a scrabble artificial intelligence game - cs.sjsu.edu endgame strategies. • evaluate performance...

AScrabbleArtificialIntelligenceGame

AdvisorDr. Chris Pollett

Committee MembersDr. PhilipHellerDr. RobertChun

ByPriyathaJojiAbraham

• Introduction

• Background

• OverviewofMavenandQuackleAI

• Endgamestrategies

• ExperimentsandObservations

• ConclusionandFuturework

• Questions

Agenda

ProjectGoal

• Buildatwo-playerScrabbleAIgameengine.

• CreatetwoAI computerplayershavingdifferentmovegenerationheuristicsandendgamestrategies.

• Evaluateperformancebasedonthewinningcriteria,qualityofmoves,andtimeconsumption.

• Developvariantsofworld-championcomputerAI,‘Maven,’andanotherAI,‘Quackle.’

• ArtificialIntelligence(AI)isacollectionoftechniquesusedtobuildintelligent

agentsthatperceiveitsenvironmentandactrationallytoaccomplishthe goal.

• Gamesmakeanidealtest-bedforAIapplications.

• Scrabbleisacrosswordboardgame,widelypopularforitsgamestrategy.

• Scrabblecomputerplayershavealreadysurpassedhumanplayersintournaments,however,efficientheuristicsarerequiredtodefeatanotherScrabbleComputerAI.

• MavenandQuackleAIcompeteagainsteachotherusingitsthree-plyfuturelookaheadsimulationtechniqueanddifferentmovegenerations.

Introduction

• Scrabbleisanimperfectinformationgame:partialinformationaboutthegamestatewithalargebranchingfactor.

• Animperfectinformationstateposesdistinctchallengesfordecisionmakingagents,e.g.,playersareunawareofopponent’srack,andit'shardtopredictnextmove.

• End-gamesarecomplexandcrucialtothesuccessofthegame.

• End-gamesarereal-worldsituationswherethemoveoptionsarelimitedandmodelstrategytomaximizerewards.

• Normalhighscoreyieldingapproachesarenotgoodenoughforendgames.

• Scrabblerequiresquickmovegenerationtechniques.

ProblemStatement

• MavenAI createdbyBrianSheppard[1]in2002defeatedseveralworldchampion,humanplayers.

• QuackleAIcreatedbyJasonKatz-BrownandJohn[2]in2006hasbeatenworldchampionDavidBoys.

• AnAIGameenginedevelopedbyStanfordstudentsin2016betweenQuackleAIandanewComputerAIwith MonteCarloSimulationsofdepth2.

• Theyfocusedonmid-gamescenariosandnotendgamesduetotimelimitations.

RelatedWorks

ScrabbleGameRulesandTerminology

• Board:15x15gridgameboard.

• Tiles:Fillseachboardsquare;holdsletterandvalue.

• TileBag:Holds100tiles,98arealphabets and2blanks.

• Rack:Groupofseventilesholdsbyeachplayer.

• RackLeave:Lettersleftoutontherackafteroneplay.

• Bingo:Playwhichusesallthesevenlettersontherack.

• PremiumSquares:Squaresthatearnbonuspoints.Fig1.ConventionalScrabblegameboard[2]

• LegalMoves:Nodiagonalplays,playermustextendthewordsonboard.

• HotSpots:Excellentsquaresontheboardwithbonus-scoringopportunities.

• Ply:Player’sturnorhalfamoveinatwoplayergame.

• Weimplemented MavenAIandQuackleAIfromscratchinJava.

• Mavenapplies3-plylookaheadstrategyandvariousheuristicsforsimulation.

• Quacklecalculateswinprobabilityestimationusing3-plylookaheadstrategy.

• QuackleAIservesasa benchmarktomeasuretheperformanceofMavenAI

variants.

MavenAIandQuackleAI

• OfficialScrabblePlayersDictionary(OSPD)size: 1.8MBcontains>100,000words.

• OurAIplayerusedatrimmeddictionaryofsize:1KBcontains232words.

• MavenusesaDirectedAcyclicWordGraph(DAWG)torepresentdictionarythat

enablesfastmove-generation.

• DAWGisaminimalrepresentationofatriedatastructure.

DictionaryandLexiconRepresentation

TrieandDAWG

Fig3.DAWGwithitslexicon[5] Fig2.Triewithitslexicon[5]

• Weusedtrieandaword-listrepresentationforstoringtheentiredictionary.

TRIE DAWG

• Maven’smovegeneratorappliesdifferentheuristicsoneachplaytofindthebest

candidatemovefrom20-30candidatemoves.

• Onlylegalplacementsareconsideredontheboard.

• E.g.:The best possibleword:“FARM,”placeacross[A]N(Horizontaldirection).

MavenMoveGeneration

Rack:MFRFGTH

Split“FARM”onanchortile[A]intoleftandrightparts

Placeleftpart“F”onboard

Placerightpart“RM”on

board

Iflegalwordformation

withadjacentcellsreturnlegal,elsereturnanillegalflag

Fig4.Anexampleofhorizontallegalplacement

• Heuristics:Setofevaluationparameterstoinstantlysolvetheproblemswhen

traditionalapproachesareoftenslow.

