wins={{1,2,3},{4,5,6},{7,8,9},{1,4,7},{2,5,8},{3,6,9},{1,5,9},{3,5,7}};

isWinner[player_]:=MemberQ[Length[Intersection[player,#]]&/@wins,3]

judge[{p1_,p2_}]:=
  If[isWinner@p1,1,
    If[isWinner@p2,-1,
      If[Length@p1==5,0,Null]]]

operators[state_]:=Complement[Range@9,Flatten@state]

game[decision1_,decision2_]:=Module[{state={{},{}},result=Null},
    While[result===Null,
      If[Length@state[[1]]==Length@state[[2]],
        AppendTo[state[[1]],decision1[Sort/@state]],
        AppendTo[state[[2]],decision2[Sort/@state]]];
      result=judge@state];
    result]

randomDecision[state_]:=With[{x=operators@state},
    x[[Random[Integer,{1,Length@x}]]]]

nextStates[{p1_,p2_},ops_]:=
  Map[If[Length@p1==Length@p2,
      {Append[p1,#],p2}&,{p1,Append[p2,#]}&],ops]

Remove[minimaxDecision];
minimaxDecision[s_]:=
  Module[{ops=operators@s,vals,isMax=Length@s[[1]]==Length@s[[2]]},
    vals=minimaxValue[#,Not@isMax]&/@nextStates[s,ops];
    minimaxDecision[s]=ops[[Position[vals,If[isMax,Max,Min]@vals][[1,1]]]]]

minimaxValue[state_,isMax_]:=Module[{result=judge@state},
    If[result=!=Null,result,
      If[isMax,Max,Min][
        minimaxValue[#,Not@isMax]&/@nextStates[state,operators@state]]]]