Numbridge — Strategy

Bridges and connection

Sudoku gives you the chance to take a cell. Where to spend it is decided by the geometry of the rhombus. In Bridge and Blitz the winner is not the one with more cells, but the one whose cells line up in a chain from side to side.

Count the remaining path, not the cells

Look at the position like this: how many cells do I still need to connect my sides, and how many does my opponent need? A cell of yours on the path shortens it by one; a cell of theirs forces a detour and lengthens it.

From that follows the main rule of the game: by hindering your opponent you build yourself. There is no positional draw on the rhombus — fill the field completely and somebody is bound to be connected. So a cell that cuts their chain stands on your own road too. A move that only builds and cuts nothing is almost always worse than a move that does both.

The bridge link

Two of your cells that do not touch each other but share two empty neighbours are connected safely: the opponent takes one of the two, you take the other. Such a pair is called a bridge link.

row 3    .   A   .   .
row 4      x   y   .   .
row 5        B   .   .   .

Here A is r3c2, B is r5c1, and the shared neighbours are x = r4c1 and y = r4c2. The link advances blue two rows for a single cell taken, and no single move can break it. Red builds the same link sideways: from r3c2 to r2c4 through the shared neighbours r3c3 and r2c3 — two columns ahead.

Hence the practice: do not place stones edge to edge when you can place them a bridge apart. A solid chain spends twice as many turns on the same road.

But: complete a link in time. If the opponent takes x, take y on your very next turn, not later. Forget, and the connection is gone.

The middle is worth more than the edge

A cell in the middle of the rhombus belongs to more paths than a cell at the edge: it has six live neighbours, a cell on the edge four, and a corner cell of the rhombus only two or three, depending on the corner. That is why the first moves of a game go to the middle: from there you can build both ways, and the same cell is in your opponent's way.

The edge is not useless — you have to touch your own side in the end — but the touch is left for last, once the approaches are secured.

Geometry against deducibility

The cell you most want on your path may be the one you cannot solve: five candidates, and the digit you need is not in your hand. Do not force it. Take the cell next to it — on a rhombus with six neighbours a detour almost always exists, and it lengthens your path by one at worst.

cell on the shortest path, digit deduced   — the best move
cell on a detour, digit deduced            — a good move
cell on the path, digit guessed            — see "Risk and mistakes" (5)
cell off both paths                        — a wasted turn

What not to do

Do not finish your chain while your opponent is closer to the goal than you are. Count both paths every turn: if they are three cells from connecting and you are four, your next move has to be a cut, not a brick.

And remember that their chain is as resilient as yours, for the same reason: six neighbours give it several roads. Cut where there is only one road — usually a narrow spot near the edge, where neighbours are few. Striking at one shared neighbour of their bridge link is pointless: they simply take the other one and you have spent a turn. Such a strike pays only when you need that cell yourself.