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A few additional calculations...
A few additional calculations...
In[]:=
TreeQ["GameGraph"]
Out[]=
False
TimeConstrainedgameTree=["GameGraph"],60
Out[]=
$Aborted
In[]:=
PathCountTTT=AssociationResourceFunction["DirectedAcyclicEvaluate"]["GameGraph"],{_List:>1}["VertexWeights"];
TotalPathCountTTT[#]&/@JoinFlattenValues["FirstWinStates"],1,["DrawStates"][9]
In[]:=
Total[Values[PathCountTTT]]
Out[]=
549946
In[]:=
gtt1=Graph[ResourceFunction["ToDirectedAcyclicGraph"][NearestNeighborGraph[Select[Tuples[{-1,0,1},4],0<=Total[#]<2&]],{0,0,0,0}],VertexCoordinatesAutomatic,GraphLayout"LayeredDigraphEmbedding"]
In[]:=
gtt2=Graph[gtt1,{{0,0,0,0}}],GraphLayout"LayeredDigraphEmbedding",AspectRatio12
Out[]=
In[]:=
PathCountTT=Association[ResourceFunction["DirectedAcyclicEvaluate"][gtt1,{_List:>1}]["VertexWeights"]];
In[]:=
Total[PathCountTT[#]&/@Select[Keys[PathCountTT],Count[#,0]==0&]]CountsBy[VertexList[gtt2],VertexOutDegree[gtt2,#]&][0]SameQ[%,%%]
Out[]=
24
Out[]=
24
Out[]=
True
Out[]=
24