Connect Four

How to win at Connect Four

Connect Four is a solved game, and the solution is blunt: the first player can force a win every time, but only by starting in the centre column. That single fact should shape your whole approach. The centre cell belongs to more potential four-in-a-rows than any other square, feeding horizontal, vertical and both diagonal lines, and whoever holds the middle controls the geometry of every threat that follows. From there the game becomes a race to build a position with two winning squares at once, because a single threat always gets blocked and a proper double never does. Play a few games with that in mind and Connect Four stops feeling like tic-tac-toe with gravity and starts feeling like what it is, a fight over a small number of key squares.

An opening recipe

First disc in the centre, and for the next few turns prefer the three middle columns unless a threat forces you wider. If the computer takes the centre against you, claim a column beside it and aim your first diagonal through the middle of the board rather than conceding it. The difficulty settings change what you can get away with. Easy falls for any straightforward floor trap. Medium punishes the vertical habit and not much else. Hard blocks the obvious and plays the long endgame properly, so against it you will need threats on the right rows, not merely more of them.

Double threats, worked out

The cleanest double threat is the open three on the floor. Say your discs sit in the third, fourth and fifth columns of the bottom row with both ends empty: the computer can plug one end, and your next disc completes four on the other. That shape wins on the spot, which is why an opponent's two-on-the-floor with space on both sides already deserves attention. The related seven trap stacks a disc on the middle of three floor discs so threats sprout horizontally and diagonally at once. Blocks can attack too: given two ways to stop a line, take the one that extends your own, because a disc that defends and builds is the quiet move that wins ten turns later.

The odd-even game underneath

Discs fall, so you never choose a square, only a column, and every square waits for the ones below it to fill. Gravity produces the deepest idea in the game: threat parity. Count rows from the floor. As the first player you want a lasting threat on an odd row; the second player wants one on an even row. The reason shows up in the endgame, when neither side has a safe move left and the remaining columns fill in forced pairs: that filling tends to deliver odd squares to the player who moved first and even squares to the other. Advanced play means steering the board so the computer is eventually forced to drop the disc directly beneath your winning square. On Hard, the Inkplay computer plays these zugzwang endings on purpose, so an extra threat on the wrong parity achieves precisely nothing.

Mistakes that lose games

• Stacking verticals: a tower is the easiest threat to spot and costs one disc to stop.
• Missing the anti-diagonal; scan both diagonal directions every turn, yours and the computer's.
• Dropping a disc that hands the computer the square directly above it. Look up before you let go.
• Chasing your own line while a three-in-a-row sits unblocked; check the computer's threats first.
• Ceding the centre column early, since it sits in the most winning lines on the board.

From toy shelf to theorem

Milton Bradley published Connect Four in 1974, from a design credited to Howard Wexler and Ned Strongin, though vertical four-in-a-row games circulated earlier; one wooden version is nicknamed the Captain's Mistress after a tale, almost certainly invented, that Captain Cook kept one in his cabin. The game's second life belongs to computer science. In the autumn of 1988 it was solved twice within weeks, independently, by James Dow Allen and by Victor Allis, whose program VICTOR reasoned with named strategic rules such as Claimeven and Baseinverse rather than raw search. Perfect play from the centre wins for the first player; the columns beside the centre only draw; the four outer columns lose outright. John Tromp later counted the legal positions of the standard 7x6 board, all 4,531,985,219,092 of them, which is why those 1988 proofs still look impressive.