Hexagonal Grids (2013)
FWIW, I strongly prefer square grids for tabletop games.<p>Hexagonal grids give you precise measurements in exactly 6 directions.<p>If you approximate sqrt(2) as 1.5 then square grids give you pretty darn accurate measurements in 8 directions, including 2 pairs of directions that are orthogonal, which is good for rectangular features like buildings.<p>Furthermore the distance between two points can be quickly calculated with (long-side + 1&#x2F;2 short-side), which is doable in your head, unlike the distance calculation on a hex grid.<p>Lastly, if you divide the circle into a large number of slices and calculate the average error for path distance using hex or squares, among those slices, the average error (compared to pythogorean) is smaller with squares (obviously for small multiples of 6 and small multiples of 8 respectively, one or the other will be preferred).