Tag Archives: Wargames

The Problem With Hexagons

Hexagons are ubiquitous in wargames now (indeed, both Philip Sabin’s War: Studying Conflict Through Simulation Games and Peter Perla’s The Art of Wargaming feature hexagons on their book covers), but this wasn’t always the case. My first wargame – the first board wargame for many of us – was Avalon Hill’s original Gettysburg  (by the way, $75 seems to be the going price for a copy on eBay these days).

No hexagons in Avalon Hill’s original Gettysburg. Remember how the map contained the original starting positions for the Union cavalry and out posts? From author’s collection. (Click to enlarge)

The American Kriegsspiel by Captain Livermore (circa 1882) only had a map grid for estimating distances. We also have a map grid in General Staff to facilitate estimating distances but you can turn the map grid on or off.

Plate 1 from The American Kriegsspiel by Captain Livermore. Click to enlarge. This image is from GrogHeads wonderful blog post on Nineteenth Century Military War Games. Link: http://grogheads.com/featured-posts/5321

And how about this picture from the Naval War College (circa 1940s)? I just needed an excuse to post this photograph:

A Fletcher Pratt Naval War Game in progress. I never understood why they didn’t use upside down periscopes to check broadside angles rather than getting down on the floor. Click to enlarge. From this blog http://wargamingmiscellany.blogspot.com/2016/02/simulating-gunfire-in-naval-wargames.html

It is pretty common knowledge among the wargaming community that Avalon Hill’s owner, Charles Roberts, introduced hexagons to commercial wargaming in the early 1950s .

“Later, he [Roberts] saw a photograph of one of the RAND gaming facilities and noted they were using an hexagonal grid. This grid allowed movement between adjacent hexagons (or hexes, as they are more frequently called) to be equidistant, whereas movement along the diagonals in a square grid covered more distance than movement across the sides of the squares. Roberts immediately saw the usefulness of this technique and adopted to his subsequent games.”

The Art of Wargaming, Perla, p. 116

In researching how the RAND Corporation – a major post-war defense think tank – came up with the original idea of employing hexagons to simplify movement calculations (as well as the invention of the Combat Resolution Table or CRT) I stumbled upon an amazing document: Some War Games by John Nash and R. M. Thrall (Project RAND, 10 September 1952; available as a free download here). Yes, that is THE John Nash; A Beautiful Mind John Nash; the Nobel Prize recipient John Nash. The Some War Games summary states:

“These games are descendants of the one originally instigated by A. Mood, and are both played on his hexagonal-honey comb-pattern board. – Some War Games Nash & Thrall.

But what appears on Page 1A of Some War Games is even more exciting:

The earliest reference of using hexagons for wargames. “The board is a honeycomb pattern of hexagonal “squares,” the same that was used in Mood’s game” – From Some War Games (Project RAND, Nash & Thrall).

Sadly, I have been unable to find an actual copy or documentation for “Mood’s game,” but did discover that A. Mood was a statistician who wrote the popular text book, “Introduction to the Theory of Statistics,” and, during World War II was involved with the  Applied Mathematics Panel and the Statistical Research Group. Moore was also the author of, “War Gaming as a Technique of Analysis,” September 3, 1954 which is available as a free download here. Unfortunately, I have yet to uncover any images of Moore’s original war game and the very first use of his ‘honeycomb pattern’ board.

Let’s take a quick look at the math behind hexagons:

The cost of moving diagonally as opposed to horizontally or vertically on a map board (from a slide in my PhD Qualifying Exam on least weighted path algorithms).

The problem of quick and easy movement calculation (as shown in the above graphic) is caused by the Pythagorean Theorem. Well, not so much caused, as a result of the theorem:

The distance to a diagonal square, d, is the square root of the square of the hypotenuse (the side opposite the right angle) which is equal to the sum of the squares of the other two sides. We all learned this watching the Scarecrow in the Wizard of Oz, right?

In other words, if everybody could just multiply by 1.41421356 in their heads we wouldn’t even need hexagons! The downside, of course, is now we’ve restricted our original eight axes of movement to six. And there’s another problem; what I call the, “drunken hexagon walk.”

An example of “drunken hexagon walk” syndrome. All we’re trying to do is go in a straight line from Point A to Point B and from Point A to Point C.

