11/542/54Game PlayingHuman Game Playing• Intellectual Activity• Skill ComparisonComputer Game Playing• Testbed for AI• Limitations23/54General Game PlayingGeneral Game Players are systems able to playarbitrary games effectively based solely on formaldescriptions supplied at “runtime”.Translation: They don’t know the rules until thegame starts.Additional Complexities: uncertainty (moves of other players) resource bounds (game clock)4/54TechnologyUnlike specialized game players (e.g. Deep Blue),they do not use algorithms designed in advance forspecific games.Artificial Intelligence Technologies knowledge representation reasoning, reformulation, learning rational behavior w/ uncertainty, resource bounds35/54Knight-Zone Chess6/54Bughouse Chess47/54Competitive Games8/54Single Player “Games”acb59/54Versatility10/54Annual AAAI Competition Held at AAAI conference Administered by Stanford (Stanford folks not eligible to participate)Reward 2005 - winner Jim Clune of UCLA 2006 - Stephan Schiffel and Michael Thielscher 2007 - Yngve Bjornsson and Hilmar Finsson 2008 - Yngve Bjornsson and Hilmar FinssonAnnual AAAI GGP Competition611/54Other Games, Other Winners12/54Carbon versus Silicon713/54General Game Description14/54Single Player Game as a State Machines3s2s5s6s8s9s4s7s10s1s11baa d b ca b aba a b b aa a c d b815/54Composite Actions for Multiple Playerss3s2s5s6s8s9s4s7s10s1s11bbbaaabb abbaaaab aaababaa aaabaabb aa bbba ab16/54Direct DescriptionSince all of the games that we are considering arefinite, it is possible in principle to communicategame information in the form of transitiongraphs.Problem:Size of description. Even though everythingis finite, the graphs can be large.Ideas: 1. Different Conceptualization 2. Compact Encoding917/54Tic-Tac-Toeinit(cell(1,1,b))init(cell(1,2,b))init(cell(1,3,b))init(cell(2,1,b))init(cell(2,2,b))init(cell(2,3,b))init(cell(3,1,b))init(cell(3,2,b))init(cell(3,3,b))init(control(x))legal(P,mark(X,Y)) :- true(cell(X,Y,b)) & true(control(P))legal(x,noop) :- true(control(o))legal(o,noop) :- true(control(x))next(cell(M,N,P)) :- does(P,mark(M,N))next(cell(M,N,Z)) :- does(P,mark(M,N)) & true(cell(M,N,Z)) & Z#bnext(cell(M,N,b)) :- does(P,mark(J,K)) & true(cell(M,N,b)) & (M#J | N#K)next(control(x)) :- true(control(o))next(control(o)) :- true(control(x))terminal :- line(P)terminal :- ~opengoal(x,100) :- line(x)goal(x,50) :- drawgoal(x,0) :- line(o)goal(o,100) :- line(o)goal(o,50) :- drawgoal(o,0) :- line(x)row(M,P) :- true(cell(M,1,P)) & true(cell(M,2,P)) & true(cell(M,3,P))column(N,P) :- true(cell(1,N,P)) & true(cell(2,N,P)) & true(cell(3,N,P))diagonal(P) :- true(cell(1,1,P)) & true(cell(2,2,P)) & true(cell(3,3,P))diagonal(P) :- true(cell(1,3,P)) & true(cell(2,2,P)) & true(cell(3,1,P))line(P) :- row(M,P)line(P) :- column(N,P)line(P) :- diagonal(P)open :- true(cell(M,N,b))draw :- ~line(x) & ~line(o)18/54No Built-in AssumptionsWhat we see:next(cell(M,N,x)) :- does(white,mark(M,N)) & true(cell(M,N,b))What the player sees:next(welcoul(M,N,himenoing)) :- does(himenoing,dukepse(M,N)) & true(welcoul(M,N,lorenchise))1019/54Game ManagerGame ManagerGameDescriptionsMatchRecordsTemporaryState DataPlayerGraphics forSpectators. . .. . .Tcp/ip20/54Start