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Connect-Four


Connect-four animation

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 n=0, 1, 2, ... have been played is 1, 7, 56, 252, 1260, 4620, 18480, 59815, 206780, ... (OEIS A090224).


See also

Checkers, Qubic, Tic-Tac-Toe

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References

Allen, J. D. "Expert Play in Connect-Four." http://www.pomakis.com/~pomakis/c4/expert_play.html.Allis, V. "A Knowledge-Based Approach of Connect-Four--The Game Is Solved: White Wins." Report IR-163 by the Faculty of Mathematics and Computer Science at the Vrije Universiteit Amsterdam, The Netherlands. 1988. Also Report CS 92-04 by the Faculty of General Sciences at the University of Limburg, Maastricht, The Netherlands, 1992. http://www.connectfour.net/Files/connect4.pdf.Allis, L. V.; van der Meulen, M.; and van den Herik, H. J. "Proof-Number Search." Artificial Intelligence 66, 91-124, 1994.Bertoletti, G. "Velena: A Shannon C-Type Program Which Plays Connect Four Perfectly." http://www.ce.unipr.it/~gbe/velena.html.Bremer, L. "Mustrum." http://www.lbremer.de/mustrum_e.html.Dockhorn, F. "Gladiator 3.06." http://www.connectfour.net/download.html.Fierz, M. "4 in a Row." http://www.fierz.ch/4inarow.htm.Halabi, D. "TitOT: Think it Over Twice." http://corporate.skynet.be/bats/TitOT/.Johnson, M. "Connect Four." http://ourworld.compuserve.com/homepages/mikejohnson/Connect4.htm.Nahay, P. "Mega Tic-Tac-Toe." http://pnahay.home.sprynet.com/games/MegaTTT.htm.Pomakis, K. "Connect 4." http://pomakis.com/~pomakis/c4/.Sloane, N. J. A. Sequence A090224 in "The On-Line Encyclopedia of Integer Sequences."Wiebus, S. "Connect4." http://www.bodo.com/Applets/Connect4/.

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Connect-Four

Cite this as:

Weisstein, Eric W. "Connect-Four." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Connect-Four.html

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