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 Post subject: Stacking Limits (Game Design)
PostPosted: Sat Mar 03, 2018 9:47 am 
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I have thought a lot over the years about stacking limits, and I don't think I have arrived at a rock-solid conclusion about how the apparent realities of warfare in real space and time can or best should be represented in a game in which space is represented in a two dimensional plane of "hexes."

I would enjoy a discussion on the topic here amongst you crusty old grogs if anyone can be bothered. To get the juices flowing, I will quote at length my recent ramblings over at the "Battlegoats" forums, re: the game Supreme Ruler Ultimate, which is a great game, but also a deeply flawed game . . .

If you have not played the game I highly recommend it: basically Civilization meets War in the Pacific.

ENTIRE map of planet Earth (remarkably accurate, though not perfectly so) divided into 16km hexes and with many major communities, resource deposits, and national identities indexed in various databases (depending on the scenario/campaign being played). In this respect and he great detail of the unit database, the game is exceptional (although even in these areas it has its flaws). The fact it has a reasonably competent computer opponent who (as of the latest games in the series, though not so much the older ones) represents a little bit more than just a speed bump is also exceptional.

http://www.bgforums.com/forums/posting. ... 2&p=188230
Quote:
This is an interesting thread which I discovered in doing a search on "stacking." I cannot say I know the underlying game mechanics well enough to confirm the observed mathematical model. What I will say is: my gameplay observations confirm the model described. So in sum, I tend to agree with the overall point and as far as I can tell, each of the sub-points you are making OP.

With that said: there is another problem which I as a "realism" fetishist observe.

I just watched this video on Youtube

https://www.youtube.com/watch?v=As5xJt7NaJ8

Not to say this is an authoritative source, it is obviously an allied propaganda piece from ca. 1943 mean to drum up war spirit . . . but, it provides quick reference for scale. Jump to 19:30 and observe the diagrams it provides showing the distribution of French forces in preparation for the German attack. In particular 20:08. The French had 78 divisions along the border with Belgium between the channel and the northeastern edge of the Maginot. The standard size of a division is 10,000 to 30,000 soldiers, with 14,000 to 15,000 being a very common "central value" in WWII.

Now if that video is correct, it means the French had 14,000 x 78 soldiers placed in the gap between the Maginot and the Channel along the Belgian border in spring 1940 (1,092,000 soldiers, or if we use the smaller ~10,000 average value for a division size ~780,000 . . . total CASUALTIES among the allies in battle of France is listed as

https://en.wikipedia.org/wiki/Battle_of_France
2,260,000 so the number of 1,092,000 for the total size of the French 1st Army seems reasonable.

In game that is a distance of 18 hexes. 78 /18 = 4.333. Which means: in order to fit the actual size of the French forces in that space, there would need to be one of the following:

1. 4.33 x (appoximately) 14,000 soldiers per hex (60,620 per hex), or
2. ~2 x 14,000 soldiers per hex but with a two to three hexes "deep" by 18 hexes long (30,310 per hex)
3, etc. correspondingly fewer soldiers per hex but with a front more hexes "deep" by 18 hexes long.

The "personnel" listed for various "units" in the game varies quite a bit. But just a quick peek at the units in reserve in a fresh Germany 1936 start reveals: around 640 for infantry (foot or mounted) and 1260 for Pioneers. As we all know, a Division does not consist entirely of only infantry and the "support units" (artillery, at, aa, etc.) tend to have smaller personnel counts.

Obviously something is amiss here. Even if we pile in one of the most populace of land units and put 7 Pioneer battalions (either largish battalions or under-sized regiments/brigades, I'm not certain), we can only get to 7 * 1260 = 8860 soldiers per hex, which is enough to constitute an "under strength" division but not the upper end for a divisions size.

