Playing Iterated Rock-Paper-Scissors with an Evolutionary Algorithm

emi B

edard-Couture

and Nawwaf Kharma

Department of Software Engineering,

Ecole de Technologie Sup

erieure, Montreal, Canada

Department of Electrical and Computer Engineering, Concordia University, Montreal, Canada

Keywords:

Evolutionary Algorithms, Learning Algorithms, Game Theory, Game Playing Agents, Rock-Paper-Scissors,

RoShamBo.

Abstract:

Evolutionary algorithms are capable ofﬂine optimizers, but are usually left out as a good option for a game-

playing artiﬁcial intelligence. This study tests a genetic algorithm speciﬁcally developed to compete in a

Rock-Paper-Scissors competition against the latest opponent from each type of algorithm. The challenge is

big since the other players have already seen multiple revisions and are now at the top of the leaderboard. Even

though the presented algorithm was not able to take the crown (it came second), the results are encouraging

enough to think that against a bigger pool of opponents of varying difﬁculty it would be in the top tier of

players since it was compared only to the best. This is no small feat since this is an example of how a carefully

designed evolutionary algorithm can act as a rapid adaptive learner, rather than a slow ofﬂine optimizer.

1 INTRODUCTION

Game-playing artiﬁcial intelligence has always been

of great interest to the research community. Games

like chess and poker are the subjects of many publi-

cations and competitions, but the game of RPS (short

for Rock-Paper-Scissors, also known as RoShamBo)

never had much interest because it seems so trivial.

Many people think that always playing random is the

best strategy, but that is necessarily true when the

game is repeated multiple times with the same op-

ponent. The ﬁrst ofﬁcial RPS competition (Billings,

1999a), led to a very innovative algorithm that em-

ployed a meta-strategy (Egnor, 2000). Over the years,

game predictors based on different algorithms such

as history matching, statistical methods or neural net-

works, were improved so much that they can now

win more than 75% of their matches (Knoll, 2011).

Among popular artiﬁcial intelligence techniques, evo-

lutionary algorithms (EAs) are competent ofﬂine opti-

mizers, but to compete against the others in this game,

they will need to become fast on-line learners, adapt-

ing quickly to the changing strategies of the opponent.

This is the main challenge we faced, one that neces-

sitated a highly customized EA, a competitive player

whose architecture and performance are described in

this paper.

It is common belief that always playing random

is the best strategy (also known as the Nash equilib-

rium). This is true if all the opponents also use that

strategy, however as soon as one player is not purely

random, it is possible to exploit, thus gaining advan-

tage over the rest of the population. This is further

studied in (Bi and Zhou, 2014; Wang et al., 2014).

Due to the nature of the game being highly ran-

dom, any algorithm using history matching tech-

niques will be prone to detection by other intelligent

algorithms. The method proposed in the paper is sim-

ilar to an LCS (Learning Classiﬁer System) which

might be more applicable to other real-world prob-

lems such as workload scheduling or data mining.

2 A BRIEF HISTORY OF RPS

COMPETITIONS

Competitions are good to drive progress and often

help to bring novel ideas to existing algorithms. There

is currently a popular website (Knoll, 2011) hosting

an ongoing competition for RPS algorithms, where

bots (algorithms able to play a game similarly to hu-

mans) go against each others for matches of a thou-

sand rounds. In this context, a round consists of one

action from each opponent, drawing from the set of

Rock, Paper or Scissors. The ﬁnal score of a match is

the difference between rounds won and rounds lost.

Bédard-Couture, R. and Kharma, N.

Playing Iterated Rock-Paper-Scissors with an Evolutionary Algorithm.

DOI: 10.5220/0008175902050212

In Proceedings of the 11th International Joint Conference on Computational Intelligence (IJCCI 2019), pages 205-212

ISBN: 978-989-758-384-1

205

2.1 First International RoShamBo

Competition

In 1999, Darse Billings, a researcher at the Uni-

versity of Alberta organized the First International

RoShamBo Competition. The format of the compe-

tition and the results can be found on his website

(Billings, 1999a). In this competition, every player

competes against every other player in matches of a

thousand rounds each. If the score is between minus

ﬁfty and plus ﬁfty, it is a tie. The results are reported

using two ranking systems. The ﬁrst one is Open

Ranking where the rank is determined by the sum of

the scores of all matches played, while the Best of the

Best considers only the number of matches won. An

analysis of the participating algorithms revealed that

all the techniques used could be grouped under two

main families of algorithms. Programs either used a

direct history method where the predictor is looking

at the history for matching patterns or alternatively

used statistical methods such as Markov Models or

frequency counters.

