Engagement at Arnhofen

Yesterday evening saw the second play of the latest Command Post game, Engagement at Arnhofen. It is the first game for my 'new' Napoleonic project and features my Bavarians and Austrians.

The game is based on the action around Arnhofen, Abensberg and the Seeholz (trust the Bavarians to name a wood after a lake) on April 19th of 1809. This was, after the Austrians crossed the Isar at Landshut against moderate opposition from Deroy's III Division (Bavarian), the first action in the 1809 campaign featuring Bavarians engaging the Austrian invader. While the action on the day was more of an encounter battle, with reinforcements arriving during the day for both sides, the wargame was a more classic set up, with part of the forces deployed on table and the rest moving onto the table at the start of the game.

Yesterdays game was played with a full house of players: Eddy and Phil took the Austrians while Alan and myself played the Bavarians (helped for one turn by my daughter :) ).

The Austrian players decided to deploy their on table command on the far side of the Seeholz woods, aiming to move to a defensible position at the edge of the fields below them and waiting for the arrival of their second brigade moving up the table. The Bavarian cavalry deployed behind the hills, with the Chevaulegers in skirmish formation and the Dragoons in column along the road, ready to dash forward should the need arise.

And so, as distant gunfire rolled across the hills (the battle of Teugn-Hausen was fought at the same time historically), the armies set out to engage each other.

The contribution of the Bavarian cavalry brigade to the following battle is easiest dealt with. Due to a remarkable lack of initiative from the brigade commander (read: bad command rolls throughout the evening) the cream of the Bavarian horse did not participate in the action, apart from some ineffectual shuffling about. While their mere presence did keep the Austrian Dragoons stationary for most of the game, one imagines that the brigade commander would have been spoken to in quite stern tones by his division commander later in the evening.

The rest of the battle developed as two separate fights. On the Bavarian left, the Austrian battalions of the Kaiser regiment (1IR) were attacked by half of the Bavarian infantry brigade, while on the right, the Lindenau regiment (29IR) tussled with the other half of the Bavarian infantry. The Bavarians, having the advantage of interior lines, were able to move units between both assaults while the Austrians, being separated from each other by the Seeholz forest, had to fight their individual battles by themselves. This is a picture of the initial stages of the battle, where the left flank fight was already underway while the right was still maneuvering:



When the smoke and dust settled and stock was taken of the situation by the end of the wargame evening, the Austrian brigade under Thierry was found to be broken. The brigade under Richter was still engaged but had one unit broken, one lost in the woods and had just had the brigade commander killed (we forgot that yesterday :) ). The Bavarian cavalry, on account of not doing much at all, was in still in perfect condition. The Bavarian infantry brigade, having bore the brunt of the fighting (well, all of it, really) was also broken (every single unit in it was shaken at the end of the last turn). So, in the spirit of the historical battle, the wargame was declared a hard fought draw, with maybe a slight advantage to the Bavarians. But then again, I played with the Bavarians so I would say that wouldn't I?

I'll leave you with some pics from the game. First up is the textbook attack of three Bavarian battalions on the left flank. The rightmost battalion would not participate in the final melee but move to the right flank to support the fight there.



Next is the situation on the right flank at the end of the game. The Austrian battalion engaged at the top of this photo and accompanied by the brigade commander was broken in that melee.



And finally the end at the left flank:



The scenario for this game will be posted once I've drawn some maps for it :).

And another convert

Some time ago, one could admire some teddy bears painted by my daughter. It seems I have a new convert:



That's a spare Victrix French Grenadier who is in the process of becoming 'the orange hunter'. Blue, white, brown and pink ones were to follow.

Crusade of Light convention

On 10 September, Gaming Club Fallen Angels in Leuven together with De Witte Ridder from Leopoldsburg are organizing their first joint convention, titled Crusade of Light:




We will be there with our Holowczyn game.

The entry is free, so there's no reason not to go and support this new convention :)

Bavarian Generals

Some freshly painted Bavarian leadership. First up, Kronprinz Ludwig, commander of the 1st Division in 1809:



Next up, GM Von Zandt, commander of the cavalry brigade of 1st division:



And finally, GM Von Rechberg, commander of the 1st Infantry Brigade of said division:



The figures are Front Rank (Ludwig & Von Zandt) and Foundry (Ludwig's escort from 1st Chevauxlegers and Von Rechberg). The size difference between these two makes is obvious when one compares the figure of Ludwig with his midget escort :)

The Lanchester Model for Combat explained with an application to unit activation mechanisms

First of all, this is a long post, so I apologize for those who are used to short snippets.
If you don't want to read the whole thing, skip to the conclusions in section 4. Or if you don't even want to do that, here's the conclusion verbatim:

If you want to write a ruleset that rewards manoeuvring, be sure the rules allow to inflict as many casualties proportional to the number of units. If you want a ruleset that puts less emphasis on manoeuvre, and more on clever use of terrain, use a fixed number of units that can activate every turn.

