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| Pythagoras, indicating the tricky diagonal |
I’ve recently been involved in a number of Real Life issues
which have left me very little time for any hobby-related
activities, but I have managed to spend the odd moment reading other people’s
rules, and scribbling and pondering ideas – some of them very old ideas, it has
to be said.
I have banged on about hexagons and their pros and cons at
great length in the past, and am confident that I don’t have very much more to
say on the matter – you would think...
In one of my odd moments, the other day, I was recalling a
series of debates that I had with a few friends – a very long time ago now – in
which we considered gridded miniatures games and their advantages, but which
mostly served as an excuse to drink beer. We agreed, very early in our discussions, that the
most innocent comment any of us had made on the topic to date was credited to our resident optimist, Alan Low, and it went along the lines of:
“It is much easier to consider the merits of hexes if you
can rise above all the prejudices and sacred cows which they seem to upset.”
Yes, Alan, we said – but you can’t really separate these
things – the problem is that the biggest single disadvantage of hexes is that
people hate them. Whether that is justifiable or even fair is beside the point
– if HG Wells had been pictured with hexagons scribed on his floor then no-one
would worry about it. As things stand, hexes are an affront to everything which
is cherished in miniatures gaming. Worst of all, they are associated with BOARD
GAMES, which are the greatest affront of all. We are, after all, talking of
orthodox religion here.
We also agreed that the only acceptable plea we might make
on their behalf was that Joe Morschauser was famous for gridded games – though
I believe that at the time Joe was regarded as less Old School than he is now.
His game was generally seen as a harmless eccentricity, and not proper
wargaming.
Morschauser, of course, used squares. Squares are easy to
draw, and have an ancient precedent in the chessboard, but for wargames they
have some inherent snags, the very largest of which is Pythagoras. Orthogonal
moves of 1 square are fine, but a diagonal move of 1 square is 1.4142135 (etc
etc) times as far. Some games get round this by prohibiting diagonal moves or
combats – somehow, units which are adjacent to each other along a diagonal
cannot see each other – or, as in the De Gre/Sweet game, the square root of two
is taken to be a rather more convenient 1.5. That certainly helps.
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| A to B is easily seen to be 4 hexes |
Hexes are not easy to draw at all – even with an accurate
template, you can get a gradual drift with accumulated small errors, so it is
necessary when marking out a hex table to have copious guidelines and
preliminary sketchings. They do have the advantage of six-fold symmetry, and
they get rid of Pythagoras, but many gamers object to the fact that they
distort straight lines. You can either lay out your hexes so that there are
straight columns going across the table (like my own hex-based games) – in
which case your units may advance in a straightforward manner (literally), but
do not line up side by side very neatly – or you may have the straight columns
running sideways across the table (like Commands & Colors) – in which case
you may form exemplary lines of battle, but your units advance in a rather odd
zig-zag.
In fact both these issues can be solved visually at a stroke
by having the hexes a good bit larger than the units, so that you can place the
units off-centre and smooth out the battle lines and the marches.
We rambled around this subject through many beers, enjoying
the scenery but not really deciding anything, and then one Sunday morning Pat
Timmins rang me and announced:
“I may have just killed Pythagoras.”
Pat had been applying square vinyl tiles to his kitchen
floor – in a very bold combination of navy blue and white. His wife objected to
the basic chequer-board configuration because, she said, it “gave her the
buzzings” and seemed likely to promote epilepsy. He had tried various
alternatives, and at one point experimented with alternate rows offset by half
a tile, like this:
He realised that such an arrangement on a wargames table
would allow movement in six directions, and was in fact a sort of hexagonal
arrangement without the hexagons. Judging distances, for example A to B in the
illustration, was not quite as intuitive as with hexes, but was still possible
with a bit of methodology (I reckon AB is 5 squares distant).
We were unreasonably enthusiastic about this – perhaps we
could pass off our offset squares (or “squexes”, as Pat called them) as a sort
of logical descendant of Morschauser’s game, and overcome some prejudices. The
next non-development was that someone suggested that the squares should not be
squares but rectangles with sides in the proportions of √3 to 2, which would
even up the six-fold symmetry so that it was a proper 60 degrees all round. It made the table layout closer to natural hexes, but made the board look even more distorted –
at this point, we actually preferred normal hexagons, which put us back where
we started. So we eventually decided that squexes had had their brief moment,
and resigned ourselves to being outcasts in the wargaming fraternity with our
conventional hexes.
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| Glinski's game - note the 3 bishops |
Also on the topic of hexes, I invented hexagonal chess in
about 1970. My excitement was tempered more than somewhat when I discovered
that there were already in existence a number of varieties of hexagonal chess,
and that my own new game had been previously invented by a man named Glinski. This was useful,
since it allowed me to drop the idea and move on to dabble with something else.
I expanded Glinski’s game into a 3-sided version. There are 3-sided chess games
now, but mine used a board with a full hexagonal grid (most of the available
games now use distorted squares) – the board was a little larger than the
normal (normal?) Glinski board, and the 3 sets of pieces set up in alternate
corners.
It looked spectacular, but it didn’t work very well. Early
experiments revealed that a game of this type for 3 players brings some
interesting problems. The first is order of turns – if red plays white into
check then white has to respond immediately, which reverses the turn cycle if
it was in fact black’s move next.
More fundamentally troubling is the very nature of 3-player
strategy. It is very difficult to have a game in which each of the players is
attacking both of the others – it makes more sense to have two gang up on the third,
and then double-cross each other at the end, which gets you into all sorts of
negotiation, time-outs for diplomacy and other stuff which we decided it was
simpler to just ban. No chat, we said – no sign language, no secret notes left
in the bathroom. This left us with a game in which the only possible
recommended strategy was a passive opening - allow the other two players to
attack each other and weaken each other. If all 3 players adopt the same
strategy, of course, you get a very strange non-game. You may feel free to draw
your own parallels from history on any or all of these.
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A very smart looking 3-sided chess set - mine was different from this, since it used the Glinski layout of pieces, and the playing board was a rather larger version of Glinski's |
So we gave that one up as well, though we did briefly
consider 3-sided soccer on a triangular pitch, but abandoned that very quickly,
not least because we could not agree how the offside rule would work. We did,
however, think that the winner might be the team which conceded the smallest
number of goals.
How very silly.