The winner of the ﬁrst competition was a pro-

gram named Iocaine Powder, developed by Dan Eg-

nor (Egnor, 2000). The source code can be found on-

line in the compilation of all the participants (Billings,

1999b). This bot uses a direct history method along

with a meta-strategy called Sicilian reasoning. The

concept of Sicilian reasoning comes from the movie

The Princess Bride. It is a meta-strategy that incorpo-

rates the level of prediction the opponent is using and

allows the algorithm to evaluate which degree of pre-

diction (simple-guessing, second-guessing or triple-

guessing) is best performing. It also allows the al-

gorithm to evaluate if the opponent is using a similar

meta-strategy. On top of that, the Iocaine Powder bot

also uses multiple strategies and a meta-meta-strategy

and shows full understanding of the complexity of

this game. Full description of the algorithm with its

source code can be found online (Billings, 1999b).

2.2 Second International RoShamBo

Competition

A second competition was held the following year

(Billings, 2000a) based on the same rules. It also in-

cluded a test suite were participants could test their

algorithm against the winners of the previous com-

petition, hoping to raise the level of the new submis-

sions. Although this new generation saw some im-

provement, most algorithms were inspired by the pre-

vious winner, Iocaine Powder. However, even with

access to its source code, the new entries did not im-

prove much on its idea (except for the new winner)

since Iocaine Powder still managed to ﬁnish in third

place, overall.

The winner of the second event was Greenberg by

Andrzej Nagorko which is a direct descendant of Io-

caine Powder. Although its source code is available

online, it is not documented nor described so it is hard

to understand the improvements executed on its pre-

decessor, but it appears to use the same idea of multi-

ple strategies along with Sicilian reasoning.

2.3 RPSContest

Eleven years later, Byron Knoll reopened the compe-

tition through an online platform known as RPSCon-

test (Knoll, 2011). Although there has not been any

update since 2012, the platform still works today and

the leader board is automatically kept up to date. The

format of the competition is slightly different from the

two previous ones. The programs must be submitted

in Python and the CPU limit is set to ﬁve seconds per

match. The ranking is also less representative than

the previous ranking schemes since it is based on the

average win ratio of random matches. The win ratio

is the number of victories divided by the total number

of matches, weighted more heavily on recent matches.

There is also no limit placed on the number of submis-

sions or their content. It is common to see an author

submitting more than ten versions of the same algo-

rithm. It is obvious that duplicating a better than av-

erage bot a hundred times will have a negative effect

on the ranking of all the other algorithms.

Daniel Lu provided a comprehensive summary of

the most common strategies and meta-strategies for

playing RPS (Lu, 2011). Following the two Interna-

tional RoShamBo Competitions, bots based on his-

tory matching or statistical methods were proven to

work well, but having an ongoing online tournament

allowed new ideas to emerge. Notably, some of the

top players are now using neural networks to analyze

the emerging history of a game and hence, predict the

opponent’s next move. Surprisingly, only two bots in

the leader board are using EAs and they are ranked

below average.

We reviewed the bots on the ﬁrst page of the leader

board (top 50) to include only the best (usually latest)

version of an algorithm and exclude all other versions.

This gave us a succinct list of the latest versions of

the best performing algorithms. The rest of the list

(comprising of weaker algorithms) was skipped over

except for any EA-based program.

At the time of this study, the number one bot

on the leader board was Tweak the best. This bot

uses multiple strategies and meta-strategies with a

Markov Model to make its prediction. The next bot to

ECTA 2019 - 11th International Conference on Evolutionary Computation Theory and Applications

206

use a different type of algorithm is dllu1 randomer.

Ranked second, it is very similar to Iocaine Pow-

der (based on direct history) but with a higher level

of meta-strategies. It is really amazing to see that

Iocaine Powder is still one of the best performing

strategies for this game, even though its rank might

be the result of a greater popularity within the RPS-

playing community. The best neural network bot,

NN2 10 0.99 0.25, is ranked 39

and the rest of the

top 50 bots are all based on either Markov Models

(such as Context Tree Weighting) or history matching

(mostly described as DNA sequencers). Lastly, the

best bot using an EA is X-Gene v4 and sits at position

1989 in the leader board.

