Board Games guide
Four in a row strategy: how to win from the first disc
To win at four in a row, start in the centre column, build places where a disc would complete four, and arrange for two of those places to come up at once so that only one can be blocked. On the standard 7×6 board the first player can always win with perfect play by starting in the centre, a result proved by computer in 1988.
The rules in brief
Two players take turns to drop one disc into any column that is not full. The board has seven columns and six rows, and a disc always falls to the lowest free place in its column. The first player to get four discs in a straight line, across, up or diagonally, wins. If the board fills with no line of four, the game is a draw.
Everything in this guide follows from one fact: you cannot place a disc wherever you like. A place can only be filled once the place below it is filled.
The centre column
The middle column is worth more than any other. A line of four across the board is four columns wide, and on a board seven columns wide every such line has to include the middle one. A disc in the centre can also reach diagonals running both ways.
- Moving first: open in the centre column.
- Moving second: answer in the centre column, on top of the first disc.
- After that: prefer the three middle columns. Discs in the two outside columns take part in few lines.
In 1988 James Allen, and independently Victor Allis, showed by computer that the first player wins with perfect play when the first disc goes in the centre column. Nobody plays perfectly, so the game is still wide open between people, but the result tells you where to start.
Threats
A threat is an empty place where your disc would complete four in a line. Some threats can be played at once, because the place below is already filled. The other player has to block those straight away.
The more useful kind is a threat that cannot be played yet, because the place below it is still empty. It sits there for the rest of the game. Neither player wants to put a disc directly below it: if the other player does, you drop on top and win. Such a threat takes a whole column away from your opponent.
Worked example
You have three discs in a row on the third row, and the place at one end is empty with two empty places below it. That end is a threat on row three. The other player cannot block it yet. If they ever play the second row of that column, you play the third and win.
Odd and even rows
Number the rows from the bottom: 1 to 6. Rows 1, 3 and 5 are odd; rows 2, 4 and 6 are even.
Each column has six places, an even number. Suppose the game goes on until only one column is left to fill. The first player will have the move, so the first player takes row 1 of that column, the second player row 2, and so on. The first player ends up with the odd rows and the second player with the even rows.
- If you moved first, try to make your threats on odd rows, in practice rows 3 and 5.
- If you moved second, try to make your threats on even rows: 2, 4 and 6.
A threat on the right kind of row wins without any more effort. As the board fills up the other player runs out of safe moves and is forced to play the place below your threat. Chess players call that being in zugzwang: having to move when every move loses.
This is a rule of thumb, not a law. When both players have threats in different columns the count changes, but a beginner who remembers "first player odd, second player even" will win many endgames that look level.
Double threats and the 7 trap
The other player has one disc a turn, so two threats that can both be played at once win the game. There are two common shapes.
- Three in a row with both ends open. If both end places can be played now, one is blocked and you take the other. This is why three in a row on the bottom row, with space either side, is already lost for the defender.
- Two threats stacked in one column. If your threats are directly one above the other, the other player blocks the lower one and you win on the upper one.
The best known way to build stacked threats is the 7 trap. Your discs form the figure 7: three in a row across the top, and two more running diagonally down from one end of that row. The row of three needs the place beside it, and the diagonal of three needs the place diagonally above its top disc. Those two places are in the same column, one above the other.
Worked example
Counting columns from the left and rows from the bottom, you hold columns 2, 3 and 4 on row 3, plus column 3 on row 2 and column 2 on row 1. Your row needs column 5 on row 3. Your diagonal, rising from column 2 row 1 through column 3 row 2 and column 4 row 3, needs column 5 on row 4. When column 5 fills to row 2, you will win on row 3 or, if that is blocked, on row 4.
The 7 can face either way. Watch for the other player building one and put a disc into its bar or its diagonal before it is complete.
Good habits and common mistakes
- Before every move, look at the place above it. Ask what the other player can do with that place once your disc is under it.
- Count the other player's threes. Three discs with an empty fourth place is a threat even when the three are not next to each other.
- Block low, build high. Stop threats that can be played now; make your own where they cannot be blocked yet.
- Do not fill a column for no reason. Each column you close is one fewer safe move later, and safe moves decide the endgame.
- Think in pairs of places. Two threats one above the other, or one each side of a row, are what win.
- Playing directly below the other player's threat and handing them the win.
- Blocking a harmless three on the edge while a double threat grows in the middle.
- Opening in an outside column.
- Looking only at rows and columns and missing a diagonal.
Other boards
| Variation | What changes | On Yuzool |
|---|---|---|
| 7 columns by 6 rows | The standard board, 42 places. | The standard game |
| 8×7 and 9×7 boards | More room, longer games, and a centre that matters a little less. | Pro rule options |
| Five in a row | You need five in a line, played on the 9×7 board. | A Pro rule option |
The odd and even advice above depends on columns having an even number of places. On a board seven rows high the count works differently.
Questions
Does the first player always win at four in a row?
With perfect play on the 7×6 board, yes, by starting in the centre column. That was proved by computer in 1988 by James Allen and, independently, Victor Allis. Between people the game is far from decided.
What is the best first move?
The centre column. Starting in either outside column gives the second player the better game.
What is the 7 trap?
Five discs in the shape of a 7: three in a row with two more running diagonally down from one end. It creates two winning places one above the other in the next column, and only one can be blocked.
Can four in a row end in a draw?
Yes. If all 42 places are filled and neither player has four in a line, the game is drawn.