Connect Four

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A Connect Four game in progress. Green to move; yellow wins.

Connect Four (also known as Plot Four) is a two-player board game in which the players take turns in dropping discs into a vertical grid with the objective of getting four of one's own discs in a line.

The game was published by Milton Bradley in 1974; a non-proprietary version is known as "The Captain's Mistress".

Contents

1 Rules
2 Strategy and tactics
3 Perfect play
4 Trivia
5 References
6 External links

Rules

The game is played on a board with 7 columns and 6 rows, which is placed in a vertical position. The players have 21 discs each, distinguished by color. The players take turns in dropping discs in one of the non-full columns. The disc then occupies the lowest unoccupied square on that column. A player wins by placing four of their own discs consecutively in a line (row, column or diagonal), which ends the game. The game ends in a draw if the board is filled completely without any player winning.

Strategy and tactics

Long term strategy. White (playing the yellow pieces) has an odd threat in the third column, but it is masked by black's lower even threat in the same column and is therefore worthless. White will however eventually be able to create an odd threat, in row 5 column 6 or 7. This threat will decide the game and white will win. White's best move is to play column 1, thereby ending all counterplay of Black in column 2. (Screenshot of the Mustrum program.)

Beginners will often overlook a simple threat to connect four discs; it is therefore important to always check all vertical, horizontal and diagonal lines before making a move. In more advanced play, one aims at forcing a win by making two threats simultaneously; conversely, one should prevent the opponent from doing so. For instance, in the top right figure, it is green's turn. Yellow will win on their next turn irrespective of green's move because of the threat of extending the diagonal of three consecutive yellow discs to four by dropping a disc either on the third or on the last column, only one of which can be blocked by green.

As a general rule of thumb, discs played in the center columns are more valuable than border column discs, because they participate in more potential four-disc lines (and accordingly limit the opponent's opportunities).

Among good players, the short term goal is to connect three discs, thereby preventing the opponent from playing in a certain column and creating a "threat" in that column. A player who manages to create two threats immediately on top of each other wins directly.

Towards the end, the game then often turns into a complex counting match: both players try to win by forcing the other to play a certain column. In these situations, it is useful to realize that, if it's your move, then after filling an even number of places, it's still your move. Every column has an even number of places.

Beyond this, it turns out that the strategies for the first player (often called "white") and second player ("black") differ markedly. Every three aligned discs of one color create a threat, a place which when filled with the right color would yield four-in-a-row. A threat is called even or odd depending on whether it occurs in an even- or odd-numbered row (with the bottom row being numbered 1). In order for white, the first player, to win, he needs more odd threats than his opponent; the even holes don't matter. In order for black, the second player, to win, she needs at least two more odd threats than her opponent, or the same number of odd threats and at least one even threat. (These rules are somewhat simplified: it gets more complicated if several threats occur in the same column; most of the time, threats occurring above other threats are useless.)

Perfect play

Connect Four in a beer bar in Pattaya, Thailand

Connect Four has been solved independently by Victor Allis and James D. Allen. With perfect play, the first player can force a win by starting in the middle column. Starting in the two adjacent columns allows the second player to reach a draw; starting with the border columns even allows the second player to force a win.

Trivia

Connect Four is a popular game among the prostitutes and customers in the beer bars of Thailand.[Phuket Tourist Information], accessed 27 June 2006; [Koh Samui bar girls], accessed 27 June 2006; [Patong Nightlife Guide], accessed 27 June 2006; [Beer Gardens and Bangala Road Reviews], accessed 27 June 2006

References

External links

[Expert Play in Connect-Four], by James D. Allen
[Connect Four] - Connect Four resources including a downloadable strong Connect Four Java applet with source code, JavaScript Connect Four programs, strategy, references, and related links.
[John's Connect Four Playground] - A perfect playing applet, a solver benchmark with source, optimal board representation, and perfect play results for various board sizes. By John Tromp.
[Victor Allis's Master's Thesis containing the solution of the game]
[Connect Four source code]
[Mustrum], a free Connect Four program for Windows

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