The issue with 1-2-2-, 2-2-2-, diagonals +1 (which is different to 2-2-2 for difficult terrain), and 2-1-1- is that they draw attention to the distinction between an orthogonal and a diagonal. 1-2-1-2- does this too, but it's doing so because it's trying to closely approximate euclidean distance within the quantisation of the grid. The others are not trying to optimise this approximation, yet still force the player to classify between different modes of "adjacent".
1-1-1- is trivial to explain: you can move to any adjacent square. Yes, this does create some oddities if you use euclidean distance to estimate distances. Instead, estimate using the gridlines.
I'd been over-thinking the distance metric stuff until I was playing on a D&D minis map with my 3 year old daughter. We were racing counters around the map. Since she was only 3, I naturally used a 1-1-1- counting metric. Half way through I suddenly realised: "this is easy, natural, and doesn't feel awkward at all".
1-1-1- is trivial to explain: you can move to any adjacent square. Yes, this does create some oddities if you use euclidean distance to estimate distances. Instead, estimate using the gridlines.
I'd been over-thinking the distance metric stuff until I was playing on a D&D minis map with my 3 year old daughter. We were racing counters around the map. Since she was only 3, I naturally used a 1-1-1- counting metric. Half way through I suddenly realised: "this is easy, natural, and doesn't feel awkward at all".