Foreign Arrow

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Board Sizes

The traditional board size is 7x6, though because it is a straight-forward change to the rules, other sizes are not uncommon (as can be seen on the Play Online page). A number of board sizes have been solved. What does it mean for a game to be solved? Victor Allis provided these definitions in his Ph.D. thesis, Searching for Solutions in Games and Artificial Intelligence:

ultra-weakly solved

For the initial position(s), the game-theoretic value [which player will win if both play perfectly] has been determined.

weakly solved

For the initial position(s), a strategy has been determined to obtain at least the game-theoretic value of the game, for both players, under reasonable resources.

strongly solved

For all legal positions, a strategy has been determined to obtain the game-theoretic value of the position, for both players, under reasonable resources.

7x6 Four in a Row was weakly solved as a win for White by James D. Allen, who published his finding in the rec.games.programmer newsgroup on October 1, 1988. Allen is sometimes credited as finding the solution in 1989, perhaps because in that year he published his result as "A Note on the Computer Solution of Connect-Four" in Heuristic Programming in Artificial Intelligence: The First Computer Olympiad (ISBN 0-7458-0778-X).

On October 16, 1988, Victor Allis added another post to the rec.games.programmer newgroup, annoucing his independent (also weak) solution of Four in a Row (agreeing with Allen's result) which is described in more detail in his Master's thesis, A Knowledge-based Approach of Connect-Four. Allis also declared that the second player, with perfect play, could at least draw on a 7x4 board, as well as on any board of even height with a width less than 7.

More recently, John Tromp claims to have strongly solved a number of boards, as described on his page. His work completes the Values for Boards table above.