• FourmainheuristicsusedinMaven, implementedinourproject:

1.Vowel-ConsonantBalance

2.U-With-Q-Unseen

3.Hotspotblock

4.First-TurnOpen

MavenHeuristics

MavenGamePhases

FirstMove

Mid-game

Pre-endgame

End-game

• Beginninguntil9orfewertilesinthebag.• Greedyscoringstrategy.

• Totalof16unseentiles.• 9inbagand7inopponent’srack.• Combinesmidandpre-endgame.

• Zerotilesinthebag.• 3endgamestrategies.

• 100tilesinthebag.• FirstturnopenexceptBingo.

• Endgamesarecomplicatedasplayershouldmakeamoveinacontrolledmannerto

maximizerewards withinthetimelimit.

MavenAIendgame

Q-Sticking

Slowendgame

Q-Stickingwith

slowendgame

MavenEnd-GameStrategies

• WhenopponentstuckwithunplayabletileslikeQorV.

• Blockthebighotspotandplaygreedyapproach.

Fig5.MavenAIvariants

• Maximizethevalueoftilesbyplayingoutslowly.

• Delaythegameusinglow-scoringtiles.

• Blocktheopponentmoves usinglow-scoringtilesifplayerisbehind.

• Ifplayerisahead,closethegamebymaximizingreward.

• Traptheopponentwithawkwardtiles.

• Mavencomputes 3plylook-aheadoffuturemoves.

• Ply1:Placethebestscoringcandidatewordforagivenrackandboardstate.

• Ply2:Findtheopponent’spossiblecandidatewordandresultantscoreifthatwordisplaced.

• Ply3:Evaluatethecurrentstateandfindthebestwordtoblockthatmoveinanendgame.

MavenAILook- AheadandSimulation

QuackleAISchematic Diagram

Fig6.Quackleworkflow[2]

• Quackleconsidersrackleaveheuristics.

• Quacklehasfollowingtwocomponents:

i)Kibitzer:Itappliesstaticevaluationandrankscandidatemovesquickly.

ii)Simulationengine:Itapplies3-plylookahead andrepeated100-300timesfor100randomracksandcalculatespointdifferential.Pointdiff=OurTotalScore– Opponent’sScore+Residualrackleavevalueestimate

23candidatewords

e.g.:30words

2300min.simulations

• Quackledetermineswinningprobability

basedonthepointdifferentialandthe

remainingtilecountforeachcandidate

move.

• Candidatemovelistissortedindescending

orderofwinningprobabilitypercentage.

• Ifwordsarefoundwiththesame

probability,breakthetiebyselectingthe

wordwithlowestrackleavevalue.

QuackleWinPercentageEstimation

Fig7.Quacklesimulationexample

Breakthetie

• Experimentsareconductedon10randomlygeneratedScrabbleendgames.

• ExecutedonaMacMachinewith16GBRAM-quad-coreprocessorrunningJava

version7.

• Weloadedreal-worldend-gamescenarios[8,11,13]usedintournamentsintoour

projectconsideringcurrentgameboardstate,playerrack,playerscore,tilebagand

scorelead.

Experiment1:MavenQ-StickingAIversusQuackleAI

Experiment2:MavenslowendgameAIversusQuackleAI

Experiment3:MavenQ-Sticking-slowendgameAIversusQuackleAI

Experiment4:MavenQ-Sticking-slowendgameAIversusNo-Q-Sticking

ExperimentsandObservations

• Howtoruntheexperiment?

• CreateMavenandQuackleAIsintwoseparateclasses.

• Makefunctioncallstofirstmove()ofgameopenAIandbestmove()ofbothAIsfor

subsequentplaysalternativelyuntilaRun experimentfor10randomScrabble

end-gamessimulatedintheprogram.

• Winnerisdetected.

• Markthescoresandcalculatetheaveragemeanscorescoreandstandard

deviation(SD).

• Determinethewinnerandcomparethepointscorespread.


I.Experiment1:MavenQ-StickingAIversusQuackleAIforEndgameconductedon

randomlygeneratedScrabbleendgames.

Hypothesis:WepredictedthatMavenQ-StickingAIwilloutscore Quackleas

MavenAIcanblockthehotspotsofQuacklewhenQuackleisstuckwithQandplay

withagreedyapproach.


Observations:

Manyfactorsinfluencedthewinner.• Blockedhot-spots• Scoredifference• Racktilevalue• Numberofracktiles• Kindofunplayabletile

Result:MavenoutscoresQuackle.Hypothesisconfirmed.

PlayerAI MeanScore+StandardDeviation

MavenQ-StickingAI 473.2± 70

Quackle 450.4± 59.2

II.Experiment2:MavenslowendgameAIversusQuackleAIforEndgameconductedon

10randomlygeneratedScrabbleendgames.

Hypothesis:WepredictedthatMavenwilloutscore Quackle.


