Saturday, February 4, 2017

'Measuring' shooting ranges on a gridded board.



This posting interrupts my Stonewall in the Valley narrative momentarily, to report on something I have been thinking about off and on.  That narrative will continue: the posting has some of the pictures. I have found more to add, and then there is the text to write up
.  

In the meantime, I have been reading a fairish bit, off and on, about the merits and problems associated with gridded war games playing surfaces.  The problem with square fields is geometric. Chess players will have encountered this, especially in end games in which Kings are playing a prominent role.  A White pawn at 'a3', scampering to promote to queen at 'a8', will get run down by a King at 'f3'.  In the 'long' Algebraic notation:


White        Black:
1. a3-a4      Kf3-e4
2  a4-a5      Ke4-d5
3. a5-a6      Kd5-c6
4. a6-a7      Kc6-b7
5. a7-a8=Q Kb7xa8.
An online chess game in progress.  I have the Black pieces,
and (in the picture)  am about to lose my h7-pawn.
 It's all part of a Cunning Plan.

The distance from a1-a8 (orthogonal) is effectively the same as from h1-a8 - along the long light-square diagonal.  For war games, that simply won't do.  But how to Solve that geometric anomaly? Short answer: hexes or offset squares.  But they have their own idiosyncrasies, to do with the number of available directions from a given point, to wit: six.  I would much prefer that there be eight!

A Neil Thomas scenario translated to my chessboard.
Not a success: the rule set needs adapting to this format.

One method I have thought quite a bit about is to measure the distance from the centre of the object square to the centre of the target square and round to the nearest whole number.  The 8x8 'table below does that.  Take the chessboard convention and regard the bottom left hand corner (where the 'Firing Unit' is) as 'a1', to top LH corner as 'a8' and the bottom RH corner as 'h1' we see that the distance between diagonally opposite corners is a little under 50% longer than orthogonally opposite corners.

Firing Ranges Ready Reckoner

7
7
8
8
9
9
9
10
6
6
7
7
8
8
8
9
5
5
6
6
7
7
8
9
4
4
5
5
6
7
8
9
3
3
4
4
5
6
7
8
2
2
3
4
5
6
7
8
1
1
2
3
4
5
6
7
Firing
Unit
1
2
3
4
5
6
7

Not only can this grid quickly determine firing ranges, it could be used for movement allocation as well.  If such moves involve passage through delaying terrain, you simply count off the delay and carry on to the destination square.

 Movement Allowance Ready Reckoner:
14
15
16
17
18
19
20
21
12
13
14
15
16
17
18
20
10
11
12
13
14
15
17
19
8
9
10
11
12
14
16
18
6
7
8
9
11
13
15
17
4
5
6
8
10
12
14
16
2
3
5
7
9
11
13
15
Move
Unit
2
4
6
8
10
12
14




I have considered allocation movement allowances along the lines of 2 'movement points' orthogonally, and 3 'MPs' diagonally, and to treat ranges in the same way.  Such a system is still a trifle generous concerning diagonals, but is a big improvement on the 'chessboard' convention.

Doubling up on movement allowances is no real hardship.  Likely enough the odd numbers that appear on this grid won't have any significance as is, but it does allow for some very fine tuning! Not only small differences in vehicular speed, say, but one might allow a single MP delay for negotiating minor inconveniences of feature - moving up an easy slope, say, or slightly rough going. Heavier penalties on movement might be enacted for difficult going.

My gridded up small games board.  10x10 4-inch squares.

I chose 4-inch squares so that my big cats could fit comfortably
within the squares (leaving aside the long guns.  The cluster of
buildings represents a 4-inch square town...

The grids I have included here are good for an 8x8 grid.  Just recently I gridded up a piece of 5-ply flooring board into 10x10 4-inch squares.  I was inclined to keep the house-like pentagonal shape and added a further dozen squares on the 'gable'.  Normally unused, I can see the odd scenario in which they might add a little something.  As the board width is about 42 inches, I gave a little extra depth along each side square.  These can still count as normal squares, but could equally well represent reserve zones in some games.



As I have been reading a friend's copy of Neil Thomas's One Hour Wargames book, I am working out ways to translate his ideas onto this gridded set up.  I might be forced to extend my 'Ready Reckoners' to a 10x10 grid...


11 comments:

  1. This is an issue that has been 'worried' about for years (as gamers conducted their campaign moves on square grids) and I think the first solution is simply not to worry about it. The same peculiarity applies to both players, so nobody is disadvantaged, though I accept not all would find such an argument particularly convincing.

    What I would avoid is putting in a 'translation' mechanic, as all you are doing is adding another process to playing and grids are meant to reduce and ease the measuring processes.

    Peter Pig rules, which use squares seem to have hit on a very easy solution, but I can't properly remember it now (no doubt Google can sort it) but it is something like the first diagonal move is free and after that they are paid for at a heavier cost. Anyway, whatever it is, it is dead easy to remember, so much so, that the extra calculation becomes second nature rather than being an obvious new step.