Manager sends Start message to players Start(id,role,description,startclock,playclock)Play Manager sends Play messages to players Play(id, actions) Receives plays in responseStop Manager sends Stop message to players Stop(id, actions)Game Playing Protocol1121/54General Game Playing22/54LogicPossible to use logical reasoning for everything Computing legality of moves Computing consequences of actions Computing goal achievement Computing terminationEasy to convert from logic to other representations Simplicity of logical formulation Simple, widely published algorithms 3-4 orders or magnitude speedup no asymptotic change1223/54State Representationcell(1,1,x)cell(1,2,b)cell(1,3,b)cell(2,1,b)cell(2,2,o)cell(2,3,b)cell(3,1,b)cell(3,2,b)cell(3,3,x)control(black)XOX24/54Legality Computationlegal(W,mark(X,Y)) :- cell(1,1,x) true(cell(X,Y,b)) ∧ cell(1,2,b) true(control(W)) cell(1,3,b)cell(2,1,b)legal(white,noop) :- cell(2,2,o) true(cell(X,Y,b)) ∧ cell(2,3,b) true(control(black)) cell(3,1,b)cell(3,2,b)legal(black,noop) :- cell(3,3,x) true(cell(X,Y,b)) ∧ control(black) true(control(white))Conclusions: legal(white,noop) legal(black,mark(1,2)) … legal(black,mark(3,2))1325/54Update Computationcell(1,1,x) cell(1,1,x)cell(1,2,b) cell(1,2,b)cell(1,3,b) cell(1,3,o)cell(2,1,b) black cell(2,1,b)cell(2,2,o) cell(2,2,o)cell(2,3,b) mark(1,3) cell(2,3,b)cell(3,1,b) cell(3,1,b)cell(3,2,b) cell(3,2,b)cell(3,3,x) cell(3,3,x)control(black) control(white)next(cell(M,N,o)) :- does(black,mark(M,N)) & true(cell(M,N,b))26/54Game Tree ExpansionXO XO XOXO XO XOXXO XO XOXXO XO XOX1427/54Game Tree SearchXO XOXO XO XOXXO XO XOXXO XO XOXXO XO XOXO XO XXO XOXXO XOXXO XOXXO XOX28/54Resource LimitationsLarge state spaces ~5000 states in Tic-Tac-Toe ~1044 states in ChessLimited Resources Memory Time (start clock, move clock)1529/54Incremental SearchIncremental Search Expand Game Graph incrementally As much as time allows Minimax/etc. evaluation on non-terminal states using an evaluation function of some sortBut how do we evaluate non-terminal states?In traditional game playing, the rules are known inadvance, and the programmer can invent anevaluation function. Not possible with GGP.30/54Non-Guaranteed Evaluation FunctionsIdeas Goal proximity (everyone) Maximize mobility (Barney Pell) Minimize opponent’s mobility (Jim Clune) Depth Charge (random probe) <insert your good idea here>1631/54AAAI-06 Final - Cylinder Checkers32/54Metagaming1733/54Automatic ProgrammingProblem Specification in the form of game rules Output is a program to play the game effectivelyFeatures: Side Effects Uncertainty (other players’ actions) Resource Bounds (playclock)Ideas: Compilation Guaranteed Evaluation Functions Reformulation34/54Guaranteed Evaluation FunctionsIdeas* Novelty with reversibility* Goal-monotonic observables* Bad states, useless moves <insert your good idea here>1835/54Hodgepodge = Chess + Othello Branching factor: a Branching factor: bAnalysis of joint game: Branching factor as given to players: a*b Fringe of tree at depth n as given: (a*b)n Fringe of tree at depth n factored: an+bnHodgepodge36/54Double Tic-Tac-ToeXOXOOXXO
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