Squared grids, diagonal movements

[The following is a ridiculous amount of math expressed in words. Which confirms most conclusions in this topic. aka. To Complex for gameplay]

Funny how I also tried with hexagons the wrong way first. It is much more difficult to picture how to do it right. But this method also requires one to have patience when figuring it out. Having a history of math helps a lot here. Which most players do not have.

(Could post about 2 more pages of math reasons here too of why things are as they are)

The thing is, while the hexagon sometimes shows the desired dodecagon. If you look closely to the corners, they are indeed still hexagons. There is only a short while of illusion at a distance of 4 and 5. But calculating backwards shows that these 2 are also hexagons mathematical speaking. In practise; the maximum movement is 5 for your desired dodecagon. If you use 6, you got your hexagon back. Period.

While 1.5 works for our square. The error is only 6%.
I don't think that 1.5 works for our hexagon. There the error is 15% (Which is 1% higher than comparing 1.5 to the root of the root of 3). Meaning that using 1.5 brings you closer to hexagons than to dodecagons.
This might sound strange. But have you tried 1.75 (1% error) instead of 1.5 for the hexagons?

BAAAM! Dodecagons!
Instead of 2 and 3. We can use 4 and 7 for movement now.

These 3 and 7 for "diagonal" movements also show at what minimum distance, you see the new desired shape.
3 for the square into an octagon.
7 for the hexagon into a dodecagon.
At 6 and 14, you have your reconfirmation.

While for the square grid, we can use a movement of 2 or more based on 2 and 3. 1 has no use here.

For the hexagon grid, based on 4 and 7, having numbers 1,2,3,5,6,9,10,13 and 17. Has no use.

Now, lets see at the required distance for the shape, and the corresponding numbers for movement.
The square has 3x2=6, next is 12
The hexagon has 7x4=28, next is 56

-->It becomes very impractical<--
No one wants to play a game that requires that much of math.
Who would like to try to get the most optimal movement out of 28? Let alone 29(4+4+4+7+7) Every time when you move your soldiers?

Back to the 2 and 3. Same reason, but ages go down. I figured that people like me have no problems with the squared grid. It is rather easy to follow.

But I would certainly not use it for a kids game. (If I ever would go as far as designing more games)

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And the above shows what iamseph is saying. It is indeed better to avoid this complexity for the simpler games. While the octagon is rather easy in my eye's. And as the previously given link shows. It can be shown on maps as well for players to count in an easier way.
However. "uuugleee!" Not going to do that either.

Regarding turning around, I think that if I use it. I will use a separate number for this.

I have seen many games where fast units can only turn slowly on the spot. And, as how you have put it, a slow soldier can actually turn fast on the spot.

If I can find a strategic value in these differences. I would like to apply it. If there is no strategic value in it; I consider it a waste of time for players.

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In my "completer" wargame, terrain does have influence. But in a sence of space that is. It is a very easy concept. You look for your path. And see if each hexagon shows sufficient space. If not, you need to move your forces in 2 or more turns. Which also simulates slower movement.
This space can be different for different units. (normal, boats, hoovers)

The down side to that was that a part of your army could still cross over at the maximum speed. Meaning they would come into range and "cross over" in a sense.

Thus you mentioning different terrain costs for movement. Was spot on! I indeed had that idea as well. Just to keep forces as big as they are.

Another approach here from me is that if you move a double move at once, the costs would be 3 instead. But still, the maximum speed is not reduced in that matter.

While templates are fun to draw. Their limit is the diversity of war games.

It looks like it is only useful if one uses the same template for several units. Maybe 2 or 3 extra.

And choose those templates that are easy to remember. Like how the diagonal movement shows a end group of 1, then adjacent away from the center 2, then 3 blocks. etc.

Which is also a possibility for any range. Some might be unfair. But if it works, these too come close to a circle.

It starts at range 1, with a block of 1.
Range 2 would be impossible to give this design.
Range 3 on the other hand would show 1 and then a group of 2. This group of 2 melts with another group of 2 into 1 big group of 3. But we assume only one corner to look at.

Ranges of 1, 3, 6 etc. are the only ones that support this principle. Thus all triangular numbers.

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Bottom line is, that when we start using that method. With books etc. We might as well, simply use a ruler and join the warhammer group :)

Clearly this octagon is a bridge that could connect both worlds regarding range and movement. But this bridge is hard to build.

Or we need a computer to simulate the maximum range for us. Like how it is done in XCOM.

The more and more that I think about it. The clearer it becomes that we should stay away from the dodecagon.
The octagon on the other hand is easy enough for the heavy wargames. As long as a relative short distance is used.

I personally use 9 as a maximum. 12 is exceptional. With the 2 and 3 rule, this would be 18 and 24.

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Now, to go back to limited moves through terrain. Instead of having penalties on the maximum number. I think it would be better to use a minimum number. And simply add bonusses for a clearer terrain type.
If an unit cannot move through a terrain, the multiplier is 0.
If an unit has a bonus through clear terrain, than a +1 would be sufficient as example. For some terrains, this bonus would count double.

While easy for players to play with. It would be harder to balance in design.