Observations:

• HighScorelead• Maventilesfinishedsoon,couldnotdrag

endgame• Highpointunplayabletile

Result:QuackleoutscoresMaven.Hypothesisinvalid. PlayerAI MeanScore+StandardDeviation

Mavenslow-endgameAI 461.9± 80

Quackle 442.6± 60

III.Experiment3:MavenQ-Sticking-slowendgameAIversusQuacklefor10random

endgames.

Hypothesis:WepredictedthatMavenwilloutscore Quackleasitblockallthespots


Observations:

• Blockedhotspots• Blockedsingleopportunity• Lowscoringtilesmaximizedrewards• Placementonpremiumbonus• Gainedpenaltyscore• Highscorevariation

Result:MavenoutscoreQuackle.Hypothesisconfirmed.

PlayerAI MeanScore+

StandardDeviation

MavenQ-Sticking

slow-endgameAI

472.2±86.79

Quackle 417.9± 54.63

III.Experiment3:MavenQ-Sticking-slowendgameAIversusNo-Q-Stickingfor10random

games.

Hypothesis:WepredictedthatMavenwilloutscoreQuackleasitblockallthespots.


Observations:

• Blockedhotspots• Blockedsingleopportunity• Lowscoringtilesmaximizedrewards• Fastplay-out• Penaltyscore• Highscorelead

Result:MavenoutscoredQuackle.Hypothesisconfirmed.

PlayerAI MeanScore+SD

MavenQ-Stickingslow-end

gameAI

479.9± 75

No-QStickingAIScore 415.1± 45

• MavenAIwithQ-Sticking-slow endgameAIplaysthebest.

• Mavenblockshotspotsaswellasearnbonuspointsbytrappingtheopponent.

• NoQ-StickingAIaremostfavorableduringmid-games.

• Projecttakes100-255stofinish100simulationsofQuackle,originally19-50s.

• MavenAItakes0-2000ms,originally0-30msforonemovegeneration.

• Infuturework,wewillreducethesimulationtime andimplementaninteractive

graphicalUIfortheproject.

• QuackledataanalysisfeaturescanbeincorporatedintoourAIwhichsimulate

deeperpliesupto1000iteration.

ConclusionsandFutureWork

[1]B.Sheppard,“World-championship-caliberScrabble,” ArtificialIntelligence,vol.134,pp.241- 275,Jan.2002.[Online].Available:https://smp.uq.edu.au/sites/smp.uq.edu.au/files/WorldChampionshipScrabble.pdf

[2]J.K.BrownandJ.O'Laughlin,“HowQuacklePlaysScrabble,”2007.[Online].Available:http://people.csail.mit.edu/jasonkb/quackle/doc/how_quackle_plays_scrabble.html

[3]S.RussellandP.Norvig,“Adversarialsearch,”inArtificialIntelligence:AModern Approach,3rded.NewJersey:Pearson,2010,Ch.5,pp.161-189.

[4]Review:ScrabbleforiPad,[Online].Available:https://appadvice.com/appnn/2010/04/review-scrabble-ipad

[5]C.JosephsonandR.Greene,“CS221Fall2016projectfinalreport:ScrabbleAI,”2016.[Online].Available:https://web.stanford.edu/class/cs221/2017/restricted/p-final/cajoseph/final.pdf

[6]N.Gupta et.al,“AIAgenttoplayScrabble,”2017,[Online].Available:https://web.stanford.edu/class/cs221/2017/restricted/p-final/rsbauer/final.pdf

References

[7]S.A.Gordon,“AfasterScrabblemovegenerationalgorithm,”Software:PracticeandExperience,vol.24,no.2,pp.219- 232,Feb.1994.[Online].Available:http://ericsink.com/downloads/faster-scrabblegordon.pdf

[8]“Endgamefinesse”,AustralianScrabble® PlayersAssociation,Mar.2005.[Online].Available:http://www.scrabble.org.au/strategy/endgame.htm

[9]J.Mandziuk,“MavenandQuackle-Thetoplevelmachinescrabbleplayers,”inKnowledge-Free andLearning-BasedMethodsinIntelligentGamePlaying,Chennai,India:Springer,2010,Ch.4,pp.45- 47.

[10] A.W.AppelandG.J.Jacobson,“Theworld'sfastestScrabbleprogram,”CommunicationsoftheACMpp.572-576,May.1988.[Online].Available:http://www.gtoal.com/wordgames/jacobson+appel/aj.pdf

[11]“Masteringtheendgame”,BattleLine GamesLLC,2013.[Online].Available:http://www.2letterwords.com/Mastering_the_End_Game.html

[12]“Breakingthegame,”2014.[Online].Available:http://www.breakingthegame.net/strategy

[13]J.Edley andJ.Williams,“EverythingScrabble:ThirdEdition,”2009,pp.255- 315.[Online].Available:https://books.google.com/books?id=Uml_kpOO64gC&lpg=PP1&pg=PR5#v=onepage&q=end%20game&f=false

References

Questions

Thank You!

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