Battle Lines, Commanders & Computers

When we look at maps of battles even the novice armchair general can quickly trace the battle lines of the armies. Recognizing battle lines is one of the most important skills a commander – or a wargaming Artificial Intelligence (AI) – can possess. Without this ability how will you identify the flanking units? And if you can’t identify the units at the end of a line, how will you implement a flanking attack around them? Equally important is the ability to identify weak points in a battle line.

The algorithm for detecting battle lines and flank units is one of the ‘building block’ algorithms of my TIGER / MATE tactical AI and first appeared in my paper, Implementing the Five Canonical Offensive Maneuvers in a CGI Environment1)http://riverviewai.com/papers/ImplementingManeuvers.pdf. I will discuss how the algorithm works at the end of this blog. For now, just accept that it finds lines and flanks.

Let’s look at some examples of the General Staff AI ‘parsing’ unit positions. First, the battle of Antietam, situation at dawn (by the way, Antietam is one of the free scenarios included with the General Staff Wargaming System):

The battle of Antietam, dawn, September 17, 1863. Screen shot from the General Staff Sand Box program. Click to enlarge.

This is how a human sees the tactical situation: units on a topographical map. But, the computer AI sees it quite differently. In the next image, below, the battle lines and elevation are displayed as the AI sees the battle (note: the AI also ‘sees’ the terrain but, for clarity, that is not being shown in this screen capture):

The battle of Antietam, September 17, 1862 dawn, with computer AI battle lines and elevation displayed. Note: the identification of flank units. Both red and blue forces are assembling on the field. Click to enlarge.

What is immediately obvious is that Red (Confederate) forces are hastily constructing a battle line while Blue (Union) forces are beginning to pour onto the battlefield to attack.  Let us now ask the question: what is the weakest point of the Red battle line? Where should Blue attack? This point is sometimes called the Schwerpunkt. German for point of maximum effort2)See also, “Clausewitz’s Schwerpunkt Mistranslated from German, Misunderstood in English” Military Review, 2007 https://www.armyupress.army.mil/Portals/7/military-review/Archives/English/MilitaryReview_20070228_art014.pdf. Where should Blue concentrate its forces?

Computer AI representation of battle lines for Antietam, dawn September 17, 1862. The AI is locating the Schwerpunkt or place to attack. Click to enlarge.

Now that the weakest points of Red’s battle line have been identified, Blue (assuming Blue is being controlled by the AI) can exploit it by attacking the gaps in Red’s battle line. The Blue AI can order either a Penetration or Infiltration Maneuver to exploit these gaps (the following images are from my paper, “Implementing the Five Canonical Offensive Maneuvers in a CGF Environment.” Note, in the TIGER / MATE screen shots below Range of Influence (ROI) is also visible:

From the paper, “Implementing the Five Canonical Offensive Maneuvers.”

Both of these maneuvers are possible because the AI has identified weak points in the OPFOR (Opponent Forces) battle lines. Equally important when discussing battle lines are the location of the flanks. The next two images use the original American Kriegsspiel (1882) map which is also included in the General Staff Wargaming System:

The original American Kriegsspiel map (1882) restored and now used in the General Staff Wargaming System. Screen shot from the General Staff Sand Box AI test program. Click to enlarge.

In this screen capture from the General Staff Wargaming System Sand Box AI test program battle lines are displayed by the AI. Note the flank units and especially the unanchored (or open) Blue flank. Click to enlarge.

Identifying flank units is vitally important in the Turning Maneuver and the Envelopment Maneuver:

Knowing the location of flank units is also important for classifying tactical positions (this will be the subject of an upcoming blog).

So, how does this algorithm work?

I’ve never been a fan of graph theory; or heavy mathematical lifting in general. One of the required classes in grad school was Design and Analysis of Algorithms and it got into graph theory quite a bit. The whole time I was thinking, “I’m never going to use any of this stuff, but I have to get at least a B+ to graduate,” so I took a lot of notes and studied hard. Later, when I was looking for a framework to understand tactics and to write a tactical AI it became obvious that graph theory was at least part of the solution. Maps are routinely divided into a grid, unit locations can be points (or vertices) at the intersections of these lines. Battle lines can be edges that connect the vertices. I need to publicly thank my doctoral advisor, Dr. Alberto Segre, for first suggesting that battle lines could be described using something called a Minimum Spanning Tree3)https://en.wikipedia.org/wiki/Minimum_spanning_tree (MST). An MST is the minimum possible distances (edge weights to be precise) to connect all the vertices in a tree (or a group, as I call them in the above screen shots).