3 REVIEW OF ACADEMIC

LITERATURE

The academic literature related speciﬁcally to genetic

algorithms applied to Rock-Paper-Scissors is rather

limited. In 2000, researchers from Japan conducted

a similar experiment by constructing a genetic algo-

rithm to play RPS (Ali et al., 2000). The results they

reported were positive against systematic and human

players, but did not show the performance of their al-

gorithm against advanced strategies and other algo-

rithms. Some papers will study different aspects of

the game (Wang et al., 2014; Lebiere and Anderson,

2011; Billings, 2000b), while others apply EAs to

game theory (Xavier et al., 2013; Kojima et al., 1997).

Iterated Rock-Paper-Scissors is a unique problem that

can not be assimilated in general game theory or other

popular games such as chess.

A history matching predictor based on an evolu-

tionary algorithm was used for reservoir simulation in

the oil industry (Xavier et al., 2013), but their contri-

bution is not applicable to the problem of competing

predictors.

In a recent study of social behaviour in Rock-

Paper-Scissors tournaments (Wang et al., 2014), re-

searchers demonstrated that in a small population, the

strategies used to play the game follow a cyclic mo-

tion to shift between the available actions. Their study

also shows that the strategies in a population are af-

fected by the magnitude of the reward. Understanding

how humans play in a variety of contexts adds valu-

able insights to those working on artiﬁcial intelligence

algorithms, as models are often inspired by solutions

found in nature.

Another research paper about decision making

(Lebiere and Anderson, 2011) explains how humans

play in sequential decision making and how they are

able to learn and recognize multiple patterns at once.

The human players make decisions that are similar to

those recommended by statistical models. The human

players balanced safe and risky choices by taking into

account both the recency of events as well as their fre-

quency.

More related to the game of Rock-Paper-Scissors,

a group of researchers published a paper demonstrat-

ing the effectiveness of a simple statistical predictor

(Valdez et al., 2014). They used the Beat Frequent

Method predictor and developed a framework to op-

timize it. Since there is a strong bias with meta-

strategies based on Iocaine Powder in the Second In-

ternational RoShamBo Competition, they focused on

the test suite of the First International RoShamBo

Competition. Their results were successful in improv-

ing the basic predictor and demonstrated that using

a shorter history is more effective, especially against

weak opponents. Still, their predictor was unable to

beat strong bots such as Iocaine Powder. Despite

its lackluster performance, another paper on the same

predictor was published in 2015 (Valdez et al., 2015).

The literature on EAs is vast and rich, and cover-

ing the latest advances in this ﬁeld is out of the scope

of this study. The reader should refer to (Eiben et al.,

2003) and (Koza, 1992) for a proper introduction to

both evolutionary and genetic algorithms. There is

also a vast number of publications on AI in games,

but the focus of this paper is on the development and

utilization of EA techniques in the playing of iterated

Rock-Paper-Scissors.

4 METHODOLOGY

The evolutionary algorithm described in this section

is somewhat similar to a Pittsburgh-style LCS algo-

rithm, but designed to be highly adaptive, with ﬁtness

values used both for the rules and the individuals. See

(Urbanowicz and Moore, 2009) for a complete intro-

duction to LCS algorithms.

An overview of our algorithm is presented in ﬁg-

ure 1; it illustrates the steps the EA takes, at every

round, to make a prediction. For the ﬁrst hundred

rounds, the algorithm executes random moves, to al-

low the EA population to be at least partially molded

by information about the opponent’s play style. This

could be circumvented by reusing prior knowledge of

good strategies established in our experiments.

4.1 Exploration

The exploration phase is governed by a genetic algo-

rithm, which its main components are described in the

following sections.

Playing Iterated Rock-Paper-Scissors with an Evolutionary Algorithm

207

Figure 1: Diagram of the Algorithm.

4.1.1 Representation

An individual consists of a set of rules and has its own

ﬁtness value and learning rate. A rule is deﬁned by a

context, an action and a target round, along with a

separate ﬁtness value and learning rate. The match-

ing of a rule is done on the history string, which is

stored from the opponent’s point of view. This repre-

sentation was chosen because it allows an individual

to capture the dependencies between the transitions of

played rules by using a separate ﬁtness value.

