Openings and tempo

Start with neighbouring values, 4 and 5, in the centre. Leave space on both sides to grow into 3–4–5–6 or 4–5–6–7. Learn a flexible position rather than memorising a promised win. These names are teaching aids in this book, not an official classification or proven optimal openings.

Rail variation: place a 4 on D5 and a 5 on E5, side by side. Think of a straight track extending through C5 and F5. Watch how it forms and how it breaks on this board.

Compass variation: place a 4 on D4 and a 5 on E5. The pair now points diagonally towards C3 and F6. It is the same opening family in another direction, not a different rule. Follow the steps to see it.

Countercentre response: remove one tile from the opposing pair and plant your own nearby. Against 4D5 and 5E5, try xE5, 5D4 and 4E5. You interrupt their growth while starting yours. Do not always remove the 5: count which tile supports more possible lines and first check whether a complete line needs breaking.

After the opening, read the board again. The centre usually offers more directions, but an occupied cell blocks a route. An isolated tile can be removed; a pair leaves a seed after removal, without guaranteeing you can preserve it. The opening prepares decisions rather than replacing them.

A line the opponent can break is not necessarily a wasted move. If you finish with exactly one valid line, their next removal must come from its four cells for play to continue. During that removal, your tiles outside the line are protected by the defensive obligation. We call this temporary restriction gaining a tempo.

The protection has a precise scope: it concerns that particular removal. After breaking the line, the opponent still places two tiles and may occupy useful cells for your next project. You have not gained an entire free turn or a guaranteed win. You have restricted one opposing decision and must check whether that restriction yields a usable advantage.

Suppose your first placement completes a blue line on A1–D1 and your second improves a blue project near the bottom. If the upper line is the only completed one, Red must remove from A1–D1. Removing the newly placed lower tile in that defense would lose by leaving the upper line alive.

Before choosing the lower tile, consider which cells Red could occupy with their two placements. If your whole project depends on one empty cell, a forced removal above does not prevent the opponent from blocking that destination below. The combination looks more promising with several compatible continuations, but judging that promise remains heuristic.

With a seven-tile straight, the global intersection contains one cell. The opponent must remove that middle tile to avoid losing, provided those are all your lines. You then know which cell opens and which number returns to your reserve. This information can simplify calculation of your next turn, although the opponent retains placement choices.

Do not confuse a predictable removal with a completely predictable reply. After removing, the opponent chooses two numbers and two positions and may create a defensive obligation of their own. On your next turn, you might have to address their line before repairing yours. Advanced calculation must include those two opposing placements for the supposed tempo to mean anything.

Replacing the tile just removed can restore a line and force another defense, but it may also consume a placement every turn without approaching a resilient structure. Ask what the second tile achieves in each repetition. If it improves no alternative, the sequence may merely move material between board and reserve while the opponent develops options.

The game needs no repetition rule: after the opening, every completed placement turn increases total board occupancy by one. A local shape can reappear, but the global state keeps changing and reserves shrink. A chain of repairs is therefore neither an infinite loop nor proof that you can secure a draw.

When there is no immediate defensive obligation, compare a placement creating a provisional line with one preparing more options without creating it. The former restricts the opponent’s removal; the latter may offer better geometry or preserve a scarce number. Assess what each achieves: threatening out of habit can distract you from a more useful continuation.

When reviewing a game, write down which removal you forced and what concrete progress it enabled. If you cannot identify a continuation, gained space or preserved structure, avoid assigning automatic value to pressure. The exact principle is the obligation to break lines; converting it into a lasting advantage requires calculation and positional evaluation.