With a hard stacking limit of 7 and assuming 8860 as a not unrepresentative upper limit for numbers of soldiers in 7 units, and working from our number of 1,092,000 total soldiers in the French First Army (10 British divisions were sandwiched in there somewhere too, so this is actually an underestimate): 1,092,000 / 8860 = 123.25

Assuming a stacking limit of 7 "units" per hex and a maximum personnel count per unit of 1260, the actual "First French Army" would have taken up ~124 hexes. 124 / 18 = 6.89. So the First French Army would have needed to be piled along northern France consistently for 6+ rows of 18 hexes long. The distance from Paris to the border is 11 hexes so in effect what this means is: with a 7 "unit" stacking limit and assuming a First French Army of ~1.092 million, half of the space between France and Belgium should be stacked full of French units. I don't believe this density of soldiers reflects actual history very well at all.

I don't want to say I'm fully convinced, but I believe that this game is not accurately representing the actual concentrations of soldiers per unit of space in the game, which would mean that rather than a hard-limit of "7 units" the actual stacking limit should perhaps be more like . . . well, I'm not sure. How many guys can fit into a area that is 16km across and still function as an effective fighting force?

https://www.reddit.com/r/AskHistorians/ ... ttlefield/

Quote:
A battalion occupying a defense area on the main line of resistance will usually be assigned a frontage of 1,000 to 2,000 yards, depending on the defensive strength of the terrain. When a battalion occupies a vital area having poor observation and poor fields of fire, such as in heavily wooded, broken terrain, the frontage should not exceed 1,000 yards. When the area is more open and affords longer fields of fire, a frontage of 1,500 to 2,000 yards may be appropriate. Exceptionally, when obstacles in front of the position, such as swamps or streams, make a strong attack against an area improbable, a frontage not exceeding 3,500 yards may be assigned.


Also

Quote:
Just to add on, in the Pacific, sometimes things got incredibly compact. During the fighting around Shuri Castle on Okinawa, battalion frontage for the USMC got down below 600 yards. High density trench warfare in WWI was generally around 800 yards, so at Shuri it was exceptionally dense.

This comes from William Manchester's Goodbye Darkness.


A "battalion" is typically in the https://en.wikipedia.org/wiki/Battalion 300 to 800 soldiers ball park, so a "high density" is one in which the frontage for a unit is about equivalent to one soldier per meter (1 yard = 0.944 meters), and a more "normal" frontage is 1.875 meters of frontage per soldier, to a maximum diffuse end of 4.375 meters per soldier.

Referring back to our 18x16km distance from Maginot to the channel 288km = 288,000 meters. So a very sparse coverage of this front would be 288,000 / 4.375 = 65,828.6 soldiers. This number of soldiers divided by 18 hexes gives us 3657 soldiers per hex.

So according to real life military doctrine (as quoted on a Reddit sub-forums! :P ), and given that units in this game vary from ~240 to ~1260 soldiers in size, "7 units" is, or probably SHOULD BE about the absolutely bare MINIMUM number of units to effectively control a hex, much less the absolute max possible in a hex. If we work with the "large" unit like Pioneers than 3 units * 1260 = 3780 is about enough to control a hex. But for the "640 personnel" of infantry, it would take at least 5.71 "units" to effectively control a hex using the exceptional reference in the quote above

Quote:
Exceptionally, when obstacles in front of the position, such as swamps or streams, make a strong attack against an area improbable, a frontage not exceeding 3,500 yards may be assigned.


If we assume that "stacking limits" must reflect a limitation in which ONLY one "row" of soldiers can fit into a hex then 16,000 soldiers per hex would be a "maximum," which would translate into something like 13 to 25 "units" per hex given the range of 640 soldiers for infantry and 1260 for pioneers.

However the fact that hexes are two dimensional means that it should be possible for multiple times this number of soldiers to operate within a hex without resulting in hindrance. Whether that would be 3, 5 or 7 times "13 to 25 units per hex" (stacking limits of 39 to 75; 65 to 125; or 91 to 175 units per hex) I cannot say.

continued in following post . . .

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 Post subject: Re: Stacking Limits (Game Design)
PostPosted: Sat Mar 03, 2018 9:48 am 
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Quote:
If we know how "deep" the ~1,092,000 soldiers of the First French Army were arranged along the Belgian border as they waited for the end of the Sitzkrieg we could probably say with some certainty what a reasonable "maximum" stacking limit should be--in order to reflect reality, which may be completely out of bounds if the goal is good gameplay.

