This submission was produced by Jennifer L. A. Hood (jenniferlhood@cmail.carleton.ca) and Pat Morin (morin@scs.carleton.ca) of the School of Computer Science at Carleton University (Canada).
The drawing (attached) was created by using LaTeX/Tikz generated by a python program.
Nodes (boards) are layered into 10 levels depending on the number of plays that have been made. The game play is modelled from the top of the graph to the bottom, starting from the node with 0 plays.
Nodes of the graph are organized into three categories, displayed as columns, depending on the outcome of the game if both players play optimal strategies for the remainder of the game. Nodes in the left (red) column, are boards which lead to games where O will win; in the middle (green) column the players will draw; in the right (blue) column, X will win.
Edges are classified into two types:
Type (1) Edges played by optimal strategies.
These edges always join two boards in the same column, and they are darker in colour than edges of type (2). They are drawn using two bends with a diagonal segment connecting two vertical segments.
These edges have a thickness that represents their multiplicity: The number of unique plays represented by the connected board with the higher number of plays (because symmetries are factored out, these multiplicities can be one, two, or four).
These edges also have a colour ranging from blue (X wins) through black (draw) to red (O wins). This colour represents the probability, assuming the next player plays randomly, that the next move will lead to a winning position for X, a draw, or a winning position for O. For example, a black edge on X's turn leads to a board that will result in a draw no matter what O's next move is.
This colouring is useful to a player who is not currently winning as it helps choose a move that makes it more likely for the other player to make a mistake during their next play.
Type (2) Edges that represent non-optimal strategies (mistakes in play).
These edges are drawn with a lighter colour using two bends with a horizontal segment connecting two vertical segments. The colour of these edges corresponds to the column they lead to.
One thing the type B edges illustrate is that the game seems to be more difficult for O, in the following sense: When O is winning, the overwhelming majority of mistakes that O can make lead to games in which O is losing. This is less true for X, for which many mistakes take X from winning to drawing.