Artificial Intelligence Applied on the Risk! Game

LuaFuligni(lua.fulignistudio.unibo.it), AndreaFranzon

(andrea.franzonstudio.unibo.it),OrfeoCiano(orfeo.ianostudio.unibo.it)

AlmaMaterStudiorum-UniversitàdiBologna

Abstrat. Ourgoalistoreateanappliationthatusesartiialplay-

ersforthegameofRisk!.SomeoftheexistingimplementationsofRisk!

present ustomizable artiial players but their behavior seems to be

neithertoosmartnornaiveandthisantireoutthehumanplayer.We

intent to ahieve the goal ina dierent way: we hose to use Prolog,

adelarativelanguage,inontrastwiththeexistingopen-soureimple-

mentations.WelearntthattheusageofPrologreduesthedevelopment

timeandeortsbyoeringagoodabstration.

Keywords:artiialintelligene,Prolog,Risk,game,dies.

1 Introdution

Ourgoal isto reate anappliation that usesartiial playersforthegame of

Risk!TheontextistheusageoftheArtiialIntelligenesonthisgamethatis

astrategy,turn-based,multiplayergame andontainssomerandomnessdue to

thethrowingofdies.MoreexatlyweuseA.I.forthegamestrategy.Wehoose

risk! beauseunlikegamesin the theory'sgamesit presentsmany problemati

for example the hoie of the attaking territories or the predition of whih

territorytheenemywillattak.

Usuallytheexistingopen-soureimplementationsofthisgameusesimpera-

tivelanguagestodesribetheA.I.strategy.We,instead,proposetoseparatethe

A.I.aspetfrom theprogrambyusing adelarativelogi language.Wehoose

Prolog beauseit inludes the rst-order logi and bakwardhaining meha-

nismnatively.Moreoverwedon'thooseanimperativelanguage,likeJava,for

theA.I. aspetbeauseall thetreesearhand inferenefuntionalityinluded

in somelibrariesarelesseientthanthePrologengine.

As adelarativelanguagewehooseProloginstead of otherlanguageslike

Lispbeausewehavetoinfermoreonreordsthanonlists.Ourintentistouse

theProloglanguagefordesribingtheartiialplayer'sdeisions.

Theabilityofeahartiialplayer(andsothediultyforahumanplayer)is

haraterizedbythesetofrulesthatdenetheinfereneengineofeahartiial

player.The partiularity ofour solutionisthe onnetionbetweenprolog that

Risk! is aturn-based strategi board game for twoto six playersin whih the

goalisindiatedbyanobjetiveard.Thegameisplayedonaboarddepitinga

politialmapoftheEarththatontains42territoriesdistributedin6ontinents.

Thereareseveralgoalsbutinourappliation,forsimpliityandforageneral

purpose,weonsider onlytheaimto own24territories.

Atthestart-upeahplayerdistributesaxednumberofarmiesontheboard.

Ineahturntherearethreephases:plaingarmies,attaking,fortifying. Inthe

rstphasetheplayerputs newarmiesintotheownedterritories.Intheseond

the player attak a nearby enemy territory, the suess or fail of an attak is

deided by the throw of dies. In the third phase the player an move some

armiesbetweentwoowned nearbyterritoriesonlyone. Thephaseswill repeat

themselvesuntilaplayerreaheshis goal.

3 Related works

Thisapproahanbeusedingameswhihpresentrandomnessandmultiplayer

issuesoringameswheretheartiialplayer'sbehaviorisstritlyonnetedwith

logialdesriptionlikeRisk!.

Nowadays there are several implementations of Risk!. The most famous is

Risk Digital of Hasbro but there are alot of Risk! lones like Lux for Linux,

DominionformobilephonesorotherashgamesanbefoundovertheInternet.

Someofthose implementationspresentustomizableartiialplayersbuttheir

behaviorseemstobeneithertoosmartnornaiveandthisantireoutthehuman

player.

Ourapproah,besidesfousingoneieny,hallengesthelogialaspetin

adierentandmoresuitablewayin ordertoimprovethegame-play.

4 Methodology

OurrstimplementationisaJavamodelaptto representthe gameboard and

alltheinformationsthat itontains(territoryborders,neighborhoodrelations,

ontinents,territoryownership, ...).WealsodenethePrologknowledge-base

struturepayingattentionondataonsistenywiththeJavamodel.

WeproposethreedierentA.I.diultylevels:easy,mediumandhard.The

easylevelperformsrandomations.Insteadthehardlevelwillbeanextension

of themedium levelthat is anintelligent implementation ofthesameProlog

prediates. Eah skill that distinguish medium and hard diulty is mapped

into Prolog prediates. We use GNU Prolog for Java to embed the Prolog

interpreterintoourJavaappliationbeauseitrespetstheISOstandards.

Weassumethattheaimistoonquer24territoriesto simplifythestudyof

thegame. We hoose toguide theA.I. throughsomewell-knownasesin eah

The Risk! Map an be onsidered as a set of ountries (territories). For eah

territorywedene:

arelationofneighborhoodbetweenterritories;

theterritory'sownership;

thenumberofarmiesaterritoryholds;

WerepresentedthisknowledgeinPrologbydeningthefollowingsetoffats:

player/1 represents a player, identied by his olor (blue, red, green, pink,

blak,yellow).

territory/1 representsaterritory,identiedbyhisname.

owner/2 represents the ownership of a territory identied by the denoted

player.

neighbor/2 representstherelationoftheneighborhoodbetweentwoterritories.

army/2 representsthearmynumberforeahterritory.

