Look at a strategy map from above and you will often see hexagons instead of squares. Board war games used them for decades before computers did, and many video games, Dot Conquest among them, still do. There are good reasons.
The trouble with squares
On a grid of squares, a square has two kinds of neighbour. Four share an edge with it; four more touch only at a corner. That raises an awkward question every game must answer: is moving diagonally one step, or more?
- If diagonal costs one step, then moving diagonally covers more ground than moving straight, and a "range of 3" is a square, not a circle.
- If diagonal costs more, the arithmetic gets fiddly, and players have to count carefully.
Either way, distances look wrong. A unit three squares away diagonally is noticeably farther than one three squares away in a straight line.
What hexagons fix
A hexagon has six neighbours, and all six share an edge. Every neighbour is the same distance away. There are no diagonals, so there is no question to answer.
That gives hex grids three nice properties:
- Distance is just counting steps. Two tiles are as far apart as the number of steps between them, in any direction.
- Ranges look round. All the tiles within a certain number of steps form a rough circle (a big hexagon), not a square. A "reach of 4" looks like a reach.
- Movement looks natural. A path across a hex map bends smoothly instead of zigzagging along rows and columns.
How to count distance
The rule is simple: count the fewest steps from one tile to the next, crossing an edge each time. Any tile touching yours is 1 away. Any tile touching those (and not yours) is 2 away. And so on outward, in rings.
A quick way to do it by eye: walk toward the target in as straight a line as the hexagons allow, and count tiles. Because all six directions are equal, the straight walk is always the shortest.
Where it shows up in Dot Conquest
Distance on the hex grid is everywhere in the rules:
- Supply. A city supplies land out to a number of tiles that depends on its type:
Those numbers are tile steps. Count rings outward from the city to see its reach.
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Movement. Dots cross the map tile by tile, at a speed that depends on the ground under them. See the terrain guide.
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Walling in. A pocket is closed when a ring of your tiles surrounds it, edge to edge. On hexagons there are no corner gaps to slip through, so a ring is a ring. See flipping land by enclosure.
A note for the curious
Programmers often store hex maps with three coordinates that always add up to zero, one for each of the three directions a row of hexagons can run. With them, the distance between two tiles is just half the sum of how far apart they are on each coordinate. Dot Conquest stores its map that way, but you never need it to play: counting rings works just as well.
Where to go next
- How far your cities reach: supply lines and attrition.
- The ground itself: terrain guide.