In the above diagram we just want to travel in a straight line from Point A to Point B. It’s a thirty degree angle. What could be simpler? How about traveling from Point A to Point C? It’s a straight 90 degree angle. It’s one of the cardinal degrees! What could be simpler than that? Instead our units are twisting and turning first left, then right, then left like a drunk stumbling from one light post to another light post across the street. In theory the units are actually traversing considerably more terrain than they would if they could simply travel in a straight line. This is the downfall of the hex: sometimes it simplifies movement; but just as often it creates absurd movement paths that no actual military unit would ever take.

So, what’s the solution? Clearly, there is no reason why a computer wargame should employ hexes. Computers are very good at multiplying by 1.41421356  or any other number for that matter. Below is a screen shot of General Staff:

Screen shot of General Staff (2nd Saratoga) based on the map of Lt. Wilkinson, “showing the positions of His Excellency General Burgoyne’s Army at Saratoga published in London 1780)  . Click to enlarge.

What’s missing from the General Staff screen shot, above? Well, hexes, obviously. Units move wherever you tell them to in straight lines or following roads precisely if so ordered. And units can obviously face in 360 degrees. Consider this screen shot from the General Staff Sandbox where we’re testing our combat calculations:

Screen shot from the General Staff Sandbox. Notes: 3D unit visibility is turned on, displayed values: unit facing, distance, target bearing, enfilade values, target offset. Click to enlarge.

For board wargames hexagons seem to be a necessary evil unless you want to break out the rulers (that never stopped us with the original Gettysburg or Jutland). But, when it comes to computer wargames, I just don’t see the upside for hexagons but I do see a lot of downside. And that’s why General Staff doesn’t use hexes.

 

 

 

 

 

 

 

 

A Wargame 55 Years in the Making (Part 2)

After The War College I created a couple of non-wargames including Online Mysteries, a massive multiplayer online mystery game that was written for AOL’s WorldPlay. WorldPlay was envisioned to be a 3D online world populated with avatars. It was similar in concept to Second Life but, like a lot of great ideas, was ahead of its time. AOL shut WorldPlay down before most of the games, including Online Mysteries, launched.

Mysteries Unlimited screen shot (Windows) was a massively multiplayer online mystery game created for AOL/WorldPlay (click to enlarge).

Mysteries Unlimited screen shot (Windows) was a massively multiplayer online mystery game created for AOL/WorldPlay (click to enlarge).

By 2000 the game publishing industry  was going through another convulsion of consolidations, buyouts and contractions. Publishers were producing fewer games but the ones that were being created had large teams, long development cycles and massive budgets. The days when an independent developer could pitch a game idea, get an advance and then develop it outside of a publisher’s studio were gone. And the last thing that the big publishers were interested in were wargames.

Over the previous fifteen years I had received inquiries from active duty military and Pentagon project managers about my wargames (known as Commercial Off The Shelf, or COTS, in Pentagon-lingo) and if I would be available to consult on various wargaming projects. Unfortunately, I was lacking a key prerequisite for this: a doctorate. I returned to academia, first to a small local college where I also taught computer game design and in 2003 I was accepted in the computer science PhD program at the University of Iowa (one of the oldest computer science departments in the world).

Before I ever set foot in MacLean Hall (the home of the Department of Computer Science at the University of Iowa) I knew what I would spend the next six years of my life researching and studying: tactical and strategic AI (I would eventually coin the phrase ‘computational military reasoning’ to describe this field).  What I soon discovered was that very little work had ever been done in this research area. What was even more surprising was my discovery that most ‘professional’ military wargames (i.e. wargames used by the US Army, NATO, England, Australia, France, etc.) had absolutely no AI whatsoever. Instead, they employed ‘pucksters’ (usually retired military officers) who made all the moves for OPFOR (Opposition Forces, AKA ‘the enemy’) from another computer in another room.

Pucksters, or humans (usually retired military officers) who make the decisions and moves for enemy (or OPFOR) units during a wargame.

Pucksters are humans (usually retired military officers) who make the decisions and moves for enemy (Opposition Forces = OPFOR) units during a wargame. Note the sign OPFOR & EXCON (Exercise Control) over the puckster’s work station.

