Connect-Four is a tic-tac-toe-like two-player game in which players alternately place pieces on a vertical board 7 columns across and
6 rows high. Each player uses pieces of a particular color (commonly black and red,
or sometimes yellow and red), and the object is to be the first to obtain four pieces
in a horizontal, vertical, or diagonal line. Because the board is vertical, pieces
inserted in a given column always drop to the lowest unoccupied row of that column.
As soon as a column contains 6 pieces, it is full and no other piece can be placed
in the column.
Both players begin with 21 identical pieces, and the first player to achieve a line of four connected pieces wins the game. If all 42 men are played and no player has places four pieces in a row, the game is drawn.
The game has been completely analyzed, so it is known that if both players play with optimal strategies, the first player can always win (Allis 1988). The numbers of
possible positions after ,
1, 2, ... have been played is 1, 7, 56, 252, 1260, 4620, 18480, 59815, 206780, ...
(OEIS A090224).
,
1, 2, ... have been played is 1, 7, 56, 252, 1260, 4620, 18480, 59815, 206780, ...
(OEIS A090224).