Context. The context is a sequence of the length

of the window size that represents a possible history

of plays, using the characters W (Win), L (Lose), D

(Draw) and a wildcard character. Using wild cards al-

lows the EA to capture simple strategies easily. It is

important to analyze the history from a win, lose or

draw perspective since the actions have a cyclical de-

pendency (R < P < S < R ...). The outcome is what

is important for this algorithm.

Action. The three possible actions are win (W), lose

(L) or draw (D). The win action means play the move

that would have won for the target round; similarly

for lose and draw.

Target. The target range is between one and the size

of the window, since round zero is the current round

(the round the EA is trying to predict).

4.1.2 Initialization

The population is initialized randomly. For each con-

text, both action and target are selected randomly us-

ing a uniform distribution.

4.1.3 Parent Selection

A new population is created at every round of the

game. The parent selection process uses tournament

selection without replacement and with a tournament

size of 3. The algorithm also uses a tolerance of

5% when comparing ﬁtness values; two individuals

whose ﬁtness values are within tolerance are consid-

ered equally ﬁt. When two or more individuals are

equally ﬁt, one of them is chosen randomly. It is pos-

sible to wait a few rounds before generating a new

population, but the algorithm reported better results

by evolving every round.

4.1.4 Genetic Operators

Crossover. Two-point crossover is performed twice

on the parents, producing 4 children. Generating

more children by crossover is helpful for exploring

the search space. The implementation follows the

standard two-point crossover: pick two position ran-

domly and swap the middle part between both par-

ents. The learning rate and winning rate of the chil-

dren are initialized the same way as new individuals

(set to 0).

ECTA 2019 - 11th International Conference on Evolutionary Computation Theory and Applications

208

Mutation. Every child is run through the mutation

operation. The overall mutation probability is 0.4.

Since every individual has 256 rules and the mutation

distribution is uniformly random over the rules, the

probability of rule mutation is 0.4/256. If a mutation

is applied to a rule, it will either change its action or

target to any other action or target, respectively, with

equal probability.

4.1.5 Survivor Selection

Crowding. In deterministic crowding with multiple

children, the distances between all the children and

both parents are measured, using both the action and

target parts of rules to compute distance. Children

are divided into two groups, each comprising a parent

and the children that are closer to it than the other par-

ent. The ﬁttest child in each group competes with the

parent of that group and the ﬁtter individual is passed

on to the next generation. This way of implementing

crowding allows exploring more of the search space

by generating more than two children while ensuring

that the size of the population stays constant through-

out the generations. Equations 1 and 2 describe how

the distance between two individuals is measured. In

equation 1, the values of pairwise distances are de-

scribed along with their condition. a

and a

refer to

the actions and t

and t

to the targets of the two rules.

A distance value of 1 is given when a feature is dif-

ferent, without comparing the actual values since they

are independent. A higher distance value of 3 is given

when both the actions and targets are different to em-

phasize the double mutation that would be required to

make them identical (only one of the two can be mu-

tated per generation). Finally, the distance measure

presented in equation 2 is simply the sum of the dis-

tances between every pair of corresponding rules, in

the two individuals.

d(i, j) =











3 if a

6= a

and t

6= t

1 else if a

6= a

or t

6= t

0 otherwise

(1)

D(i, j) =

∑

i, j

d(i, j) (2)

Injection. The EA uses injection to help maintain

diversity. The injection rate is set at 5% of population

size. When creating the population of the next gen-

eration, the worst 5% of the current generation is re-

placed by new, randomly initialized individuals. The

ﬁtness of the newly created individuals is initialized

by replaying the last 16 rounds, which was found to

give a good approximation of their ﬁtness value, as if

Figure 2: Computing the Prediction of a Rule.

they had been in the population from the beginning of

the match.

Elitism. The algorithm also uses elitism by copying

the current hero into the new population.

4.2 Context Matching

The context matching step consist of identifying

which rules are applicable given the current history

by comparing the history string with all the contexts,

taking into account wildcards.

4.3 Prediction Calculation

Each applicable rule computes the prediction of the

opponent’s next move. The target of the rule is used

to extract the move played by the opponent at that spe-

ciﬁc round of the game (the target value is relative to

the most recently played round, where a target value

of 1 represents the latest round played). The action of

the rule can be read like this: play the move that will

[win/lose/draw] against move [Rock/Paper/Scissors],

given the opponent’s move history. In the example il-

lustrated in ﬁgure 2, the targeted move is P (Paper)

and action is W (Win), so the move that would win

against Paper is Scissors. Thus, the prediction is that

the opponent will play Scissors on the next round.