    Hexes bring their own quirks, in that the staggered effect causes compression of the battlefield in one direction, while the flat to flat grain remains constant, though to my mind, getting more cells (or playing locations) onto the same table space probably is more advantageous than a problem.

    Anyway, it might be worth you checking out how Peter Pig have solved the problem. They use to have a free quick learn download 4 page for the PBI (Poor Bloody Infantry) rules and they might explain it.

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    1. from what I have seen is that Peter Pig hasn't really solved the problem: merely fudged it. Mind you all solutions - even mine, even hexes and what not, are fudges. My suggestions are attempts to 'circle the square', which is what the colours are supposed to indicate. Over very short distances, one two squares, there simply is no real solution, but the further out you you go the more the distances start to resemble the radius of a circle.

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  2. Hi Guys,

    Yes, Norm is correct that Peter Pig's PBI game is a great solution. Units move orthogonally but may move diagonally once per movement phase at any stage in their movement. There is no additional movement cost (which is in action points) for moving diagonally. Each square moved costs action points depending on terrain type. Simple is always best!

    Jay

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    1. I actually thought my ideas were simple! Are you telling me they aren't? That is a point of view that never crossed my mind. As I haven't really tried it out in practice - only recently have I started to take a serious interest in gridded war games - I guess I'll just have to suck it and see.

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  3. One Hour Wargames have movement allowances of 6, 9 and 12 inches and shooting ranges of 12 or 48 inches. So your 4 inch squares will probably work nicely for using OHW on a grid. I have been a using 6 inch grid and on a 6x4 foot table and not worrying about any adjustments for speed of play purposes. The reason I go for 6 inch squares is so I can fit in terrain and a unit (another consideration with squares).

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    1. It did cross my mind that that might work. I tried that idea in the chessboard game pictured, but it did not work out very well. I didn't really think it through. It was that game, by the way that set me once more thinking about the whole problem of square grids rather than hexes.

      In about 1990 I 'invented'/came up with the idea of 'offset squares' as a 'hex; substitute, simply because a field of hexes is bally hard to draw (I know it was probably invented by others before then, but I did think it up all by myself!). But my main beef with that system is the wasted space on the playing surface. On my 40-inch by 40-inch surface, 5% of the area would be wasted. That's a consideration when you have only a small area to play with. Hexes have the same problem.

      I also have a 6ft by 4ft table. I could grid that too, but I use it more for 'free form' sort of games.

      On the matter of terrain, the cluster of buildings in the photos was an experiment. I am thinking of making 4-in square town profiles, upon which buildings might be stood but unfastened. They could be removed to fit troops. To retain the look of 'town' when occupied, I'm considering a narrow cardboard wall surrounding the whole. An alternative is to make 2D buildings around the perimeter, leaving a hollow interior that might be occupied. Attempts I've seen in this line look surprisingly effective.

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  4. If you are measuring from the center of a small unit this looks simple enough but if not using a grid and close range was 4" and the distance to the target was 5", would you say well, I'll round that diwn to close range?

    The problem I run into is the visual aspect when a unit is as wide as an area and when firing, appears to be shooting slmost sideways. I have been known to refuse the flank or face the unit on a diagonal just for looks. Actually adding rules for suchlike things though seems to merely end up sapping away the ease of play and focus on the overall battleplan and thus be counterproductive for my goal.

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    1. You are right to point out that if I want to pursue this idea it will need work. Those distances in my first diagram are in fact the distances from the centre of the 'Firing' square to the centre of the 'Target' square rounded to the nearest whole number. That is a fudge, of course, but it is really part of the whole 'fudge' of using grid areas to define distances anyhow. After all, isn't their purpose to obviate the need for measuring anything? Compromises have to be made.

      When thinking about the 'movement allowance' grid, I did toy with the idea of a 1MP cost for changing (infantry) frontage of more than 45 degrees per move. A unit facing through a side can turn to face either of the adjacent corners for free. One would also have to work out arcs of fire. A 90-degree arc looks simplest.

      Adjusting the line 'for the look of the thing' sounds perfectly reasonable to me, whether or not there is a 'change-front' rule. A couple of other possibilities occur to me:
      1. Automatic change of front to face target that is already in the 'legal' firing arc. OR
      2. The 90-degree firing arc is not angled upon the square occupied by the firing unit, but upon the square immediately in front of it.

      These two ideas are mutually exclusive, and would have to be play tested separately to determine which is the simpler/works better/looks better...


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    2. I have had to pull myself out of the rabbit hole a couple of times when I got into thinking about the things like thinking how a unit in line that wheeled forward would end up in the next square and essentially take the same amount of time as advancing straight forward and the same amount of time as a unit changing face on the same ground.

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    3. I think it is well at least to consider these issues. If we do reject them, at least we will know why!

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    4. I agree! Of course I also think that time spwnt considering sonething is time well spent even if nothong cones of it.

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