### Some suggestions about TTT processing...

Here are some useful lists for processing the TTT data...

The data below assume that a TTT board consists of a
string of 9 characters of 'x', 'o', and '_' . The board positions are
numbered from 0 to 8, in reading order.

For instance, the string "x_xoo_x_o" represents the
following board:

x | | x

---------

o | o |

---------

x | | o

Wins =
[[0,1,2],[3,4,5],[6,7,8],[0,3,6],[1,4,7],[2,5,8],[0,4,8],[2,4,6]]

# Transformations (rotations are counter-clockwise)

Rot90 = [6,3,0,7,4,1,8,5,2]

Rot180 = [8,7,6,5,4,3,2,1,0]

Rot270 = [2,5,8,1,4,7,0,3,6]

VertFlip= [2,1,0,5,4,3,8,7,6]

Transformations =
[[Rot90],[Rot180],[Rot270],[VertFlip],[Rot90,VertFlip],[Rot180,VertFlip],[Rot270,VertFlip]]

There are 7 unique symmetry transformations, other than
the identity, which consist of the 3 pure rotations, a flip, and combinations of
a rotation and a flip. Every other symmetry transformations can be reduced
to one of these.