Playing Iterated Rock-Paper-Scissors with an Evolutionary Algorithm

209

4.4 Rule Selection

Once all applicable rules have made their prediction

on the opponent’s next move, the individual will se-

lect the one with the highest ﬁtness value for its ﬁnal

prediction. Fitness values of the rules are compared

using a tolerance and in case of a tie, a random se-

lection is made. This selection has an impact on the

ﬁtness of the individual as a whole.

4.5 Hero Selection

The individual with the highest ﬁtness value is se-

lected as the hero and the algorithm will use its pre-

diction to counter the opponent’s next move. The ﬁt-

ness evaluation process is the same one as the rule

selection process (see section 4.4). In order to capture

the relationships between context as the match pro-

ceeds, the selection of a new hero only happens every

4 rounds (synchronized with the window size).

The ﬁnal step of the EA is to determine if the hero

is good enough to play by comparing its ﬁtness to a

predeﬁned threshold (set to 0.75). This is a defensive

measure that instructs our player to make a random

move if the ﬁtness of the hero is too low.

4.6 Fitness Update

The algorithm has two levels of ﬁtness values, rep-

resented by the symbol Ω, and calculated using the

same formula (equation 3) shown below. Each rule

has its own ﬁtness value, and each individual (con-

sisting of a set of rules) also has its own ﬁtness value.

Once the round is played, the opponent’s move is

compared to the predictions of both the matching

rules and the individuals of the population, and their

ﬁtness values are updated following equation 3. The

initial ﬁtness value is 0 and β is the learning rate,

which is set to 0.4 for the entire algorithm. One would

think that in order to be highly adaptive, a high learn-

ing rate would be required, but anything greater than

0.5 induces overﬁtting. Self-adaptation of the learn-

ing rate, at the individual level, might yield better re-

sults. With this equation, the range of possible ﬁtness

values is between 0 and 1 inclusively.

Ω(t +1) =

(

Ω(t) · (1 − β) + 1 · β, if predicted right

Ω(t) · (1 − β) + 0 · β, otherwise

(3)

4.7 Termination Criteria

The algorithm is active throughout the whole match.

The only termination criteria is the end of the match,

or equivalently a thousand rounds.

Table 1: Summary of the Evolutionary Algorithm for RPS.

Representation Integer

Recombination Two point crossover

Recombination probability 80%

Mutation Random variation

Mutation probability 40%

Parent selection Tournament(k=3)

Survival selection Deterministic crowding

Injection 5%

Elitism 1

Population size 500

Number of offspring 4

Initialization Random

Termination condition 1000 rounds

Window size 4

4.8 Algorithm Parameters

Table 1 presents the different parameters required to

run the algorithm, which were determined empiri-

cally, except for the termination condition that is set

by the context of the competition. As EAs are gener-

ally robust, changes to those values did not have a sig-

niﬁcant impact on the results. The exceptions to that

were the population size and window size, which have

a larger impact on the search space. A population of

500 was found to be optimal as lower values would

degrade the performance too much while higher val-

ues would only bring marginal beneﬁts. Smaller win-

dow sizes did not seem to capture complex strategies

and bigger window sizes had too much impact on the

computational cost of the algorithm.

5 RESULTS

The results are summarized in table 2 and two match

examples are illustrated in ﬁgure 3. The metric used

to rank a bot is the percentage of matches won over

all the matches played. This gives the overall per-

formance but hides the details of performance against

each speciﬁc opponent. The percentage of rounds

won over all the rounds played gives a second layer of

detail as to the efﬁciency of the algorithm, but suffers

the same problem of hiding the speciﬁc one-on-one

performance.

