Category Archives: Game Design

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 Map of Waterloo Created by an Eyewitness

Screen shot of the Map of Waterloo painted by an Eyewitness from Antiques Roadshow. This image has been brightened and the contrast increased for legibility. Click to Enlarge.

I happened to be watching Antiques Roadshow from Exeter on BBC America last night when this extraordinary map of the battle of Waterloo was presented. Though it bears no date or signature, it clearly was painted, “by an Eyewitness” shortly after the battle itself. I was immediately struck by the lettering  and how similar it was to our efforts in General Staff to recreate the look and feel of 19th century maps for our wargames.

Below is the link to the entire segment hosted on the BBC web site:

Link to Antiques Roadshow BBC clip, “Map of Waterloo A beautifully detailed map of the 1815 Battle of Waterloo drawn by an unnamed eyewitness.”

A Tale of Two Wargames

I first conceived of General Staff as a very simple, introductory wargame that might be the first real wargame to be released for the Xbox (clearly, an under-served market). However, two things stopped this plan dead in its tracks: first Microsoft closed down the independent online games channel for Xbox and then, after being approached by a major wargame publisher, I was told that there was, “no market for wargames on the Xbox,” however a new version of my UMS series, could, “sell 25,000 units in its first year.”

So, I went back to the proverbial drawing board but I also asked you, the Grognards, what kind of a game you wanted. And here are the results:

Clearly, almost as many people want a simple, Kriegsspiel type game as want a complex military simulation.

After pondering this conundrum I had an epiphany: ‘simple’ wargames and ‘complex simulations’ actually share about 80% of the same code and data. Why not make a wargame that the user can decide which he wants to play? Sometimes people aren’t up for hours long complex simulations; other times people are.

Screen capture from General Staff showing the set up for ‘Simulation’ mode (note the button in the upper-left hand corner). Click to enlarge.

In the above screen capture the user has selected ‘Simulation’ mode. Note that there are headquarters units displayed. Headquarters play an important role in General Staff in simulation mode. All orders are given through the commanding general to the subordinate commander (via courier) and then (again via courier) to the actual unit. For example:

In this screen capture an order from Marshal Beresford will take 8 minutes of game time to be delivered to ths subordinate commander. (Click to enlarge)

It will take 8 minutes for the courier to ride from Marshal Beresford headquarters to the subordinate’s headquarters.

It will take an additional 6 minutes for a courier to deliver the order to the subordinate infantry unit. Click to enlarge.

Additional time (based on the headquarter’s Leadership value) will be added before the next courier is dispatched to deliver the order to the infantry unit. So for a command to go from Marshal Beresford, to Major General Stewart to Colborne’s Brigade will take a minimum of 14 minutes of game time plus additional time penalties based on the leadership abilities of Beresford and Stewart.

Detailed information about a unit in Simulation mode. Even the number of volleys remaining are tracked. Click to enlarge.

Lastly, the leadership of Colborne’s Brigade is used to calculate how quickly the unit will act upon the received orders. This is an example of the detailed Simulation mode for General Staff.

However, in Kreigsspiel mode,  all headquarters units are removed and the user issues orders directly to the units that immediately respond to the commands.

General Staff in Kreigsspiel mode. Note the button in the upper left-hand corner, headquarters units have been removed and unit strength is either 1,2,3 or 4.

Also, all unit information except a simple value (1-4) is ignored. Kriegsspiel mode is the simple, introductory wargame that I originally envisioned.

 

Announcing the Scenario Editor!

The Scenario Editor Module for General Staff allows the user to combine any two armies created in the Army Design Module with any map created in the Map Design Module and create a scenario or battle. In the screen capture before we’ve combined the Allied Anglo-Portuguese Army from the Battle of Albuera (May 16, 1811) as the Blue Army with Napoleon’s Imperial Guard as the Red Army and placed them on a map of our own design.

Screen shot of the General Staff Scenario Editor. Note that the time to deliver orders via courier between units is displayed. Click to enlarge.

Also, note that when you slick on a headquarters unit the route, distance and time that a courier will take to deliver orders to the next subordinate unite are displayed. This is just the beginning because General Staff is actually two wargames in one.

We will be posting a video showing off some of the new features shortly.

 

 

Victorian Typography

Last week we ran a quick survey to get your opinion on the legibility of two Victorian typefaces (see here). The clear favorite was the font ‘Monastic’ garnering 73% of the votes. However, we also received numerous personal emails and comments from grognards that were also very fond of the Phectic font. The decision was made to go with Monastic but to use Phectic in a larger point size when appropriate.

Below is a screen shot of how we will be using Phectic:

Screen shot of the Unit Types information display. The ornate Victorian font at the top is Phectic.

Your comments were greatly appreciated (it was especially enjoyable to hear from a letterpress operator who fondly remembered metal type). The interactive Army Design Module is almost completed and we will be posting a video of it shortly.