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Why Gomoku Starts in the Centre: The Maths of Potential Fives and What Happens If You Start Elsewhere

Why almost every gomoku game starts on h8: counting potential fives through each point, what off-centre starts cost, and how to answer an unusual first move.

Why Gomoku Starts in the Centre: The Maths of Potential Fives and What Happens If You Start Elsewhere

Watch a hundred gomoku games and you will see the same first move in almost all of them: the centre point, h8. This is not tradition or superstition. It follows from a simple piece of counting that also teaches you something important about every move in the game.

Counting potential fives

A mark is useful only because it can become part of a five. So a natural way to measure a point's value on an empty board is to count how many different five-in-a-row windows pass through it.

Take the centre, h8. Along row 8, the five-mark windows that include h8 are:

  • d8–h8
  • e8–i8
  • f8–j8
  • g8–k8
  • h8–l8

That is five windows. The same count applies along the column and along both diagonals, because the board is big enough in every direction. Four directions times five windows gives twenty potential fives through the centre.

Now take a corner, a1. Along row 1 there is only one window containing a1: a1–e1. Along column a, one window: a1–a5. Along the diagonal a1–e5, one window. The anti-diagonal through a1 has no room at all. Total: three potential fives.

a1b2c3d4e5f6g7h8i9j10k11l12m13n14o15
The highlighted row shows the stretch d8–l8: every five-mark window through the centre h8 on row 8 fits inside it. A corner mark like a1 has only one window per direction.

Any point at least four steps from every edge has the full twenty. On a 15×15 board, that is a central block from e5 to k11. Points closer to the edge have fewer, and the corners have the fewest.

Why the count matters in play

Potential fives are the fuel of threats. A mark with twenty potential fives can later contribute to lines in all four directions; a mark with three can contribute to very little. When the board is empty, the difference between the centre and anywhere else is small in absolute terms — one mark is one mark — but it compounds. Every later mark placed near a central mark also enjoys lots of room, while marks near the edge keep running out of space.

This is why the first player starts in the centre, and why the second player answers close by: O wants to share the valuable central space rather than let X own it.

What happens with an off-centre start?

Nothing is forbidden. X can start anywhere. But the further from the centre, the more of the board's space X gives away.

A start one or two points from the centre, such as h9 or g7, is almost as good as h8 — both still have the full twenty potential fives. The difference is essentially stylistic.

A start near the edge is a real concession. The opponent simply plays toward the centre and enjoys more room for every future line. Beginners sometimes start in a corner to "surprise" the opponent; the surprise lasts one move.

Answering an unusual first move

If you are O and X starts off-centre:

  • Stay close to X's mark, as you would after a central start, but place your mark on the centre side of it. That way your mark has more room than X's, and X's natural growth direction runs into your mark.
  • Do not chase X toward the edge. Let X's shape grow toward the edge if it wants; your marks should stay where the space is.

If X starts right at the edge, O can even consider playing near the centre instead of adjacent. The extra space may be worth more than blocking a single edge mark. This is one of the few situations where staying close to the opponent is not the priority.

The centre in later moves

The counting idea does not stop after move one. At every stage, a point's value depends partly on how many potential fives through it are still alive — not blocked by the opponent. On a crowded board, a point with three alive directions is usually better than a point with one, even if both extend one of your lines.

Strong players do a rough version of this count almost without noticing. They feel that a move "has room" or "is cramped". You can train that feeling by occasionally counting deliberately: for a candidate move, check each direction and ask whether a five could still fit through it.

Centre and the blocked-ends rule

Under Vietnamese caro rules, space matters even more. A line needs not only room for five marks but at least one end not blocked by the opponent. Near the edge and near enemy marks, that condition fails more often. Central play is therefore even more important in blocked-ends games, and marks that drift toward the edges tend to become dead weight.

Space is shared, not owned

One subtle point: the centre's value is shared by both players. When X takes h8, O does not lose the centre — O simply plays next to it and gets almost as much room. What the first move really does is set the location of the fight. Both players will build in the central region; the question is who builds more efficiently there.

This is why the opening quickly becomes a contest of shape rather than a race to occupy points. After the first few moves, the board has a busy central cluster with lines radiating out in every direction. Every new mark either adds to one player's shape or cuts into the other's. The player whose marks do both — build and cut at the same time — usually comes out of the opening with the initiative.

The centre on bigger and unbounded boards

On a 19×19 board, or on an unbounded paper grid, the exact centre loses some of its special status because the edges are further away: a much larger block of points has the full twenty potential fives. Players on paper often start wherever is convenient on the page for exactly this reason. What does not change is the local version of the principle — keep your marks where there is room, and away from walls of enemy marks.

A quick exercise

Place a single mark on an empty board — say f10 — and count its potential fives in each direction. Then place an enemy mark two points away on the same row and count again. You will see how quickly one enemy mark shrinks your options. Doing this a few times makes the value of space concrete.

Then open the home board and play a few games where you consciously choose, among good candidate moves, the one with the most room. You will notice your attacks lasting longer before they run out of space.

Frequently asked questions

Is h8 always the best first move?

It is the most common and one of the strongest. Points one or two steps away are practically as good.

Why not start in a corner to surprise the opponent?

Because a corner mark has only three potential fives compared with twenty in the centre. The opponent simply takes the central space.

Where should O answer if X starts in the centre?

Adjacent to X's mark, either directly beside it or diagonally.

Does the centre matter later in the game?

Yes. At every stage, moves with more open space around them are generally stronger.

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