Sothisisthesimplestknowledgebaseweanhave:

player(red).

player(green).

territory(siberia).

territory(jauzia).

territory(ita).

owner(siberia ,red).

owner(jauzia, red).

owner(ita ,green).

neighbor(siberia ,jauzia).

neighbor(siberia ,ita).

neighbor(jauzia ,ita).

neighbor(jauzia ,siberia).

neighbor(ita ,jauzia).

neighbor(ita ,siberia).

army(siberia ,3).

army(jauzia ,4).

army(ita ,2).

4.2 Moves

armyshouldbeplaed.

attak/3 Givenaplayer'solor,itgivesbaktwoterritories:anattaksoure

(territoryownedbytheplayer),andanattakdestination(territory

ownedbyanenemyplayer).

move/3 Given a player's olor,it gives bak two territories: the territory-

soure from whih the armies should be moved, and the territory-

destinationtowhihthearmiesshould bemoved.

Herearesomesamplequeries:

?

−

Yes, Destination=siberia.

?

−

Yes, Soure= yauzia, Destination=ita.

?

−

Yes, Soure=siberia ,Destination =jauzia.

TheimplementationofthoseprediateswillvaryaordingtoA.I.diulty.

InthiswaytheresponsibilityoftheJavaengineistoupdatetheknowledgebase

andperformthemovesuggestedbytheprologengine.

4.3 Randomnessrepresentation in Prolog

Beause of randomness omponentof thegame, exploring adeisional tree to

hoosewhihterritorytoattak, ouldleadto agenerallow-responsivity.This

is beausewe'dhaveto inserttworandomnesslevel (attakand defensedies)

into thedeisiontreeinreasingexponentiallythenumberofthenodes in that

level.

Thereforewedeideto representtherandomnessomponentsusing atable

thatontains,giventhenumerofattakeranddefenderarmy,theprobabilityto

winanattak.InsidetheKnowledgeBaseinPrologwerepresentthisinformation

withvitory/3:

vitory(Attak#Army, Defense#Army, Probability).

Sothattheprediateattak,givenaxedthresholdvalue,knewtheong-

urationattakerarmy/defenderarmythattwoterritoriesmusthavetoperform

anattak.

4.4 FromJava to Prolog

Javahastheresponsibilityofgeneratingtheknowledgebase.Inordertoaom-

2 for(Continent ontinent:ontinents)

3 {

4 for(Territory territory:ontinent.getTerritories())

5 visitor.visit(territory);

6 }

Onetheknowledgebaseisupdated,itisloadedbythePrologengine:

1 Environment env = new Environment();

2 //Loading the knowledge base file and A.I. implementation

3 env.ensureLoaded(AtomTerm.get("knowledge.pl"));

4 env.ensureLoaded(AtomTerm.get("easy.pl"));

5 interpreter = env.reateInterpreter();

6 env. runInitialization(interpreter );

Theexeutionofaquery:

1 //Calling the query: ?

−

2 VariableTerm answerTerm = new VariableTerm("Territory");

3 Term[℄ args = {AtomTerm.get(playerColor),answerTerm};

4 CompoundTerm goalTerm = new CompoundTerm(AtomTerm.get("

plae_army"), args);

5

6 //Exeuting the query and testing if sueded

7 int r = interpreter.runOne(goalTerm);

8 if(r==PrologCode.SUCCESS || r==PrologCode.SUCCESS_LAST)

9 {

10

11 //Getting the Prolog indiated territory from the

game table

12 Term value = answerTerm.dereferene();

13 String n a m e = TermWriter.toString(value);

14 Territory destination = table.getTerritory(n a m e);

15 }

TheresultofthisquerywillbeusedbytheRiskgameenginethatperforms

theorrespondingmove.

5 Case-study

During an attak,to handle the randomnessof the dies, wegenerate a table

(based onMarkov hains)whih ontainstheprobabilityof winning anattak

bythenumberofattakanddefensearmies.

Eahplayer'sdiultyisharaterizedbyathresholdvalue,onlyiftheprob-

movesarmiesbetweentheterritories.Tobreakthedeadlokweneedtohardode

somespei Prologonditions.

Afterthitweagaintestedthesystembyletting twoplayers,withthe same

A.I. diulty level, ght eah-other.Otherwise, if there is at least oneplayer

with adierent diulty level,then the spei onditionsare notso evident,

sotheTuringtestispassed.

Tooverometheseproblemsanersolutionouldbetorepresentthemodel

asaConstraintLinearProgrammingprobleminwhiheverydeisionisdrivenby

anobjetivefuntion thatwilleitherbeminimizedormaximized,dependingon

theationthattheplayerhasperformed.Theobjetivefuntionvariesaording

totheevaluationofdierentvariables.Thisevaluationiseitherroughorrened

dependingontheplayer'sdiultylevel.

6 Conlusions

Our implementation grants a good level of playing for every kind of player.

OtherwisetheCPLsolutionwouldrequireanetuningoftheobjetivefuntion

for eah diulty in order to meet the optimal value for eah A.I. level. This

will produe an unnatural playing style. The Prolog interpreter is an optimal

solutionforthesekindsofproblems.ByusingPrologitiseasiertoswithbetween

dierentA.I.logis(andapproahes)leavingtheoreappliation unhanged.

Referenes

1. Osborne,JasonA.April 2003:"MarkovChains for theRISKBoardGameRevis-

ited",MathematisMagazine76

2. S.RusselleP.Norvig,2005:"Intelligenzaartiiale.Unapproiomoderno"volume

1SeondaEdizione.

3. L.Console,E.Lamma,P.Mello,M.Milano,1997:"ProgrammazioneLogiaePro-log"

SeondaEdizioneUTET.