Note that the trailing \ solutions are not recommended by PEP 8. One reason is that if space is added by mistake after a \ it might not show in your editor, and the code becomes syntactically incorrect.
The PEP changed at hg.python.org/peps/rev/7a48207aaab6 to explicitly discourage backslashes.
The preferred way of wrapping long lines is by using Python's implied
line continuation inside parentheses, brackets, and braces. Long lines
can be broken over multiple lines by wrapping expressions in
parentheses. These should be used in preference to using a backslash
for line continuation.
Another thing is that, here (for example) -
if self.board["TL"] == player.type and self.board["TM"] == player.type and self.board["TR"] == player.type or \
self.board["ML"] == player.type and self.board["MM"] == player.type and self.board["MR"] == player.type or \
self.board["BL"] == player.type and self.board["BM"] == player.type and self.board["BR"] == player.type or \
self.board["TL"] == player.type and self.board["ML"] == player.type and self.board["BL"] == player.type or \
self.board["TM"] == player.type and self.board["MM"] == player.type and self.board["BM"] == player.type or \
self.board["TR"] == player.type and self.board["MR"] == player.type and self.board["BR"] == player.type or \
self.board["TL"] == player.type and self.board["MM"] == player.type and self.board["BR"] == player.type or \
self.board["BL"] == player.type and self.board["MM"] == player.type and self.board["TR"] == player.type:
the lines are too long. According to PEP 8 -
Limit all lines to a maximum of 79 characters.
Therefore, these statements could simply be written as -
if (self.board["TL"] and self.board["TM"] and self.board["TR"] == player.type or
self.board["ML"] and self.board["MM"] and self.board["MR"] == player.type or
self.board["BL"] and self.board["BM"] and self.board["BR"] == player.type or
self.board["TL"] and self.board["ML"] and self.board["BL"] == player.type or
self.board["TM"] and self.board["MM"] and self.board["BM"] == player.type or
self.board["TR"] and self.board["MR"] and self.board["BR"] == player.type or
self.board["TL"] and self.board["MM"] and self.board["BR"] == player.type or
self.board["BL"] and self.board["MM"] and self.board["TR"] == player.type):
Overall, in terms of code readability and style, this is what you need to improve. You should make your code more PEP 8 compliant.