If we assume that there were 1,092,000 French soldiers (78 divisions) lined up shoulder to shoulder, then 1,092,000 soldiers (at one meter per soldier) / 1000 would allow that many soldiers to cover 1092 km of frontage. This leads to the obvious implication that, assuming the sources I'm using are accurate and I haven't made a math error (which is quite possible at this time of night) then those 78 divisions were not arranged in a single line of soldiers shoulder to shoulder.

If we use the "intermediate" value of 1.875 meters of frontage covered per soldier in a unit, then 1,092,000 / 1.875 = 58,2400 meters or 582.4 km of coverage. This suggests that the French First Army was probably arranged with half or more of its reserve or support troops some distance behind the immediate front. Given that a single row of eighteen 16km wide hexes is both 288,000 meters long and 16,000 meters "deep" that gives us a rough cubic volume of 460,800,000 m^2 give would given each of each of the 1,092,000 soldiers about 4219 m^2 of space EACH, or a square of about 64.95 m on each side for EACH soldier.

Clearly, there is plenty of space for ~78 divisions numbering some 1,092,000 soldiers to fit in a 18 long row of hexes 1 hex deep (and 16km wide hexes). If we use this number as a "reasonable though not maximum troop density and translate it into game terms:

1,092,000 / 18 = 60,667 soldiers per hex In game terms, this would require 48.2 of the pioneer units (with 1260 soldiers) or 94 of the "infantry" units (with 640 soldiers).


Also worth noting about the game:
1. first created in the late 1990s as a text only game
2. reborn some 10 or 15 years later as a hex map game in Supreme Ruler 2010
3. 2nd title in the series was SR 2020 (the first one I played and the one I feel the computer opponent does the least bad job with posing a challenge to the player in)
4. SR 1936 was next, then
5. SR Cold War and then
6. SR "Ultimate" (which allowed starting a sandbox or campaign in 1936 and playing all the way through to the near future, along with near future techs, etc.)
7. Supreme Ruler Great War, apparently a DLC for ultimate that was released a year or so ago, though I have yet to buy it. Probably won't.

Mostly I regard the game as an interesting case study in what can be done, and what NOT to do in designing such a game. For one thing the real-time pauseable design seems daft as fuck.

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 Post subject: Re: Stacking Limits (Game Design)
PostPosted: Mon Mar 12, 2018 12:30 pm 
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In real world the roads have limits and urban etc. obstacles prevent even offroad transit creating further bottlenecks.

When you cram a shit ton of units into same tiny area (think of WWII Nazi invasion of Belgium) and they're all in a rush you get funny things - units get mixed up, suddenly that AA company's guns are moving with a motorized battalion etc., immense traffic and so - complete chaos, soldiers unable to physically locate things like logistics, commanders and their own units.

But the worst - there's nowhere to hide when facing indirect fire and the guys who are firing will hit something with every round because there are targets on top of targets. Hit anywhere near the target and your artillery shell will topple at least three tanks.

As far as game design goes, accuracy improves with smaller hexes and micromanagement increases. When you try to eliminate micromanagement with automation you tend to lose all sense of control and the experience can feel like going on tracks oblivious to your actions.

And going for more abstract macroscale you again lose accuracy and things become increasingly statistical which again leads to ever lesser accuracy and bean counter strategy instead of realistic war simulation.


Inherently, Game < --- > Simulation axis. Simulation optimizes accuracy at the cost of possibly limiting player impact in the world. Game maximizes player experience and amount of decision making at the cost of accuracy.

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 Post subject: Re: Stacking Limits (Game Design)
PostPosted: Mon Mar 12, 2018 12:56 pm 
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Units were stacked pretty high in WW1. I think something like half a million people died in a 5 x 5km square at Verdun? At the Somme on day 1, 19 Entente divisions attacked a front about 10 miles across. So 2 divisions per mile of frontage.

In 1916 their solution to stalemate was 'focus more force against the enemy'. Naturally packing such a dense mass of troops into an area meant a lot of them were mown down by modern weapons.

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 Post subject: Re: Stacking Limits (Game Design)
PostPosted: Mon Mar 12, 2018 1:11 pm 
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EUBanana wrote:
Units were stacked pretty high in WW1. I think something like half a million people died in a 5 x 5km square at Verdun? At the Somme on day 1, 19 Entente divisions attacked a front about 10 miles across. So 2 divisions per mile of frontage.

