Ultimate Tic-Tac-Toe is an extended version of the traditional game of Tic-Tac-Toe; it involves two players and a large board split into nine small games. The object is to win three small games of Tic-Tac-Toe in a row, column, or diagonal to win the large game. A small game that results in a tie does not count as a win for either opponent in the large game. Each player's move is based on the opponent's previous move. If your opponent played in the upper-right in a small game, you must play in the upper-right game, and so on, even if that game has already been won. If you are sent to play in a small game that is full, you can play anywhere.
Special thanks to the University of Illinois NetMath Program and the mathematics department at William Fremd High School.