Can You Win Connect Four Going Second? Second Player Strategy

Yes, you can win Connect Four going second, just not against a perfect opponent who starts in the middle column. The game is solved: the first player wins only by starting in the middle, a start in column 3 or 5 lets the second player hold a draw, and a start in any of the four outer columns loses. Against real opponents, answer the middle with the middle, build your threats on even rows (2, 4 and 6), and play the long game: in a 1,000-game match between two of our Medium computers, every second-player win came with the very last disc.

This guide is for the player who moves second. The perfect-play results come from the two people who solved the game in 1988, and every other number comes from seeded games between copies of the computer player behind Poozee's Four in a Row, with every board replayed by its engine. Red moves first in all the diagrams, rows are counted from the bottom and columns from the left. (Connect Four is a Hasbro trademark. Poozee's Four in a Row is our own version of the classic game, and we aren't affiliated with Hasbro.) For the basics of double threats and odd and even rows, start with how to win Connect Four.

What perfect play says about going second

James D. Allen and Victor Allis solved Connect Four independently in 1988 (John Tromp's page has the history). In his thesis, Allis showed that the first player can always win by starting in the middle column, and only with that first move (chapter 13), and he gave the second player a strategy that at least draws after any other start (appendix B). Allen's Complete Book of Connect 4, which he has put online for free, lists the perfect-play result of every three-disc opening in its Table I. Reading the second player's best answers out of that table gives:

Columns 5, 6 and 7 are mirror images of 3, 2 and 1, so flip the replies: after a start in column 6, the winning reply is column 5. Allis's drawing strategies use the same answers: column 2 after column 1, column 3 after column 2, and column 4 after column 3. For the same openings from the first player's side, see our guide to the best first move in Connect Four.

After a middle start: make them find the only move

Every reply to a middle start loses with perfect play, but not equally. Allen's Table I counts how many third moves keep the first player's win after each reply:

• Reply in column 4, on top: 1 winning third move (column 4 again).
• Reply in column 3 or 5: 2.
• Reply in column 2 or 6: 2.
• Reply in column 1 or 7: 5.

Allis says the same in section 13.2 of his thesis: after this opening, every third move except column 4 gives the second player at least a draw. If red does find it, stack again. Allen's Table II shows that after four discs in the middle column, red again has exactly one winning move, the fifth disc in column 4. A strong opponent may know all this, but a casual one has to find the only move twice in the first five discs.

How the second player does against each first move

To see what each first move means between imperfect players, we forced the first disc and let our computer players finish the game. Medium searches four discs ahead, never misses a one-move win or block, and breaks ties at random. Hard was held to eight discs of lookahead so every game replays exactly (in the game itself, Hard searches as deep as it can in 0.7 seconds). We played columns 1 to 4; 5 to 7 are their mirror images. The results are the second player's wins, draws and losses in 200 games between two Medium computers, and in 50 games with Hard playing second against Medium:

Against a middle start, even the stronger second player lost most games. Against starts in columns 1 to 3, Hard as the second player won 144 of 150 games. Two Medium computers only split the games after a start in column 1 or 2, though perfect play says the second player wins them: knowing the result isn't the same as finding the moves.

The best reply to the middle, measured

Here is the same test after a middle start, forcing the second player's reply as well. Medium, playing second, never answers in the middle by itself: in our 1,000-game Medium match it replied in columns 2, 3, 5 and 6 and won just 44 games. Forced to drop on top, it did far better. Below, "Hard second" is Hard replying against Medium (50 games) and "Hard first" is Medium replying against Hard (50 games):

The on-top reply was the best one in every match. It turned Medium from a 44-in-1,000 second player into a 166-in-200 one, and against Hard, where every other reply lost at least 43 of 50 games, it drew all 50. The first player still wins with perfect play, so don't expect it to beat a strong opponent by itself. It just makes their job as hard as it can be.

A seeded computer can repeat itself, so these matches are smaller than they look: the 200-game Medium matches in the two tables contain between 18 and 114 different games, and the 50-game matches with Hard between 1 and 37.

How second-player wins actually happen

In the 1,000-game Medium match from our rules guide, where Medium chose its own replies, the second player's wins were slow: all 44 of them came with the 42nd and last disc. A win on the last disc is always on row 6, an even row, because the last empty spot is the top of the last column. In all 44 games that last column was on the edge: column 1 in 28 games and column 7 in 16.

