
The Problem With Hexagons - everbody
http://general-staff.com/the-problem-with-hexagons/
======
tgb
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.

~~~
dalore
But then one might say you miss the point of war games. The point isn't to
have exact movement and have it calculated like chess, it's meant to be messy.
War is messy and analog. The war games are trying to capture the real life
element of war which isn't at all like go or chess with exact movements.

------
bestouff
Great article about how to use hex grids in games:
[https://www.redblobgames.com/grids/hexagons/](https://www.redblobgames.com/grids/hexagons/)

~~~
bovermyer
This article can't be recommended enough. It goes into a lot of the theory
behind hexagonal grid systems. Other articles on that site are well worth
reading, too.

~~~
jihadjihad
Agreed, I'm not a game developer at all but I've spent quite a bit of time on
that site just because it's so darn interesting!

------
kod
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](http://www.simmonsgames.com/products/Austerlitz/Map.html)

~~~
crooked-v
The computer games Europa Universalis IV, Crusader Kings 2, Imperator: Rome,
and others by Paradox Development use something like this by splitting up the
map into irregularly-shaped provinces that can have a variable number of
connections with other provinces (including tactical considerations such as
penalties from river crossings) and have different travel speeds for armies
based on the sizes of particular provinces.

A simple visual example of somebody looking at the diplomacy view of their
country in EU4:
[https://i.imgur.com/hfI8NnM.jpg](https://i.imgur.com/hfI8NnM.jpg)

~~~
yellowapple
Stellaris applies the same to star systems and their hyperspace
interconnections. I miss the other forms of FTL travel possible in that game
(warp drives were nice for their simplicity, and wormhole generators were a
great challenge), but the hyperlanes do make it feel more like "EU4 in
Space™".

------
smogcutter
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.

------
Udo
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.

~~~
murphysbooks
>There are trade-offs involved with any paradigm,...

Reminded me of the aphorism, "All models are wrong, but some are useful" [0]

[0]
[https://en.wikipedia.org/wiki/All_models_are_wrong](https://en.wikipedia.org/wiki/All_models_are_wrong)

------
dsr_
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.

~~~
scj
Hexes have the advantage of being able to eyeball the situation when making a
decision.

Measuring gives an opponent information about what you're thinking.

Deciding which one is appropriate would need to be decided on a game-by-game
basis.

~~~
jandrese
The other downside of measuring is that it can be SLOW. Especially if the
distances are close and you're having to precisely measure. Even worse if you
allow premeasuring and people start checking all of the angles before deciding
on a course of action.

But if you don't allow premeasuring the game becomes more about who can
accurately eyeball distances than who has the best strategic mind. Hexes
replace all of that nonsense with a simple counting step that can be done in
less than a second.

~~~
heavenlyblue
>> accurately eyeball distances than who has the best strategic mind

Are you implyng upper eschelons of command didn’t have to do that themselves
historically?

------
VyseofArcadia
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.

------
woliveirajr
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!

~~~
Qwertystop
Well, there's a wide variety of drawing/painting software. Anything that has
layers and transparency and allows freeform, Bézier curve, and straight-line
drawing should be plenty. And that's most of them. Personally, I like Krita.

------
QuercusMax
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.

~~~
alanbernstein
I don't think of traversing a hex path as following the "drunken" trajectories
shown in the article. The hexes are just a guide to estimate distance; the
trajectory "actually followed" is simply a line from A to B.

This article is about a weird, arbitrarily chosen, ultra-pedantic
_interpretation_ of the tool, and not at all about its practical use.

~~~
jandrese
It depends if the game makes you pay for facing changes. In that case the
drunken walk ends up being much slower.

Of course you can say "so make facing changes free", but that can be a
substantial chunk of the movement strategy, especially if the units are fairly
slow. And it definitely won't feel right if your Roman Legions can do
doughnuts right outside the city.

The best compromise I've seen is Dream Pod 9's system that allows one free
hexside change when you enter a hex. I don't know why more games don't adopt
that rule.

------
anderskaseorg
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.

------
_bxg1
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.

~~~
dalore
So you take the first diagonal step, which counts as 1 and then instead of
going diagonal again you go one of the straights. Then you can go diagonal
again for 1? or 2?

Either way it now needs to keep track of your last diagonal. What's the rules?
is it the second diagonal ever? or the second diagonal in a row? or the second
diagonal in that turn? If I go a diagonal and come back the same way, is that
now 3? If I have one movement point left, can I use it to traverse a 2
diagonal?

This also means you need to keep state of the last movement and makes things a
bit unclear to the user what the next movement point will cost.

~~~
_bxg1
The next diagonal would be 2; doesn't matter if the diagonals are sequential
or not, each one alternates. If you're on 2 and you have 1 movement point
left, you can't use it for a diagonal.

You could track the state across turns for slightly more accuracy, though we
haven't ever bothered to do that when we use this method in D&D. Even
perfectly implemented, it's still just an approximation. But the simplest
version works pretty well: "Every diagonal move, regardless of direction or
sequence, alternates between costing 1 movement point and 2." And most of the
time you're attempting to move in a straight line anyway, so you rarely have
to deal with double-backs or non-sequential diagonals.

------
mcguire
" _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._ "

------
grawprog
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.

------
sch1zo
[https://web.archive.org/web/20190426112003/http://general-
st...](https://web.archive.org/web/20190426112003/http://general-
staff.com/the-problem-with-hexagons/)