I ended up implementing Kruskal’s algorithm4)https://en.wikipedia.org/wiki/Kruskal’s_algorithm for identifying battle lines. It is what is called a ‘greedy algorithm’ and it runs in O(E log V) which means it gets slower as we add more units but we’re never dealing with gigantic numbers of individual units in an Order of Battle (probably around 50 is the maximum) so it takes less than a second to calculate and display battle lines for both Red and Blue.

Lastly, and I guess this is my contribution to military graph theory, I realized that the flank units of any battle line must be the maximally separated units. That is to say, that the two units in a battle line that are the farthest apart are the flank units.

Obviously, this is a subject that I find fascinating so please feel free to contact me directly if you have any questions or comments.

 

References   [ + ]

Maps, Commanders & Computers

How a map of the battle of Antietam looks to us humans. Screen shot from the General Staff Map Editor. Click to enlarge.

How the computer sees the same map (terrain and elevation). This is actually a screen shot from the Map Editor with the ‘terrain’ and ‘elevation’ layers turned on. Click to enlarge.

Computer vision is the term that we use to describe the process by which a computer ‘sees'1)When describing various AI processes I often use words like ‘see,’ ‘understand,’ and ‘know’ but this should not be taken literally. The last thing I want to do is to get in to a philosophic discussion on computers being sentient. the world in which it operates. Many companies are spending vast sums of money developing driverless or self-driving cars. However, these AI controlled cars have had a number of accidents including four that have resulted in human fatalities.2)https://en.wikipedia.org/wiki/List_of_self-driving_car_fatalities The problem with these systems is not in the AI – anybody who has played a game with simulated traffic (LA Noir, Grand Theft Auto, etc.) knows that. Instead, the problem is with the ‘computer vision’; the system that describes the ‘world view’ in which the AI operates. In one fatality, for example, the computer vision failed to distinguish a white semi tractor trailer from the sky.3)https://www.theguardian.com/technology/2016/jun/30/tesla-autopilot-death-self-driving-car-elon-musk Consequently, the AI did not ‘know’ there was a semi directly in front of it.

In my doctoral research I created a system by which a program could ‘read’ and ‘understand’ a battlefield map4)TIGER: An Unsupervised Machine Learning Tactical Inference Generator http://www.riverviewai.com/download/SidranThesis.html. This is the system that we use in General Staff.

The two images, above, show the difference in how a human commander and a computer ‘see’ the same battlefield. In the top image the woods, the hills and the roads are all obvious to us humans.

The bottom, or ‘computer vision’ image, is a bit of a cheat because this is how the computer information is visually displayed to the human designer in the General Staff Map Editor. The bottom image is created from four map layers (any of which can be displayed or turned off):

The four layers that make up a General Staff map.

The background image layer in a General Staff map is the beautiful artwork shown in the top image. The place names and Victory Points layer are also displayed in the top image. The terrain and elevation layers are described below:

The next three images are actual visual representations of the contents of memory where these terrain values are stored (this is built in to the General Staff Map Editor as a debugging tool):

Screen shot from the Map Editor showing just terrain labeled as ‘water’. Click to enlarge

Screen shot from the General Staff Map Editor showing the terrain labeled as ‘woods’. Click to enlarge.

Screen shot from the General Staff Map Editor showing the terrain labeled ‘road’. Click to enlarge.

A heightmap for Antietam. This is a visual representation of elevation in meters (darker = lower, lighter = higher). Click to enlarge.

To computers, an image is a two-dimensional array; like a giant tic-tac-toe or chess board. Every square (or cell) in that board contains a value called the RGB (Red, Green, Blue5)Except in France where it’s RVB for Rouge, Vert, Bleu  ) value. Colors are described by their RGB value (white, for example, is 255,255,255).  If you find this interesting, here is a link to an interactive RGB chart. General Staff uses a similar system except instead of the RGB system each cell contains a value that represents various terrain types (road, forest, swamp, etc.) and another, identical, two-dimensional array, contains values that represent the elevation in meters. To make matters just a little bit more confusing, computer arrays are actually not two-dimensional (or three-dimensional or n-dimensional) but rather a contiguous block of memory addresses. So, the terrain and elevation arrays in General Staff which appear to be two-dimensional arrays of 1155 x 805 cells are actually just 929,775 bytes long hunks of contiguous memory. To put things in perspective, just those two arrays consume more RAM than was available for everything in the original computer systems (Apple //e, Apple IIGS, Atari ST, MS DOS, Macintosh and Amiga) that I originally wrote UMS for.

