The Problem With Hexagons

There's a huge upside the article misses. Having discrete movement allows the rules to be easily and exactly mentally simulated by humans. And that is key to a lot of tactical thought where you enumerate the possible responses and counter responses you and your opponent can have.

For the opposite side of the spectrum, see the excellent game Frozen Synapse which has non-discrete motion and so to allow this "simulate the future" aspect they actually allow you to plan future moves for both yourself and the opponent and test them out. Without that, exact movement loses a certain appeal that is shared by chess and go and hex-based games. There's still pleasure to be had in free-form movement and it should be better explored too. But don't forget why the old ways were great.

Great article about how to use hex grids in games: https://www.redblobgames.com/grids/hexagons/

For games that simulate a particular conflict, irregular polygons are a better option than hexes or squares. They still have the benefits of discrete movement, but allow for baking terrain related factors directly into the map, instead of having a separate table.

Great example of this is Napoleon's Triumph: http://www.simmonsgames.com/products/Austerlitz/Map.html

The article is interesting (and I want to look further into their game), but I think misses the part of the downside of removing hexes: more precision isn't always a good thing.

I play a lot of tabletop wargames, and the convention there is to measure with a ruler rather than hexes. The intent of the rules, generally, is to model real performance: say a turn represents 15 minutes, and an inch on the tabletop is 25 yards, then a napoleonic battalion (or whatever) should be able to move a distance that reflects how far they could actually march in 15 minutes.

The problem with that level of precision is that you have a degree of control that's totally inaccessible to a real commander. You wind up moving units in fiddly, ahistorical ways in order to take best advantage of the rules.

Most modern wargame rules try to overcome this in various ways, but hexes totally eliminate it: anything subtle enough to happen in an area smaller than a hex gets abstracted away. This isn't just a rules mechanism, it's a philosophical position on how much detail a commander has access to.

There are trade-offs involved with any paradigm, be it squares, hexes, even with continuous movement. The question is rather: what fits your design intent best? The player's experience is what counts in the end.

Squares and hexes are discretized environments. Again, this brings benefits and drawbacks. The advantage of hexes in this scenario lies in the fact that they often provide a richer medium for quantized movement in games. There is nothing inherently complicated about simulating movement and areas of effect in hex maps, neither for computers nor for humans.

If your game requires straight lines to be modeled perfectly, both hexes and squares provide two "clean" axes for that. Realism is a relative goal in a war game. It's all a set of models in the end.

Moving in straight lines using arbitrary angles is also not something that can realistically happen on battlefields.

There's this great thing called a flexible curve ruler. Assign each unit a movement speed in centimeters of map per turn, apply penalties and bonuses, and measure out the path that you want them to take.

They're expensive compared to cheap dice and cheap compared to expensive dice. With high-end board game prices the way they are now, bundling one in is reasonable. Then you can use any map of the right scale.

So with squares you have 4 sides, and you typically go in 8 directions, the problem being that the diagonals cover 1.41 and change times as much distance.

With hexes you have 6 sides and you typically go in 6 directions... huh? Why are we suddenly leaving out the "diagonals?" Well if you did take them we're off by 1.15 and change.

If left the diagonals out of square movement you'd have the same "drunken walk" problem as hexes. If you allowed diagonal movement on hex grids you'd have the same problem as diagonal movement on square grids.

Every hexes vs. squares debate leaves out that most of the pros and cons are totally imaginary and only exist because we artificially restrict our available options on the hex grid or, on the other side of the coin, artificially inflate our options on square grids.

I remember when I was a kid and tried to draw my own map. By hand, of course, as printers have barely been invented and having a PC in your house was a thing for few 100s families in the world.

Now that we have PCs and color printers everywhere, I ask: is there any software ("app" for the younger ones) for creating your own maps for wargames? Which one does the HN community recommend?

And I think I found a new use for my 3d printer... infantary!

The "drunken hexagon walk" doesn't really seem like a big deal to me. In the real world, terrain will prevent you from moving in a straight line in many cases. Just like any type of 2D map projection, hexes distort the world to some degree, but it's a lot less than square grids.

Meh. A plain square grid has a speed range of 1.414 to 1 (because of the diagonal approximation error); a plain hexagonal grid has a speed range of 1.155 to 1 (because of the “drunken hexagon walk” at 30° angles); and a square grid with the complicated diagonal adjustment for people who can multiply by 1.414 in their heads still has a speed range of 1.082 to 1 (because of the analogous “drunken octagon walk” at 22.5° angles). Not much of an improvement for forcing people to do mental floating-point arithmetic.

Furthermore, hex grids have a neat property that square grids lack: every path is also a wall that blocks other paths from crossing it from one side to the other, and vice versa. This is the property that makes Hex (the board game) work.

There's a trick you can do with squares that makes them much more accurate than normal; not sure how they would then compare to hexagons.

Instead of treating each diagonal step as "1", you treat the first diagonal step as 1, the second as 2, the third as 1, the fourth as 2, etc. Averaged out, this makes diagonal movements cost 1.5 steps each, which happens to be attractively close to 1.414.

"One of the main reasons that I got a doctorate in computer science was because I was constantly being told by professionals in the wargaming community that with a PhD I would be a PI (Principal Investigator) and have more funding than I would know what to do with.

Yeah.

A philosophy professor I used to know always had as an example of false belief a man who got a PhD in math to meet women.

"It was great for a few years and then around 2012 DARPA, Army, Marines, DoD, et. al., suddenly had no interest in not just wargaming but C4I decision support in general."

Oh...i've got a copy of that battle for Ghettysburg map. I ended up taking all my dad's DnD books and maps and things. That's one of them. I remember playing around with it as a kid trying to figure out how I could use it as a DnD map. My dad explained it was from a war game. There's so many different random maps and papers and books in those boxes but as soon as I seen that I recognized it immediately. Cool.