人工智能游戲開發(fā)課件

ConnectFourusingAlpha-BetaPruningBillyLandowskiCptS5407December2010ConnectFourusingAlpha-Beta1OverviewBackgroundConnectFourasasearchproblemAlpha-betapruningDetailsaboutwinningHeuristicsImplementation/DemoConclusionOverviewBackground2BackgroundSoldbyMiltonBradleyinFebruary19742playersAlternateturnsGoal:Connectfourtilesinarowhorizontally,vertically,ordiagonallyBackgroundSoldbyMiltonBradl3ConnectFourasaSearchProblem≤7possiblemovesperturnEnumerateeachmoveContinueforeachboardconfigurationPlayer1Player2ConnectFourasaSearchProbl4ConnectFourasaSearchProblemStates:Anyboardconfigurationwithatmostoneplayer’stileineachlocationInitialState:Anemptygameboardwithnotiles.Actions:Placeatileofthecurrentplayer’scolorintoanycolumnthatisnotfull.TransitionModel:Returnsaboardconfigurationwithatileaddedtothespecifiedcolumn.Goal/TerminalTest:Aplayerhasfourofhertilesinalineeitherhorizontally,vertically,ordiagonally,orthegameboardisfull(indicatingatie).Utility:+∞ifplayerhasconnectedfour,0ifboardisfull,–∞ifopponenthasconnectedfour.ConnectFourasaSearchProbl5Alpha-betapruningO(bd/2)timecomplexityb=branchingfactor=7d=depth=7×6=42ComputationallyintensiveNeedcut-offdepthCanalsoaddheuristicsAlpha-betapruningO(bd/2)tim6WinningConnectFourTowin,playerneedsa“winningline”of4WinningConnectFourTowin,pl73-out-of-4HeuristicTowin,playerneedsa“near”winninglineof33-out-of-4HeuristicTowin,pl83-out-of-4Heuristic(cont.)Counttotal3-out-of-4“unblocked”winninglinesComparetoopponentUtility(p,G)=f(p,G)–f(opponent(p),G)f(a,G)=#of3-out-of-4winninglinesforplayeraonboardG3-out-of-4Heuristic(cont.)Co9ScoreboardHeuristicExtend3-out-of-4heuristicton-out-of-4forn≤3AwardweightedpointsbasedonthevalueofnScore(p,G)=100(n3)+10(n2)+1(n1)niisthenumberofi-out-of-4winninglinesforplayerpongameboardGScoreboardHeuristicExtend3-o10ScoreboardHeuristic(cont.)Five1-out-of-4winninglines(n1=5)Five2-out-of-4winninglines(n2=5)Score=100(0)+10(5)+1(5)=55ScoreboardHeuristic(cont.)Fi11ScoreboardHeuristic(cont.)Compareplayers’scoresUtility(p,G)=Score(p,G)–Score(opponent(p),G)ScoreboardHeuristic(cont.)Co12ImplementationWritteninC#under.NETFrameworkMicrosoftVisualStudio2008WindowsFormsapplicationImplementationWritteninC#un13CPUDifficulties4difficultiesBeginner–randomModerate–alpha-betapruningwithcutoff-depth3andsimpleutilityfunctionHard–alpha-betapruningwithcutoff-depth6and3-out-of-4heuristicExpert–alpha-betapruningwithcutoff-depth6andscoreboardheuristicAspectofrandomnessCPUDifficulties4difficulties14ComparisonofCPUDifficultiesComparisonofCPUDifficulties15DemonstrationDemonstration16ConnectFourusingAlpha-BetaPruningBillyLandowskiCptS5407December2010ConnectFourusingAlpha-Beta17OverviewBackgroundConnectFourasasearchproblemAlpha-betapruningDetailsaboutwinningHeuristicsImplementation/DemoConclusionOverviewBackground18BackgroundSoldbyMiltonBradleyinFebruary19742playersAlternateturnsGoal:Connectfourtilesinarowhorizontally,vertically,ordiagonallyBackgroundSoldbyMiltonBradl19ConnectFourasaSearchProblem≤7possiblemovesperturnEnumerateeachmoveContinueforeachboardconfigurationPlayer1Player2ConnectFourasaSearchProbl20ConnectFourasaSearchProblemStates:Anyboardconfigurationwithatmostoneplayer’stileineachlocationInitialState:Anemptygameboardwithnotiles.Actions:Placeatileofthecurrentplayer’scolorintoanycolumnthatisnotfull.TransitionModel:Returnsaboardconfigurationwithatileaddedtothespecifiedcolumn.Goal/TerminalTest:Aplayerhasfourofhertilesinalineeitherhorizontally,vertically,ordiagonally,orthegameboardisfull(indicatingatie).Utility:+∞ifplayerhasconnectedfour,0ifboardisfull,–∞ifopponenthasconnectedfour.ConnectFourasaSearchProbl21Alpha-betapruningO(bd/2)timecomplexityb=branchingfactor=7d=depth=7×6=42ComputationallyintensiveNeedcut-offdepthCanalsoaddheuristicsAlpha-betapruningO(bd/2)tim22WinningConnectFourTowin,playerneedsa“winningline”of4WinningConnectFourTowin,pl233-out-of-4HeuristicTowin,playerneedsa“near”winninglineof33-out-of-4HeuristicTowin,pl243-out-of-4Heuristic(cont.)Counttotal3-out-of-4“unblocked”winninglinesComparetoopponentUtility(p,G)=f(p,G)–f(opponent(p),G)f(a,G)=#of3-out-of-4winninglinesforplayeraonboardG3-out-of-4Heuristic(cont.)Co25ScoreboardHeuristicExtend3-out-of-4heuristicton-out-of-4forn≤3AwardweightedpointsbasedonthevalueofnScore(p,G)=100(n3)+10(n2)+1(n1)niisthenumberofi-out-of-4winninglinesforplayerpongameboardGScoreboardHeuristicExtend3-o26ScoreboardHeuristic(cont.)Five1-out-of-4winninglines(n1=5)Five2-out-of-4winninglines(n2=5)Score=100(0)+10(5)+1(5)=55ScoreboardHeuristic(cont.)Fi27ScoreboardHeuristic(cont.)Compareplayers’scoresUtility(p,G)=Score(p,G)–Scor