So, not surprisingly, a computer stores its map of the world in which it operates as a series of numbers 6)Yes, at the lowest level the numbers are just 1s and 0s but we’ll cover that before the midterm exams. that represent terrain and elevation. But, how does a human commander read a map? I posed this question to Ben Davis, a neuroscientist and wargamer, and he suggested looking at a couple of studies. In one article7)https://www.citylab.com/design/2014/11/how-to-make-a-better-map-according-to-science/382898/, Amy Lobben, head of the Department of Geography at the University of Oregon, said, “…some people process spatial information egocentrically, meaning they understand their environment as it relates to them from a given perspective. Others navigate more allocentrically, meaning they look at how other objects in the environment relate to each other, regardless of their perspective. These preferences are linked to different regions of the brain.” Another8)https://www.researchgate.net/publication/251187268_USING_fMRI_IN_CARTOGRAPHIC_RESEARCH reports the results of fMRI scans while, “subjects perform[ed] navigational map tasks on a computer and again while they were being scanned in a magnetic resonance imaging machine.” to identify specific, “involvement or non-involvement of the brain area.. doing the task.”

So, how computers and human commanders read and process maps is quite different. But, at the end of the day, computers are just manipulating numbers following a series of algorithms. I have written extensively about the algorithms that I have developed including:

  • “Algorithms for Generating Attribute Values for the Classification of Tactical Situations.”
  • “Implementing the Five Canonical Offensive Maneuvers in a CGF Environment.”
  • “Good Decisions Under Fire: Human-Level Strategic and Tactical Artificial Intelligence in Real-World Three-Dimensional Environments.”
  • “Current Methods to Create Human-Level Artificial Intelligence in Computer Simulations and Wargames”
  • Human Level Artificial Intelligence for Computer Simulations and Wargames.
  • An Analysis of Dimdal’s (ex-Jonsson’s) ‘An Optimal Pathfinder for Vehicles in Real-World Terrain Maps’

These papers, and others, can be freely downloaded from my web site here.

As always, please feel free to contact me directly if you have any questions or comments.

References   [ + ]

1. When describing various AI processes I often use words like ‘see,’ ‘understand,’ and ‘know’ but this should not be taken literally. The last thing I want to do is to get in to a philosophic discussion on computers being sentient.
2. https://en.wikipedia.org/wiki/List_of_self-driving_car_fatalities
3. https://www.theguardian.com/technology/2016/jun/30/tesla-autopilot-death-self-driving-car-elon-musk
4. TIGER: An Unsupervised Machine Learning Tactical Inference Generator http://www.riverviewai.com/download/SidranThesis.html
5. Except in France where it’s RVB for Rouge, Vert, Bleu
6. Yes, at the lowest level the numbers are just 1s and 0s but we’ll cover that before the midterm exams.
7. https://www.citylab.com/design/2014/11/how-to-make-a-better-map-according-to-science/382898/
8. https://www.researchgate.net/publication/251187268_USING_fMRI_IN_CARTOGRAPHIC_RESEARCH

How Will You Play General Staff?

Every wargame that I’ve designed allows the user to adjust important variables such as leadership and morale and how they affect combat. Usually included is the ability to design your own armies, maps and scenarios as well. However, with the General Staff Wargaming System we’ve added a new feature: the ability to control the realism level before playing a scenario.

The General Staff Wargame has two basic levels of play:

Simulation mode uses HQ units and a chain of command that passes orders down from the General HQ to the sub-commander to the individual unit. How fast the unit responds to the orders are affected by the distance that the courier must travel and the Leadership Value of the HQs.  Simulation mode also employs a more detailed combat resolution model and tracks the actual number of troops in every unit.

An example of Simulation Mode: the path (red line) and time (16 minutes) it will take for a courier to travel from JEB Stuart’s HQ to Munford’s cavalry with orders. Click to enlarge.

Kriegsspiel mode does not have HQ units and friendly units are moved directly and immediately (no transmission of orders via couriers). The combat resolution model is simpler and units have a value of 1-4 displayed by the number of unit icons on the map.