Anyway, the long story:

When I was reading through some old issues of Wargames Illustrated, I came upon the model of battle proposed by Frederick Lanchester during WW1 ('Aircraft in Warfare: The Dawn of the 4th Arm'). The fundamental question he was faced with was how to judge the relative strengths of 2 opposing forces, and more specifically two groups of aircraft facing each other.

This led to the well-known 'law of squares': when 2 forces are meeting each other, and when trying to predict the outcome of battle, one should take the square of their strengths, subtract them from each other, and take the square root of the result. The outcome is the number of soldiers/units/... left to the numerically biggest side.
E.g. suppose Red with 10 soldiers (or units, tanks, aircraft ...) is facing Blue with 6 soldiers. Let's also assume the quality of soldiers on both sides is equal. Red, due to its numerical superiority, will be victorious. But how many soldiers will Red have left after the fight? Lanchester's law provides the answer: 10.10 - 6.6 = 100 - 36 = 64; sqrt(64) = 8; hence Red will have 8 soldiers left after all Blue's soldiers have been eliminated. This is a simple example, but Lanchester's model also allows for the difference in troop quality to be factored in.

The classic application of Lancester's model is to show how a large force can be defeated by a smaller force, by splitting the large force in 2 smaller forces and defeat them one by one. Real-world examples cited in this context usually are Trafalgar or a number of Napoleonic battles. Suppose Red has 8 soldiers/unit/ ... and Blue has 10. Through clever manoeuvring Red has managed to split Blue's force in 2 halves, one of 4 strong and another of 6. Red takes on the first half first, emerging victorious with sqrt(8.8-4.4) = sqrt(48) = 7 soldiers. Red then continuous to battle the remaining Blue force of 6 soldiers, again victorious with sqrt(7.7-6.6) = 3.6 units left.

This model is simple enough, and relatively well-known, but as I was reading through the article, I was wondering what the underlying mathematical model was; exactly what assumptions were being made; and how it could be applied to some issues of games design. Often, the assumptions stated are along the lines of: 'What's important is that all units involved have an equal opportunity to kill or to be killed'. This seemed a bit vague to me, so I thought I could quickly reconstruct the mathematics myself by applying some discrete probablistic Monte Carlo model, but never arrived at the square law. So, I was even more intrigued about the underlying mathematics.

Theory

A quick search on the net provided me with the following article (2006), which explains the mathematical model underlying Lanchester's model (download pdf from http://arxiv.org/abs/math.HO/0606300 - Warning: this article uses differential equations, so if you're not familiar with those, stay away :-)). The fundamental assumption is as follows: During a unit of time, the number of casualties lost on side A, is proportional to the number of troops on side B. Or, in other words, if your opponent would have twice the number of troops as he has now, he would inflict twice as many casualties on you. The number of casualties inflicted scales linearly with your troop number. Is this is a valid model? The idea is that ALL of your troops add to the casualties inflicted: every tank/soldier/plane shoots at the enemy all the time during the battle. No troops are held in reserve, no troops are kept away from the fight.

Now, over time, both sides will lose troops, linearly proportional to the number of troops on the other side. By integrating the underlying equations, the square law as stated above is achieved. More specifically, the square law states: R(t).R(t) - B(t).B(t) = constant, with R(t) and B(t) being the number of troops at any point in time t. Since the constant value will never change, the sign of the difference never changes, and the strongest side always wins. Since the equation holds at time 0 (when the battle starts), we can say that for any point in time:

R(t).R(t) - B(t).B(t) = R(0).R(0) - B(0).B(0)

When the battle ends at time tfinal (and without loss of generality, we assume R is the biggest force, and hence Red wins), we have:

R(tfinal).R(tfinal) = R(0)*R(0) - B(0).B(0)

or

R(tfinal) = sqrt(R(0).R(0) - B(0).B(0))

The interesting thing is, that is you changes the assumptions, a different model comes out. Suppose that the number of casualties inflicted over a unit of time is not proportional to your strength, but is a fixed number. E.g. you have 100 soldiers, but only 5 are ever engaged, and when these are eliminated, others step in. Your actual number of 100 soldiers is not relevant for the casualties inflicted, but only the 5 you throw in the fight during a given time unit.
Using similar principles, the following equation is arrived at:

R(t) - B(t) = constant

or when the battle ends:

R(tfinal) = R(t) - B(t).