The game was decided much earlier than that. We worked back from the end of each game with the engine's exact search, which plays perfectly when it has unlimited time and is quick once about 24 or fewer spots are empty, to find the disc after which red could no longer avoid losing. In 29 of the 44 games it was the 21st disc of the game (red's 11th), which turned a drawn position into a lost one. In the other 15 it was the 23rd disc, which threw away a red win. Either way, yellow then needed 19 to 21 more discs to collect. (Medium's ties don't vary much: these are 40 different games, but they share only 4 different first 20 discs.)

Here is one of those mistakes.

Exact search says every red move except column 4 loses, even though red already has two threats, at column 1, row 4 and column 7, row 4. Both are on row 4, an even row. In these games the edge columns filled last, and in the last column to fill, the second player gets the even rows, so red's threats were never going to be played.

Zugzwang and follow-up: the second player's endgame

Zugzwang means having to move when every move hurts you. In Connect Four it decides close games because nobody can pass. Allis explains the second player's version in sections 4.1 and 4.2 of his thesis. When every column has an even number of empty spots and it's the first player's turn, the second player can answer each disc by dropping on top of it, in the same column. Allis calls this follow-up. The first player then gets only the odd rows and the second player only the even rows, whatever order the columns are filled in.

That makes even-row threats yours to keep, and the first player's even-row threats worthless: under follow-up you take every even spot, including the ones they were threatening. (Allis works through every pairing of odd and even threats in section 3.3.) Here is the same game 10 discs later:

Yellow wins this without calculating anything:

1. Whatever column red plays, yellow drops on top of it. Every column has an even number of empty spots, so the answer always fits.
2. Red only ever gets odd rows. Red's threats are on row 4, so yellow fills both of them.
3. Column 1 is last. Red avoids it as long as possible, but once columns 6 and 7 are full, red has to play there: rows 1 and 3 for red, rows 2 and 4 for yellow, then red is forced onto row 5 and yellow wins on row 6.

We checked every possible red continuation, and follow-up wins in all of them. In 21 of the 44 games, yellow could have switched to pure follow-up from the 30th disc and won without another decision, and in 33 of them by the 32nd.

There's a catch, which Allis also points out: you can't play follow-up from the first move. If you copy every move from the start, the first player gets the whole bottom row and wins on it. Follow-up is the finish, not the plan.

A plan for going second

Against a strong player who starts in the middle:

1. Reply on top, in column 4. If they play column 4 again, do it again.
2. Survive the middle game. Most games are lost to a missed block or a disc that sets up the spot above it. Run the three checks from how to win Connect Four before every move.
3. Build threats on rows 2, 4 and 6, and watch for the first player's odd-row threats, especially on row 3. Allis's section 3.3 shows that a first-player odd threat beats a second-player even threat in another column.
4. Count the empty spots. When every column has an even number left and your threats are on even rows, switch to follow-up and let the board fill.
5. Be patient. Your win will often be the 42nd disc.

Against a casual player, watch the first disc. If it isn't in the middle, you're the favorite: reply with the moves in the first table, take the center yourself, and play for double threats as you would going first. Even after a middle start, they have to keep finding single moves: after the on-top reply, our Medium computer playing first found the right third move in all 200 games and still lost 166 of them.

Pro tip: James D. Allen, one of the two people who first solved the game, wrote that in casual games against players of medium skill, he "usually wins almost effortlessly moving second." Against an expert who starts in the middle, the first player almost always wins, but going second against everyone else isn't a lost cause. It's a different, slower game.

On Poozee, you always play red and the computer moves first in every other game. So when you go second, the computer opens with yellow: swap the colors in the diagrams above. Hint shows the column the Hard computer would pick for you, and Medium is a good opponent for practicing the on-top reply and the follow-up finish.

Keep playing

• Play Four in a Row and go second against Medium or Hard
• How to win Connect Four: the middle column, double threats and odd and even rows
• How to play Connect Four: the rules, ties and who goes first
• The Connect Four 7 trap: when the famous shape wins, and how a threat under it stops it
• Dots and boxes strategy, another game where counting decides who has to make the bad move