Antietam in Kriegsspiel mode. Notice that there are no HQ units (so no couriers to deliver orders) and units are represented by 1-4 icons. Units in column have a ‘tail’ that indicates the unit strength. Click to enlarge.

In addition to the two game modes (Simulation and Kriegsspiel) there are three Scenario Options:

Order of Battle (OOB) displayed / not displayed. Enemy units with known positions appear dark; enemy units ‘on the map’ but with unknown locations appear grayed out. This, of course, gives the user complete knowledge of the enemy’s OOB and, more importantly, knows when units from certain formations are not directly observable.

A mock up of how the Order of Battle option will appear (note this image was created from screen captures of the Scenario Editor and the Sand Box). Click to enlarge

Only friendly units directly observed by the General HQ are displayed. All other friendly units fade at their last known location. Couriers bring in unit location updates, but they are outdated by the time they arrive.

Only enemy units directly observed by the General HQ are displayed. All other enemy units fade at their last known location. Couriers bring in unit location updates, but they are outdated by the time they arrive.

If both of these above options are selected (only friendly and enemy units that are directly observable by your commanding General HQ) you will be simulating the Fog of War that field commanders of the age of gunpowder experienced.

What General George B. McClellan could actually see at Antietam. Screen shot (General Staff Sand Box). Click to enlarge.

We would like to hear from you and get your opinion on what realism features you will use in General Staff:

“What Ifs” at Little Bighorn

I‘m used to learning a lot when researching a battle but nothing prepared me for the ‘what ifs’ of Little Bighorn. My doctorate is in computer science but I have been an American Civil War buff since I was about five years old. I’m very familiar with brevet Major General George Armstrong Custer’s achievements during the Appomattox campaign where he commanded a division that smashed Pickett’s right flank at Five Forks. I knew that after the war Custer returned to his previous  rank in the U. S. Army of Lt. Colonel, that he fell under a cloud with U. S. Grant, was stripped of his command, and had to beg for it back from President Grant, himself, at the White House.

Brevet Major General George Armstrong Custer taken May 1865. Credit: Civil war photographs, 1861-1865, Library of Congress, Prints and Photographs Division.  Click to enlarge.

And, of course, I knew of the debacle at the Little Bighorn.

After I wrote UMS, the first computer wargame construction system, users began to send me Little Bighorn scenarios that included Gatling guns. I assumed that these were science fiction ‘what if’ scenarios. such as a story I read back in the ’60s about what if Civil War units had automatic weapons from the future. But, recently, while reading Stephen Ambrose’s Crazy Horse and Custer I learned that General Alfred Terry, Custer’s superior and the commander of the expedition, had indeed offered Custer not just three Gatling Guns (manned by troops from the 20th Infantry 1)The Guns Custer Left Behind; Historynet
https://www.historynet.com/guns-custer-left-behind-burden.htm
) but four extra troops from the 2nd U. S. Cavalry.  Custer turned down Terry’s offer of reinforcements and more firepower with these infamous words:

“The Seventh can handle anything it meets.” – Custer to Terry

Photo taken by F. Jay Haynes of one of the Gatling guns that were available to the 7th Cavalry. Click to enlarge.

Screen capture of the Order of Battle of the 7th US Cavalry with the addition of 3 Gatling guns and 4 companies of the 2nd US Cavalry. Click to enlarge.

As for the battle of Little Bighorn, itself, I didn’t know much more than the broad outline that Custer and his command were killed to the last man by an overwhelming number of Native American warriors (this, of course, wasn’t correct as members of Reno’s and Benteen’s columns survived). Custer, himself, was the text book image of hubris and became the butt of late night comedians and humorous pop songs. But the reality turned out to be much more complex and nuanced.

Custer had a reputation of being dashing, headstrong, and gallant; the iconic description of a cavalry commander. The traditional narrative of the disastrous battle of Little Bighorn is that Custer impulsively attacked a vastly superior enemy force; possibly propelled by a belief that Native American warriors were no match for organized cavalry armed with 45-70 trap door carbines. Indeed, Napoleon’s maxim was that, “twenty or more European soldiers armed with the best weapons could take on fifty or even a hundred natives, because of European discipline, training and fire control.” 2)Crazy Horse and Custer” p. 425 Stephen Ambrose To make matters worse, Custer had pushed the 7th mercilessly and by the time they arrived at the battlefield both men and horses were exhausted.