To earn a doctorate at an American ‘Research One’ university requires 90 graduate credits (about 30 classes), a GPA > 3.5 (out of 4.0) and passing three major examinations. The first examination on the road to a doctorate is the Qualifying Examination (or Q Exam as everyone calls it). The topic of my Q exam was “An Analysis of Dimdal’s (ex-Jonsson’s) ‘An Optimal Pathfinder for Vehicles in Real-World Terrain Maps’.” This is the area of computer science and graph theory known as ‘least weighted path algorithms’. GPS devices and Map apps use a least weighted path algorithm, except they’re only interested in roads; they don’t consider terrain, slope and other things (that are important to a military unit maneuvering on a battlefield).

Now, if you were to wander into the ivied halls of academic computer science  (like MacLean Hall) and inquire of a tenured faculty member how to calculate the fastest path between two points on a sparse grid they would almost certainly reply to you, “Dijkstra’s algorithm.”  Dr. Dijkstra invented his algorithm in 1956 and it works like this: first calculate the distance between every point on the map and every other point on the map. Then figure out the fastest path. Yeah, it’s that obvious, and painfully slow. In fact, it’s so slow that it isn’t used for GPS or game AI. In computer science we us ‘Big O’ notation to describe how fast (or slow) an algorithm takes to run. Dijkstra’s algorithm runs in O(|V|2). This means that as the number of vertices, or points on the map, (that’s the |V| part) increases, the time it takes for the entire algorithm to complete goes up by the square of the number of vertices. In other words, as the map gets bigger the algorithm gets a lot slower.

Dimdal, and I and most of the gaming world do not use Dijkstra’s algorithm, Instead we use A* (pronounced ‘A Star’) which was designed in 1968 primarily by Nils Nilsson with later improvements by Peter Hart and Bertram Raphael. Below is an example of A* used in General Staff (note that the algorithm doesn’t look at every point on the map, just ones that it thinks are relevant to the problem at hand). A* runs in O(n) time.

A screen shot of A* algorithm running. The green areas are where the algorithm searched for a least weighted path, the brown line is the shortest path (mostly following a road).

A screen shot of A* algorithm running. The green areas are where the algorithm searched for a least weighted path, the brown line is the shortest path (mostly following a road).

Graph showing the difference between Dijkstra's algorithm and the A* algorithm. The blue line that increases rapidly shows that Dijkstra's algorithm gets much slower as the map gets bigger. A* is not affected as much by the size of the map.

Graph showing the difference between Dijkstra’s algorithm and the A* algorithm. The blue line that increases rapidly shows that Dijkstra’s algorithm takes much more time as the map gets bigger. A* (the green line) is not affected as much by the size of the map.

As part of my research into computational military reasoning I made further modifications to A* to take into effect the slope of the terrain (which can affect speed of some units), the range of enemy units (OPFOR ROI, e.g. areas controlled by enemy artillery) and to avoid enemy line of sight (LOS). My MATE (Machine Analysis of Tactical Environments) project used all of these options:

A slide from my presentation to DARPA showing how my modified A* avoids enemy range of weapons.

A slide from my presentation to DARPA showing how my modified A* avoids enemy range of weapons. The likelihood of taking casualties is indicated by the darkness of the red coloring.

While working on General Staff I came up with a new optimization of the A* algorithm which I’ve called EZRoadStar. EZRoadStar first looks at the roadnet and attempts to utilize it for rapid troop movement. Only after ascertaining how far using roads will get it to its goal does the algorithm look for nonroad paths. EZRoadStar is much faster than traditional A*; especially for wargames and military simulations.

An example of the EZRoadStar least weighted path algorithm. What's the fastest way point A to point B (the yellow line)? Taking the road, of course. This algorithm looks at a battlefield like a commander and utilizes the roadnet first before looking at other options. Click to enlarge.

An example of the EZRoadStar least weighted path algorithm. What’s the fastest way from point A to point B (the yellow arrow)? Taking the road, of course. This algorithm looks at a battlefield like a commander and utilizes the roadnet first before looking at other options. Click to enlarge.

Well, this wargame may be 55 years in the making and it looks like describing some of the key things that went into it may take almost as long. Clearly, I’m going to have to continue this story with yet another post. We’ve just barely scratched the surface of my work on wargame AI. The next installment will (hopefully) cover algorithms for ‘the five canonical offensive maneuvers’ (i.e. The Envelopment Maneuver, The Turning Maneuver, Penetration, Infiltration and Frontal Assault. These are the algorithms that are ‘under the hood’ of General Staff. If any of my readers would like to know more about these topics (links to my published papers on the subject or whatever) please drop me a line at Ezra [at] RiverviewAI.com.

