Tic-tac-toe
Tic-tac-toe, also called noughts and crosses or Xs and Os is a game for two people that only requires pencil and paper, although you can also use a board with tokens.
The board (which can be a drawing on a paper or other place) consists of a square that is crossed by two vertical and two horizontal lines, so in total there are three small squares left in the top line, another 3 in the center line and 3 more in the bottom line.
Each player takes turns drawing a cross or a circle in a square (or placing tokens of different shapes or colors) The winner is the one who manages to place three equal pieces in a row, either vertically, horizontally or diagonally.
Tic-tac-toe Media
A typical game of tic tac toe
Game of Tic-tac-toe, won by X
Incidence structure for tic-tac-toe
Optimal strategy for player X if starting in upper left. In each grid, the shaded red X denotes the optimal move, and the location of O's next move gives the next subgrid to examine. Note that only two sequences of moves by O (both starting with the center, top-right, left-mid) lead to a draw, with the remaining sequences leading to wins from X.
Optimal strategy for player O. Player O can only force a win or draw by playing in the center first.
Example of a Magic Square