In 1916 their solution to stalemate was 'focus more force against the enemy'. Naturally packing such a dense mass of troops into an area meant a lot of them were mown down by modern weapons.


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 Post subject: Re: Stacking Limits (Game Design)
PostPosted: Mon Mar 12, 2018 1:40 pm 
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Kameolontti wrote:
In real world the roads have limits and urban etc. obstacles prevent even offroad transit creating further bottlenecks.

When you cram a shit ton of units into same tiny area (think of WWII Nazi invasion of Belgium) and they're all in a rush you get funny things - units get mixed up, suddenly that AA company's guns are moving with a motorized battalion etc., immense traffic and so - complete chaos, soldiers unable to physically locate things like logistics, commanders and their own units.

But the worst - there's nowhere to hide when facing indirect fire and the guys who are firing will hit something with every round because there are targets on top of targets. Hit anywhere near the target and your artillery shell will topple at least three tanks.

As far as game design goes, accuracy improves with smaller hexes and micromanagement increases. When you try to eliminate micromanagement with automation you tend to lose all sense of control and the experience can feel like going on tracks oblivious to your actions.

And going for more abstract macroscale you again lose accuracy and things become increasingly statistical which again leads to ever lesser accuracy and bean counter strategy instead of realistic war simulation.


Inherently, Game < --- > Simulation axis. Simulation optimizes accuracy at the cost of possibly limiting player impact in the world. Game maximizes player experience and amount of decision making at the cost of accuracy.


All seems perfectly legit.

Nonetheless, I think the Supreme Ruler game model underestimates "ideal" troop density ENORMOUSLY. Perhaps by a factor of 20, but at least by a factor of 5.

To synthesize (from memory, i.e., without consulting my wall of text in first post): "units" in the game are battalion or company sized (arty, at, aaa, are all company sized, so personnel counts in the 50 to 250 range) infantry ~600 to 800, some others a bit bigger like "pioneers."

It takes only ONE of these units to "control" a hex that is 16km across. This is utterly preposterous. Just to control one FACE on the perimeter of such an area would take in the ballpark of thousands of troops (depending on how they were equipped). To completely control such a hex might well require multiple divisions.

Despite this, MAXIMUM stacking limit in the game is "7 units." So if one uses the most populated units the game has, the most troops one can stack up in a 16km hex is ~< 9000.

In sum: completely out of whack. Sadly, cannot be fixed with modding because of how the combat model works. What the game really needs is a modular "Brigades/Division/Corp/Army/Army Group building system."

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 Post subject: Re: Stacking Limits (Game Design)
PostPosted: Mon Mar 12, 2018 1:46 pm 
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EUBanana wrote:
Units were stacked pretty high in WW1. I think something like half a million people died in a 5 x 5km square at Verdun? At the Somme on day 1, 19 Entente divisions attacked a front about 10 miles across. So 2 divisions per mile of frontage.

In 1916 their solution to stalemate was 'focus more force against the enemy'. Naturally packing such a dense mass of troops into an area meant a lot of them were mown down by modern weapons.


Two divisions per mile . . . :shock: lessee . . . lets just say 15,000 for "estimated' Div size 1 mile = 1.6 km (amazingly, I seem to think better in metric as I age . . .)

so 16,000 m

(15,000 troops * 2) / 16,000 meters of frontage

30,000 / 16,000 = 1.875 troops PER METER of frontage

In order for all those guys to literally stand there next to each other along a 16,000 m line they would have to turn one shoulder toward the enemy! :P Obviously that isn't exactly what happened. There would have been "depth" to those units at all times as well, and with local clumping and less densely packed areas in between, but yeah . . . insanely dense packing!

ADDIT: going back to OP to cross-reference . . .

Quote:
A "battalion" is typically in the https://en.wikipedia.org/wiki/Battalion 300 to 800 soldiers ball park, so a "high density" is one in which the frontage for a unit is about equivalent to one soldier per meter (1 yard = 0.944 meters), and a more "normal" frontage is 1.875 meters of frontage per soldier, to a maximum diffuse end of 4.375 meters per soldier.