 

A Wargame 55 Years in the Making

I was introduced to wargames (Avalon Hill, of course) about 55 years ago when I was seven years old by my buddy Carl Hoffman who lived down the street. Carl and I ended up owning every Avalon Hill wargame and we played them all. Eventually, Carl and his family moved away (I think Carl became a professor at LSU but I can’t confirm that) and I was faced with the grim realization that all of us Grognards inevitably confront: there was nobody to play wargames with.

Tactics II from Avalon Hill. The first wargame I played. What was the first wargame you played?

Tactics II from Avalon Hill. The first wargame I played. What was the first wargame you played?

Over the years I would occasionally find someone interested in playing  (or, more likely, coerce a friend who really had little interest in wargames) to set up a game but rarely would we ever complete a full campaign or battle.  By the late 1970s playing wargames for me was a rare event (the one exception being my good friend from my undergrad college days, Corkey Custer). Then, about this time, I saw an episode of PBS’s NOVA on what was then the infancy of Computer Graphics (CGI). There, flickering on my black & white TV, was what we would eventually call ‘wire frame’ 3D. Wire frame 3D just shows the edges of 3D objects. They are not filled in with a texture (as CGI is done now). Computers just didn’t have the processing power to pull this off back in the late ’70s and ’80s. But, I immediately thought to myself, “this technique could be used to render 3D battlefields!” And that was the spark from UMS: The Universal Military Simulator was born.

Screen capture of the original UMS running in 640 x 400 x 2 resolution in MS DOS. This is an example of wire frame 3D.

Screen capture of the original UMS running in 640 x 400 x 2 resolution in MS DOS. This is an example of wire frame 3D.

By the mid 1980s I was about to graduate with a bachelor’s degree in computer animation and, more importantly, a working demo of UMS. I had hypothesized that one of the biggest selling points of computer wargames was the ability to always have an opponent handy (the artificial intelligence or AI). I borrowed a copy of the Software Writers Market from the library and sent out dozens (maybe even hundreds) of letters and, eventually, papered an entire wall of my apartment with rejection letters from game publishers. But, Dr. Ed Bever, who designed Microprose’s Crusade in Europe, Decision in the Desert and NATO Commander (pretty much the only computer wargames that were out at the time) saw my pitch letter and gave me a call. Microprose wasn’t interested in publishing UMS per se, rather their CEO, “Wild Bill” Stealey, wanted me to come work for Microprose (and they would own UMS). That deal didn’t appeal to me but a short time later, at the 1986 Consumer Electronics Show in Chicago, Ed Bever introduced me to Microprose’s competitors, Firebird/Rainbird. Within 48 hours I had my first game publishing deal.

Crusade in Europe from Microprose (1985) designed by Dr. Ed Bever, originally programming by Sid Meir.

Crusade in Europe from Microprose (1985) designed by Dr. Ed Bever, originally programming by Sid Meir.

UMS sold about 128,000 units and was the #1 game in the US and Europe for a while.

The European Microdealer Top 30 Chart with UMS as #1 with a bullet on the 16 game chart. What other classic games can you find on the charts? (Click to enlarge)

The European Microdealer Top 30 Chart with UMS as #1 with a bullet on the 16-bit game chart. What other classic games can you find on the charts? (Click to enlarge)

Ed Bever helped on the design of UMS II: Nations at War which was an extremely ambitious global wargame that had unprecedented detail and allowed the user to edit numerous variables and equations:

UMS II: Nations at War screen shots from the MS DOS version. Click to enlarge.

UMS II: Nations at War screen shots from the MS DOS version. Click to enlarge.

UMS II screen shot (Macintosh) showing active weather systems.

UMS II screen shot (Atari ST) showing active weather systems.

An example of the numerous variables that the user could adjust in UMS II. Click to enlarge.

An example of the numerous variables that the user could adjust in UMS II.; in this case adjusting the attrition level based on experience for ground units. Macintosh screen shot. Click to enlarge.

UMS II was named “Wargame of the Year” by Strategy Plus magazine and enjoyed strong sales. In many ways it was the ‘ultimate’ in complex wargaming.  It was far more detailed than any other wargame I’ve seen before or since (and that includes my work on DARPA, Department of Defense, US Army, Office of Naval Research and Modeling Simulation Information Analysis Center (MSIAC) wargames. Ironically, it was published by Microprose because they bought out Firebird/Rainbird and with it my publishing contract.