In any EA, the diversity of the population is criti-

cal to its success, thus it is important to have an accu-

rate measurement method to ensure equilibrium be-

tween exploitation and exploration. Every time the

population is evolved, the diversity of individuals is

measured by sampling 10% of the population. For

instance, if the population is made from a hundred

individuals, ten are selected randomly and compared

to each other. The distance measure is the same as

ECTA 2019 - 11th International Conference on Evolutionary Computation Theory and Applications

210

Figure 3: Outcomes and diversity measurements of one match (out of ten) against two opponents. These examples were care-

fully selected to demonstrate the differences in behavior of a completely random opponent as opposed to a more predictable

strategy. The top part of the graph shows the win ratio (

Wins

Losses

) and percentage(

Wins

Rounds

) of the algorithm and the grey zones

mark the rounds that it played random. The dark lines identify short sequences where the algorithm took action. In order

to win, the win ratio of the algorith should be above 1 at the end of the match. The bottom part of the ﬁgure shows the

mean and standard deviation of the diversity measurements. Crowding and injection help to maintain such high diversity and

occasionally the diversity would collapse but only for a few rounds.

that used for the deterministic crowding (presented at

equation 2). The distances between every pair of in-

dividuals in the sample are calculated and hence, the

mean and standard deviation of those distance values

are used as approximate, but on average accurate, re-

ﬂections of population diversity. Further explanations

of the performance measures are provided within the

legend of ﬁgure 3.

Table 2: Results of a 10 matches tournament.

Rank Bot

Matches

Won(%)

Rounds

Won(%)

1 dllu1 randomer 74 34.4

2 GAiRPS 60 33.3

3 NN2 10 0.99 0.25 56 36

4 Tweak the best 52 37.1

5 Random 38 33.1

6 X-Gene v4 14 27.2

To measure the quality of the algorithm, an of-

ﬂine tournament was held against the best bots for

each category of algorithm. The four opponents are

Tweak the best (Markov model), dllu1 randomer (his-

tory matching), NN2 10 0.99 0.25 (neural networks)

and X-Gene V4 (genetic algorithm). An extra bot

always playing random was also included as a con-

trol. Each algorithm played ten matches against every

other one and the results are reported in tables 2. Ta-

ble 3 reports the number of games won (out of 10)

against each of the other types of algorithm, provid-

ing additional information on the performance of the

proposed algorithm.

The results are quite positive, as our customized

Evolutionary Algorithm (named GAiRPS) beat the

other EA and took second place. The ranking is

Table 3: Number of matches won against each opponent.

Opponent Wins (out of 10)

dllu1 randomer 4

NN2 10 0.99 0.25 6

Tweak the best 8

Random 6

X-Gene v4 6

close to the ofﬁcial leader board with only X-Gene

V4 placed below the random bot, but the top three al-

gorithms have swapped places. Again, the bot using a

history matching approach similar to Iocaine Powder

has a deﬁnitive edge over others.

We were able to demonstrate that an EA could

perform better than a random bot, and compete with

other types of artiﬁcial intelligence methods in play-

ing RPS. Still, to achieve this result, the algorithm had

to play a lot more random than originally planned, and

the difference in computational resources is consider-

able in comparison to the opponents.

The complexity of GAiRPS could be greatly im-

proved by borrowing ideas from opponents. The com-

plete source code will be provided upon request.

6 CONCLUSION

This study demonstrates that a carefully designed

Evolutionary Algorithm can be competitive in a tour-

nament of Rock-Paper-Scissors, where rapid adap-

tation (learning) and exploitation of temporal pat-

terns are essential for winning. Obtaining the sec-

ond place in a custom tournament against only the

Playing Iterated Rock-Paper-Scissors with an Evolutionary Algorithm

211

top performing algorithms of the online competition

(Knoll, 2011) is a notable feat and demonstrates that

EAs should not be automatically excluded for on-line

learning algorithms. In this speciﬁc case, the robust-

ness of the algorithm comes from playing random

very often, a popular technique among the other com-

petitors as well. In order to achieve these good re-

sults, the restriction on computational resources has

been removed.

In our EA, the search space was limited to (4 ×

256

possibilities, but chances are that the optimal

solutions lay outside this space. Hence, one way to

improve the algorithm would be to make the window

size a self-adaptive parameter of individual predic-

tors, although it would probably increase complex-

ity. To gain popular traction, the efﬁciency should

be hugely improved, to the point where it could be

submitted online for an ofﬁcial ranking on the rp-

scontest leader board. Also, the introduction of meta-

strategies might well have a positive impact on EA

performance.

The meta-strategies developed by the community

for this game (notably the Sicilian reasoning from

Iocaine Powder) are extremely efﬁcient; the best of

them are able to win more than 75% of their matches.

Such good predictors would be great candidates for

performing other tasks such as predicting the trend of

a stock market or other multi-agent games.

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