Custer’s plan of attack is also widely condemned as overly optimistic. He split his command of 616 officers and enlisted men of the 7th cavalry into three battalions. If the four companies of 2nd Cavalry had come along, Custer’s force would be 30% larger.3)Ibid The main force led by himself would be the right flanking column, Reno would have the left flanking attack column and Benteen and the pack train would be in the middle.  Custer also drastically underestimated the Native American force at about 1,500.

In theory, Custer’s plan of attack wasn’t that bad:

  • If Custer was up against a force that was only two or three times his size and
  • If Reno had pressed home his attack drawing the Native American warriors east toward him and
  • If Custer had been able to cross the Little Bighorn above the Native American camp and
  • If Custer had been able to attack the village while the warriors were engaged with Reno

Custer might have, indeed, had a great victory that would have propelled him to the US Presidency (as he had hoped). But none of these suppositions were correct.

Screen shot of the General Staff Scenario Editor where the battle of Little Bighorn scenario is being set up. Not the Order of Battle of the 7th Cavalry (with attached units of the 2nd Cavalry and Gatling guns) on the left. Units are positioned by clicking and dragging them from the Order of Battle Table on the left onto the map. Click to enlarge.

So, the question remains: what value for Leadership would you give to Custer?

Screen shot of the General Staff Army Editor showing the slider that sets the Leadership value for a commander. What value would you give Custer? Click to enlarge

By the way, there will be three separate Little Bighorn scenarios for the General Staff Wargaming System: historically accurate Order of Battle for the 7th Cavalry, the 7th Cavalry plus four companies of the 2nd US Cavalry and 7th Cavalry plus four companies of the 2nd US Cavalry and 3 Gatling guns.

References   [ + ]

1. The Guns Custer Left Behind; Historynet
https://www.historynet.com/guns-custer-left-behind-burden.htm
2. Crazy Horse and Custer” p. 425 Stephen Ambrose
3. Ibid

New Battles on Old Battlefields

Plate 1 from, “The American Kriegsspiel. a Game for Practicing the Art of War upon a Topographical Map,” by W. R. Livermore, Captain, Corps of Engineers, U S Army published in 1882. Click to enlarge.

When I was about ten years old my father brought home an original copy of Esposito’s The West Point Atlas of American Wars. My life was forever changed. I had always been interested in military history and maps but now I could clearly see the complexity of tactical maneuvers and how these battles unfolded.

In previous blogs, I have written about my introduction to wargaming through Avalon Hill’s superb games. While diving deeper into the history of American wargaming I discovered Livermore’s American Kriegsspiel (by the way, it is available online from the Library of Congress here). When I first saw Plate 1, above, I couldn’t help but think of the officers at West Point, ‘practicing the Art of War’ on that black and white map.

Consequently, one of the first things that I wanted to do with the General Staff Map Editor was bring Plate 1 back to life so new battles could be fought on it:

The American Kriegsspiel map imported into the General Staff Map Editor and converted for use with the General Staff Wargaming System. Grid lines are optional. Click to enlarge.

My good friend, Ed Isenberg, did the colorization and we added some new features in the Map Editor to support importing rivers, roads and other terrain features, from a PhotoShop image (for more information see the online documentation for the Map Editor here).

Importing the American Kriegsspiel map into the General Staff Wargaming System was a good beta test of the Map Editor. If you are an early backer you should have the location and password to download it. If, for some reason, you don’t have these, please contact me directly.

One of the interesting features of the General Staff Wargaming System is that any two armies created in the Army Editor can be combined to create a battle scenario on any map created in the Map Editor. Thinking about all the ‘mix and match’ combinations I decided to create an army, in the Army Editor, from the Order of Battle Table (OOB) for the French Imperial Guard, August 1, 1813 from George Nafziger’s, superb “Napoleon at Dresden,” book:

The French Imperial Guard Order of Battle in the General Staff Army Editor. Click to enlarge.

We are currently beta testing the General Staff Scenario Editor. Here I’ve imported the American Kriegsspiel map (from above) and the French Imperial Guard (from above). To position units, just click and drag from the OOB on the left:

Screen shot of the General Staff Scenario Editor where the French Imperial Guard is being positioned on the original American Kriegsspiel map. Click to enlarge.

Hopefully, this will get your imagination going and thinking about what maps, armies and scenarios you would like to see. In addition to the ability to create your own new scenarios on old battlefields, General Staff will ship with 30 historical scenarios (the list is published in previous blogs).

Please feel free to contact me directly if you have any questions.