fails overall help the
good or evil team, and how the size of the first mission factors in
to this.
2.2.3 Evil coordination failures. When two or more evil players
are on a mission team, they each have to choose whether to throw
in a fail or success card, not knowing what their teammates are
planning to do. As a result, sometimes evil players may end up
passing the mission, or may put in more than one fail card, revealing
key information about the make-up of the team. As such, a team
with more than one evil person is not ideal for the evil team, and
they may be cautious about proposing or approving teams with
this make-up.
How often do coordination failures happen, and how do they
affect evil’s chance of winning? We investigate these questions in
this paper.
3
METHOD
A body of 38 graduate students played games of Avalon (20 of
which played “semi-regularly” i.e. five or more times during the
data collection period). In total, 66 games were recorded although
5 were discarded due to incomplete information, resulting in 61
games overall.
All games were played using the Merlin, Percival, Morgana, and
Assassin special roles. In addition, 10 of these games added the
special roles Mordred and/or Oberon.
The following data were collected for each game:
• Number of players and role of each
• Approved mission teams and mission outcomes (but not
proposed mission teams)
• Outcome of each mission (pass/fail)
• Outcome of game (win for either good or evil), including
the win condition (three mission fails (evil win), mission
success but Merlin assassination (evil win), or mission success and failed Merlin assassination (only good win condition))
• Which player(s) claimed to be Percival and when (if applicable)
Is it Percival time yet?: A preliminary analysis of Avalon gameplay and strategy
SIGBOVIK’17, April 2017, Pittsburgh, PA USA
Figure 1: Number of games played for each size of game.
• Which player was assassinated (if applicable)
• Duration of game (measured from the end of night-time
phase to either three mission fails or evil’s Merlin assassination choice)
Linear regression was used to determine whether game size
affected duration.
Chi-squared tests were used to determine whether (1) the presence of Percival claims affected the evil’s team Merlin guess rate
(Percival claim/no claim vs. Merlin guess/good win condition); (2)
evil failing the first mission affected the chance of evil winning (first
mission pass/fail vs. winner of game); (3) the presence of missions
requiring evil coordination affected the chance of evil winning
(zero/non-zero coordination missions in game vs. winner of game).
4 RESULTS
4.1 Number and size of games
Fig. 1 shows how many games of each size were played in the
dataset. Although Avalon can in theory be played with game sizes
of 5 to 10, players did not enjoy games of size 5 and so only played
Avalon if at least 6 players were present. A game of size 11 can
be played with the 10-player board and 4 evil characters (as in a
10-player game), and an extra set of vote tokens.
4.2
Win ratio
Overall, the win rate of the good team was .34. Fig. 2 shows how
this win ratio changes with the size of the game. The good win
ratio for 9-player games stands out as unusually high. This is also
the game size with the fewest data points (see Fig. 1), so that may
be part of the reason.
Under Supposition A of game funness, 6- and 9-player games
are the only ones close to the ideal difficulty for good. 7-, 8-, and
10-player games fall short of both ideal win ratios. As such, it may
be worthwhile to use gameplay mechanics that tilt the game in
favor of good (Oberon as one of the evil roles, Lady of the Lake,
etc.).
Under Supposition B of game funness, the 6- and 9-player games
need to be altered to be more difficult. In particular, a 9-player
Figure 2: Good’s win record at each game size. The dotted
line shows the ideal .5 win ratio under the supposition that
good and evil should be equally likely to win. The dashed
line shows the ideal win ratio under the supposition that
people earn wins equally as good people as they do as evil
people.
game might benefit from 4 evil roles (instead of 3), one of which is
Oberon.
4.3
Game duration
Fig. 3 shows the distribution of game length. The mean game length
is 57.3 minutes and the median game length is similar – 57 minutes. Most (80% of) games can be played within 80 minutes. This
is markedly longer than the 30 minutes estimated in marketing
materials.2
We can break down game length by the size of game, resulting
in Fig. 4. Games of size 9 are again an outlier, being unusually
quick, and being the only game size that approaches the 30-minute
estimated play time.
