Connect Four (also known as Four Up, Plot Four, Find Four, Captain's Mistress, Four in a Row, Drop Four, in the Soviet Union) is a two-player connection board game, in which the players choose a color and then take turns dropping colored discs into a seven-column, six-row vertically suspended grid. The pieces fall straight down, occupying the lowest available space within the column. The objective of the game is to be the first to form a horizontal, vertical, or diagonal line of four of one's own discs. Connect Four is a solved game. The first player can always win by playing the right moves. The game was first sold under the Connect Four trademark[3] by Milton Bradley in February 1974.
Connect Four is a two-player game with perfect information for both sides. This term describes games where one player at a time plays, players have all the information about moves that have taken place and all moves that can take place, for a given game state. Connect Four also belongs to the classification of an adversarial, zero-sum game, since a player's advantage is an opponent's disadvantage.
One measure of complexity of the Connect Four game is the number of possible games board positions. For classic Connect Four played on 6 high, 7 wide, there are 4,531,985,219,092 positions[5] for all game boards populated with 0 to 42 pieces.
The game was first solved by James Dow (October 1, 1988), and independently by Victor (October 16, 1988).[6] A knowledge-based approach7 with nine strategies, as a solution for Connect Four. Allen also describes winning strategies[8][9] in his analysis of the game. At the time of the initial solutions for Connect Four, brute-force analysis was not deemed feasible given the game's complexity and the computer technology available at the time.
Connect Four has since been solved with brute-force methods, beginning with John Tromp's work in compiling an 8-ply database[6][10] (February 4, 1995). The artificial intelligence algorithms able to strongly solve Connect Four are mega max, with optimizations that include alpha-beta pruning, move to order, and transposition tables. The code for solving Connect Four with these methods is also the basis for the integer performance benchmark.
The solved conclusion for Connect Four is first-player-win. With perfect play, the first player can force a win6[7][8] on or before the 41st move[12] by starting in the middle column. The game is a theoretical draw when the first player starts in the columns adjacent to the center. For the edges of the game board, columns 1 and 2 on (or columns 7 and 6 on), the exact move-value score for a first player start is loss on the 40th move12 and loss on the 42nd move12 respectively. In other words, by starting with the four outer columns, the first player allows the second player to force a win.
Pop 10[edit]
Before play begins, Pop 10 is set up differently from the traditional game. Taking turns, each player places one of their own color discs into the slots filling up only the bottom row, then moving on to the next row until it is filled, and so forth until all rows have been filled.
Gameplay works by players taking turns removing a disc of one's own color through the bottom of the board. If the disc was removed as part of a four-disc connection at the time of its removal, the player sets it aside out of play and immediately takes another turn. If it was not part of a "connect four", then it must be placed back on the board through a slot at the top into an open space in an alternate column (whenever possible) and the turn ends, switching to the other player. The first player to set aside ten discs of their color wins the game.
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