Tic Tac Toe Variations and Questions
Standard Tic-Tac-Toe:
Two players alternate placing Xs and Os in a 3x3 array. X goes first. Goal is to get
three in a row, across, down, or diagonally.
Questions: How many distinct (up to symmetry) terminal tic-tac-toe boards are
there? What is the optimal strategy for each player? (What moves are "mistakes" at
various stages of the game, moves that will allow your opponent to win if you play
perfectly after that?)
(m,n,k):
Same as tic-tac-toe, but playing on an m x n board, and trying to get k in a row.
It is not known for many of these whether the outcome under "best play" is a draw
or if there is a winning strategy.
Avoidance (Toe-Tac-Tic):
Same rules of play as standard tic-tac-toe, but the goal is to avoid having three in a
row. (It can be shown that a 3x3 game is a draw with best play.) Same questions as
for Standard
Drawbridge:
Same play as standard tic-tac-toe, but one player wins if the game ends in a draw,
and the other player wins if either player ends up with three in a row. This game
must end with one or the other player winning.
Questions: With optimal play, does the first player want to play for the draw or the
three-in-a-row? What is the optimal strategy? How many distinct terminal boards
are there for this game?
Achi:
Each player has 4 tokens and takes turns placing them on the tic-tac-toe board,
trying to get 3 of his/her tokens in a row. After all are placed, if neither player has
won, players take turns moving by sliding one of their tokens into the open space
from a position that adjoins the open space horizontally, vertically, or diagonally.
Questions: If nobody has won after the tokens have been placed, can each player
always slide a token until someone wins? Is it better to be the first player or the
second player, or does it not make a difference? Does one player have a winning
strategy?
Movables:
Each player has 3 tokens and takes turns placing them on the tic-tac-toe board,
trying to get 3 in a row. After all are placed, if neither player has won, each player
can move his or her token to any open space on his/her turn.
Questions: Is there a winning strategy for this game? Is it possible that the game
continues indefinitely, or must someone eventually win?
Multiplayer (3-6 people):
Play on a 10X10 board and win with four in a row.
Numbers (Magic Square):
Two players take turns selecting a number between 1 and 9; each number can only
be used once. The first player who has chosen three numbers who sum to 15 wins.
Questions: Is there a winning strategy? Why is this included in a list of tic-tac-toe
games?
Numbers (Odds & Evens):
Players take turns placing the numbers 1 through 9 on a tic-tac-toe grid. The first
player places odd numbers and the second player places even numbers. The player
who completes a row, column, or diagonal with a number that brings the sum to 15
wins.
Ultimate Tic-Tac-Toe:
In each cell of a standard tic-tac-toe board, draw another smaller tic-tac-toe board.
On each turn, place an X or O in one of the cells of a small tic-tac-toe board. Whoever
wins the small board places their symbol (X or O) in the big cell in which the small
board lies. The goal is to get three in a row on the big board.
Here is the catch: whatever square of the small board your opponent played in on
his last turn, that is the square of the big board in which you must play on your turn.
(For example, if your opponent places his X in the upper left-hand corner of a small
board, then you must take your next turn on the small board that is in the upper lefthand corner of the big board.) And then, whichever square on that small board you
play in will determine where your opponent must play next. But: if the board in the
position where your opponent's move would send you has already been completed
(win or draw), you can choose to play in any board you want.
What if one of the small boards ends up in a draw?
Standard version: it counts as neither an X nor an O.
Variation: it counts as both an X and an O.
(Players should agree before the start of play which version they want to play,
standard or variation.)