There seems to a slight trend of longer games with more players
in line with our hypothesis; however linear regression (removing
the 9-person games) does not quite reach significance (F(1,45)=3.54,
p=.0663) and game size has low explanatory power for duration
(R2 =.0524).
4.4
Percival claims
Fig. 5 compares the outcome of games where a Percival claim is
made vs. ones where no Percival claims are made. Games with
Percival claims are much more likely to end in mission failure,
which makes sense because one reason why Percival might claim
is because several failing missions have happened, and Percival (or
Merlin) is trying to increase the chance of choosing an all-good
team (i.e. scenarios with multiple failing missions are scenarios
where Percival is likely to claim).
2 It
is possible that this particular group of graduate students discusses an unusually
large amount during Avalon.
SIGBOVIK’17, April 2017, Pittsburgh, PA USA
Yuzuko Nakamura
8
6
4
0
2
Frequency
10 12
Histogram of game length
20
40
60
80
100
Duration (minutes)
Figure 3: Histogram of game lengths.
Figure 5: Portion of games that end with mission fails (evil
win), Merlin assassinations (evil win), or neither (good win)
under the conditions of Percival not revealing and Percival
revealing.
Table 2: Merlin assassination successes under the conditions
of a Percival claim vs. no such claim.
80 100
Merlin assassinated
Good wins
16
10
11
10
60
Percival claim
No Percival claim
20
40
Table 3: Game victor under the conditions of a first mission
fail vs. a first mission pass (games sizes 8+).
First mission fail
First mission pass
0
Duration (mins)
Duration by game size
6
7
8
9
10
Evil
Good
13
5
3
4
11
Game size
Figure 4: How length of game changes with game size.
Among the remaining cases where three missions succeed, we
are interested in comparing how often Merlin is assassinated in
each case (Percival reveal vs. no reveal). Table 2 shows the number
of games in each condition. The Merlin assassination chance when
Percival reveals (.59) is higher than when there is no Percival reveal
(.50). However, the chi-squared test shows no significant difference
(χ 2 =.11, p=.738).
There was not enough data to do an analysis of how the timing
of Percival claims affect good’s chance of victory. We leave this to
future work.
4.5
The first mission fail
Although the intent was to analyze how first mission team size (twoperson first missions (in games with 5-7 players) vs. three-person
first missions (in games with 8+ players)) affects the outcome of
the game, in practice, only one two-person first mission with an
evil player (out of 16) was failed by the evil player. This is a difficult
strategy to pull off for the evil player because for the rest of the
game, at least one good person knows for sure one member of the
evil team, and the evil person must consistently behave to give the
impression of being someone in that situation.
Therefore, we instead look only at games with three-person first
missions. Of the 24 games with evil players present on the first
mission, 16 (67%) were failed by those players. Table 3 shows how
evil’s play during the first mission affected the victor of the game.
There is not enough data to perform a reliable chi-squared analysis, but it is possible that failing the first mission is overall a good
strategy for the evil team.
Is it Percival time yet?: A preliminary analysis of Avalon gameplay and strategy
Figure 6: Number of games featuring zero, one, two, or three
missions with more evil people than the required number
of fails.
SIGBOVIK’17, April 2017, Pittsburgh, PA USA
Figure 7: How often zero, one, or two fails come out for onefail-required missions.
Table 4: Game victor under the conditions of zero or at least
one evil coordination mission.
4.6
Evil coordination failures
Of the 61 games, 32 (52%) featured no evil coordination missions,
while the rest had at least one evil coordination team. Fig. 6 indicates
how often games featured a certain number of evil coordination
teams. Overall, this suggests the chance of any mission containing
multiple evil people is roughly 15%. Note: It is impossible to have
coordination issues on the fifth mission because any number of fails
is acceptable for the evil team. Coordination issues on the fourth
mission of games of 7+ players, where two fails are required, are
rarer (as this only happens when three evil people are placed on
the team) but are still important to the game.