So based on that sub-reddit a "high density" (it referred to some of the WWII pacific island combats . . .) is ~about 1 troop per meter, and 1 troop per 1.875 is a more "normal" frontage.

1.875 troops per meter is almost twice as densely packed!

So to put it on a continuum (Troop to Frontage Ratio using "Battalion scale to frontage" method)

High Density: 2:1

'Normal' density 1:2

Diffuse but defensible: 1:4.4

Obviously if we go to a finer grain than a theater and instead focus down at the level of battalions or companies, or smaller, then these numbers are pointless. At higher resolutions scales, the actual "front" is probably more like "mostly empty" but with isolated pockets of men/machines in some cases with local densities that even exceed 2:1.

A 3 or 4 man crew operating an AT gun is probably at a density of ~>2:1 in terms of men to the width they fill. Same thing with mg crews, tank crews, arty crews, aa crews, etc. On the other hand, one fire team can, depending on terrain and exact size, exert "zone of control" over quite a large cone and if it is a 4 man fire team might be able to passive recon an cone that is close to 180-degrees wide . . . ??

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 Post subject: Re: Stacking Limits (Game Design)
PostPosted: Mon Mar 12, 2018 7:51 pm 
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Stacking limits are a real concern. For example - Stationing 8k Marines on Guam might cause it to become over populated. Could tip over and capsize.

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 Post subject: Re: Stacking Limits (Game Design)
PostPosted: Wed Apr 04, 2018 5:01 am 
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Anthropoid wrote:
All seems perfectly legit.

Nonetheless, I think the Supreme Ruler game model underestimates "ideal" troop density ENORMOUSLY. Perhaps by a factor of 20, but at least by a factor of 5.

To synthesize (from memory, i.e., without consulting my wall of text in first post): "units" in the game are battalion or company sized (arty, at, aaa, are all company sized, so personnel counts in the 50 to 250 range) infantry ~600 to 800, some others a bit bigger like "pioneers."

It takes only ONE of these units to "control" a hex that is 16km across. This is utterly preposterous. Just to control one FACE on the perimeter of such an area would take in the ballpark of thousands of troops (depending on how they were equipped). To completely control such a hex might well require multiple divisions.

Despite this, MAXIMUM stacking limit in the game is "7 units." So if one uses the most populated units the game has, the most troops one can stack up in a 16km hex is ~< 9000.

In sum: completely out of whack. Sadly, cannot be fixed with modding because of how the combat model works. What the game really needs is a modular "Brigades/Division/Corp/Army/Army Group building system."


There are a shit ton of real world problems with that too.

Even games like Operational Art of War never got it right, they just didn't.

For instance, you have a battalion of recons in a hex, big hex. Tank battalion drives 50km past them and spots them, this kind of bullshit. Pretty good eyes on those tankers, considering they're driving in very hilly woodlands with average line of sight extending ~200-800m.

In general the units see way too much, evasion and camouflage are non-existant and light infantry, special forces and recons act as if they were infantry of the line standing there in bright jackets ready to face any charge.

For instance an elite light infantry unit such as Sissi can remain undetected and has superior mobility to normal infantry - simply through superior physique, even the weakest in the unit have physique on par with the best of a regular unit. They can ambush a unit, fighting against 1:3 odds and destroy the enemy unit in doing so. You almost never see these kinds of things in war games, things like infiltrators simply going through occupied enemy territory, penetrating their patrol lines and so on.

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 Post subject: Re: Stacking Limits (Game Design)
PostPosted: Mon Apr 09, 2018 1:02 pm 
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One thing about stacking in general is that it adds a tremendous amount of overhead to the AI player. The number of combinations that have to be examined grows exponentially once you allow even 2 units to occupy the same hex.

I'm pretty sure that's why so many WWII grand strategy games don't allow stacking at all.

OTOH, there is one positive tradeoff with allowing stacking for the AI player. Pathfinding can be greatly simplified as you can often move 'through' your own units. Things humans are extremely good at like moving a bunch of units out of the way to let another one through are much more difficult to program than you might imagine.

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