Editing Tic-tac-toe (section)

== Combinatorics ==
When considering only the state of the board, and after taking into account board symmetries (i.e. rotations and reflections), there are only 138 terminal board positions. A [[combinatorics]] study of the game shows that when "X" makes the first move every time, the game outcomes are as follows:<ref name=":0">{{cite book|last=Bolon|first=Thomas|title=How to never lose at Tic-Tac-Toe|url=https://books.google.com/books?id=oG-qvnEj_QkC&pg=PP7|year=2013|publisher=BookCountry|isbn=978-1-4630-0192-6|page=7}}</ref>
*91 distinct positions are won by (X)
*44 distinct positions are won by (O)
*3 distinct positions are drawn (often called a "cat's game"<ref>{{cite web|url=https://www.timesdaily.com/opinion/columnists/bernie_delinski/searching-for-the-cat-in-tic-tac-toe/article_b3b90782-8328-11e3-9f53-001a4bcf6878.html|title=Searching for the cat in tic tac toe|author=Delinski, Bernie|date=January 21, 2014|publisher=[[Times Daily]]|website=timesdaily.com}}</ref>)