38 of the 41 coordination missions (92%) involved two evil people
on one-fail-required missions. Fig. 7 summarizes how frequently
zero, one, or two fails come out in this situation. This figure shows
that the number of fails that come out in Mission 2 and Mission 3 are
roughly what you’d expect based on random chance (independent
events with .5 probability of occurring). However, Mission 1 is much
more skewed toward zero fails, corresponding to roughly a 20-25%
chance of each person throwing out a fail. This makes sense as a
two-fail result on the first mission can be costly to the evil team.
We also analyze how evil coordination missions affect the chance
of good or evil winning the game. Removing from consideration
games where evil never gets the chance to go on any mission,
Table 4 summarizes the game outcomes when there are no evil
coordination missions vs. when there’s at least one. Evil’s win ratio
in the presence of coordination missions (.76) is higher than when
there are no coordination missions (.60), although this effect does
not reach significance (χ 2 (1)=.92, p=.338).
Figs. 8 and 9 break down the effect of evil coordination further.
Fig. 8 takes into account evil’s coordination performance – success
means throwing out exactly the number of fails needed to fail the
mission, and failure means throwing out more or fewer fails than
needed. Fig. 8 separates the data into three conditions: games where
evil mostly failed at coordinating (14 games), games where evil both
succeeded and failed at coordinating once (4 games), and games
No evil coordination missions
1+ evil coordination mission
Evil
Good
15
22
10
7
Figure 8: Evil win rate broken down by ability of evil to coordinate.
where evil more often succeeded at coordinating (11 games). Fig. 9
shows how evil’s win rate changed as the number of coordination
missions in the game increased.
In all cases, there is not enough data to draw any definitive
conclusions. However, contrary to expectations, it is possible that
evil coordination situations might be slightly beneficial to the evil
team.
5
DISCUSSION
We analyzed data from 61 games of Avalon. We found that games of
size 9 were unusual in the amount they were played (less popular),
SIGBOVIK’17, April 2017, Pittsburgh, PA USA
Yuzuko Nakamura
for taking better care of the Avalon stats sheet than the author, and
Liam K. Bright for listening to the author’s shaky probability math.
REFERENCES
[1] Don Eskridge. 2012. The Resistance: Avalon. Indie Boards and Cards. Board
game.
Figure 9: Evil win rate broken down by how many times during the game evil needed to coordinate.
how long they lasted (shorter), and game difficulty (good team
more likely to win). Some games might require adjustment to their
difficulty. In particular, 9-player games might require more evil
characters, and 7-, 8-, and 10-player games might require a slight
good handicap. Typical game time is more than one hour.
In this particular dataset, Percival reveals resulted in slightly
more Merlin assassinations; evil failing the first mission resulted
in more evil wins; and the presence of evil coordination missions
resulted in more evil wins. One possible explanation for this last
finding is that it is hard for good people to reason about teams
where more than one of the members was evil, and so they may
be more likely to make decisions that assume only one evil person
was on the team.3 However, more data might reveal these trends to
be spurious/random noise.
A notable gap in the dataset is the general absence of two-person
first missions failed by an evil player on the team. In the future, it
would be interesting for evil to experiment with failing two-person
missions to see if this strategy might be beneficial for evil overall.
A more detailed analysis of Percival claim timing would be also be
good to do with more data. Another promising avenue of future
work would be to analyze the effect of rejecting missions on good
and evil’s chance of winning.
5.1
Conclusion
Hidden role games like Avalon provide a large space for both game
design (e.g. number of players, set of specialized roles) and player
strategy (e.g. failing the first mission, claiming Percival, team approval strategies, etc.). As such, collecting and analyzing data under
different game conditions can be useful in improving the player
experience and evaluating the strength of different strategies. Although limited by the amount of data, this work represents a preliminary step in the direction of analyzing the gameplay of Avalon.
ACKNOWLEDGMENTS
The author would like to thank Kristy Gardner for kick-starting
this collective Avalon Problem in the department, Ryan Kavanagh
3 If
evil does indeed benefit from coordination issues, this might interestingly increase
the value of Zhu-Brown strategies (multiple evil proposing multiple evil people on
their teams).
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