Hexline is played on a triangular grid with three triangles to a side, but with only the vertices shown, not the lines. The rules say that each player gets 20 small sticks (e.g. matchsticks) to use, in different colors, but lines may simply be drawn in. A move is placing or drawing a line between two adjacent dots (vertices).
In each round one player attempts to make as long a continuous line as possible and the other player attempts to stop them. The linemaker plays first and afterwards must always play at one end of their line, unless a loop is formed with no ends in which case it may branch anywhere. The linemaker may never have more than two ends.
The other player may play on any open line segment.
When the linemaker can no longer play they score the number of lines they used and players swap roles.