My next wargame, in 1993, was The War College.  We used data from US Geological Survey to create the 3D maps. Again, it was very detailed and allowed the user to edit combat values and featured an interactive hyperlinked history of each scenario (it shipped with Antietam, Austerlitz, Pharsalus and Tannenberg). Unfortunately, our publisher, GameTek, pretty much ceased to exist just as we were about to release this game. To this day I have no idea how many units it sold. We never got a royalty statement.

Screen shot (MS DOS) of the Austerlitz scenario in The War College. Click to enlarge.

Screen shot (MS DOS) of the Austerlitz scenario in The War College. Click to enlarge.

The War College also had an interactive history for each battle (screen shot from MS DOS, click to enlarge).

The War College also had an interactive history for each battle (screen shot from MS DOS, click to enlarge).

The War College allowed users to adjust melee effectiveness and values. MS DOS screen shot, click to enlarge.

The War College allowed users to adjust melee effectiveness and values. MS DOS screen shot, click to enlarge.

I also would be terribly remiss if I did not mention my good friends who worked on various ports of the above mentioned games, Ed Isenberg (Amiga and MS DOS), Andy Kanakares (Apple IIGS and MS DOS) and Mike Pash (MS DOS).

(left to right) Ed Isemberg, Andy Kanakares, Ezra Sidran. Not pictured; Mike Pash.

(left to right) Ed Isemberg, Andy Kanakares, Ezra Sidran. Not pictured; Mike Pash.

One of the problems of getting old is that your stories get longer to tell. This blog post is far longer than I intended and we haven’t even got to this century and all my research into computational military reasoning (Tactical and Strategic AI) and my new wargame, General Staff.  I’m afraid we’ll have to end this here and pick up the story in Part 2 next week.

GrogHeads Interviews Dr. Ezra Sidran

Grenadier of the Old Guard in 1813; an original Grognard. Public Domain from Wikipedia

Grenadier of the Old Guard in 1813; an original Grognard. Public Domain from Wikipedia

GrogHeads, a blog for very serious wargamers, recently interviewed our Dr. Ezra Sidran. The interview can be found here. The term ‘grognard‘ (French for ‘grumbler’) came from Napoleon’s Old Guard; who were the only unit that had the privilege of grumbling in the Emperor’s presence. The term grognard is now used to describe very ‘hard core’ wargamers.

We were very happy for this opportunity to talk about wargames with interviewer Jim Owczarski.

Please jump over to GrogHeads and take a look at this interview and look around.

Announcing a new computer wargame: General Staff!

I am extremely pleased to announce the development of my first new computer wargame in over twenty years: General Staff.  The decision to write a new wargame came about because I simply couldn’t find a computer wargame that I wanted to play. Yes, I know, there are dozens – if not hundreds – of really good computer wargames out there; but none of them appealed to me at the moment.

Most computer wargames have taken advantage of the ability of the computer to handle scores of complex rules and hundreds of units. This often resulted – and I want to make clear that as a designer I was also guilty of this – in massive wargames that weren’t all that fun to play. Sure, they were incredibly accurate. Indeed, I would market my wargames as simulations; because that’s what they were. And, truth be told, they were as good, if not better, than many computer simulations currently used by the world’s largest armies, Defense departments and ministries.

A slide from my Computer Game Design class at the University of Iowa.

A slide from my Computer Game Design class at the University of Iowa. Click to enlarge.

However, what I was looking for was something simple and fun. When I taught Computer Game Design at the University of Iowa I would tell my students that these kind of games were sometimes referred to as, “Beer & Skittles” games. They were simple, fun and addictive. Yes, I wanted to think (I didn’t want just a twitch game). I wanted something strategic or tactical; but I certainly didn’t want to get involved in micro-management of  logistics, factory production and national will. I just wanted to have fun.

Modern Kriegspiel (Waterloo).

Modern Kriegsspiel. Click to enlarge.

About this time I read an article about wargaming in Nautilus magazine. The one thing that caught my eye was an illustration for the article of Kriegsspiel. Kriegsspiel was a  wargame invented in 1824 and used by the Prussian staff for training. A very good article about the original Kriegsspiel can be found here. It has been recreated from time to time and I recently found this picture of a modern version.

I don’t think there’s been a modern computer version done of Kriegsspiel; at least I haven’t been able to find one. So I decided to create it.

This blog will be about the development of General Staff. Your comments and questions will be greatly appreciated.