In other words, Red is still victorious, but only with the difference of actual numbers in troops left. Hence the linear comparison of strengths, not the quadratic comparison.

So, in order to keep as many troops alive at the end of the battle, you should throw in ALL of your force (square law), and not enter the battle piecewise (linear law).

A quick example:
Suppose Red attacks a force of Blue of 6 with 10 soldiers.

• According to the quadratic law (ALL units are engaged in battle all the time and inflict casualties), Red wins with sqrt(100-36) = 8 soldiers left. Tactically, this means all 10 soldiers of Red are thrown at all 6 soldiers of Blue in one big attack.
• According to the linear law (fixed number of casualties per time unit, e.g. units pick each other off 1 by 1), Red still wins, but only with 4 soldiers left. Tactically, this means that e.g. both sides send in 3 soldiers first (they eliminate each other). Then, both sides send in the next 3 (kill each other as well). Red remains with 4 soldiers. Note that the fixed number (3 in this example), is rather irrelevant (the example works with any number small enough).

Tactical Consequences

As stated above, the main advantage of the square law is that you can defeat a bigger force by trying to split the force in half. Would this also work in case of the linear law? Working out a few examples show that it doesn't. There is no advantage in cleverly outmanoeuvring your opponent - at the end of the battle the linear difference is always the result. But it does pay off to do that when the square law is in effect.

Now, let's go to the wargaming table. Our unit of time is the turn. So, during a single turn, can you inflict a number of casualties equal to your strength, or only a fixed number of casualties irrespective of your strength? And will it affect your tactics?

• Suppose the number is fixed (linear law): clever manouvring doesn't help (see above). The only thing you can do to gain an advantage on top of the linear difference is to try to prevent your opponent from killing his quotum in any given turn. How can you do that? By making it more difficult for your opponent to hit you (e.g make use of terrain and go into cover).
• Suppose the number is proportional to your strength (quadratic law). Now, if you are the weaker force, you have every interest to try to outmanoeuvre your opponent and hitting with everything you can on small chunks of his force. So taking the initiative is much more important than when the linear law would be in effect.

Whether we are working in one model or the other is governed by the rules system. So, the rules used might affect your tactics on the wargaming table.

Application to unit activation

Let's consider 3 broad categories of unit activation in wargaming rules:

1. All units are activated during your turn all the time (classig IGO UGO).
2. Only a FIXED number of units are activated during your turn. Examples are card activation such as Memoir44/Battlecry: typically on average, you can expect to activate 2 units, irrespective of the total number of units in your force. Or e.g. in rules like Black Powder or Blitzkrieg Commander (roll against command value to activate a unit), you can activate an (expected) fixed number of units per turn per commander. It doesn't matter whether the actual number activated is by itself a stochastic variable - what does it matter it that it does not depend on the total number of units in your army.
3. A number of units PROPORTIONAL to your total force is activated. E.g. in a card-driven system, you can vary the # cards played, or change the content the single card you can play during your turn. When using rules that use general activation as the central mechanism, command quality of generals or the number of generals should scale with the number of units. However, it should remain proportional over the course of the battle. E.g. if you lose units, the number of units you can activate in one turn should scale down proportionally (less cards can be palyed, generals should also be lost, etc...). Otherwise, if this last thing doesn't happen, you're really in case b.

In case 1, the quadratic law applies: all units can attack in every turn, and you can expect to inflict casualties equal to the number of troops. So, manoeuvring and splitting the opponent's force is a valid tactic.

Case 2 results in the linear law. It doesn't matter that much how many units you have, the stronger force usually will win (everything else being equal, of course). In a game such as Memoir44 this is very obvious: since you only can activate a fixed number of units each turn, your excess units are actually a reserve - attacking in force and using your numerical advantage is often not possible in the sense of the quadratic law.

Case 3 is again the quadratic law, providing the amount of units that can attack each turn scales down linearly as you lose units. Keeping the same #cards (or quality), or keeping the same #generals (or quality), actually moves you to case b.

The analysis above makes of course abstraction from other factors: initial setup, the amount of units that can be thrown at the enemy given their dispositions at the start of the turn, etc. But it's always possible to make the analysis on subparts of the battlefields.

Conclusion

If you want to write a ruleset that rewards manoeuvring, be sure the rules allow to inflict as many casualties proportional to the number of units. If you want a ruleset that puts less emphasis on manoeuvre, and more on clever use of terrain, use a fixed number of units to activate every turn.

I know this is a long piece of text, but I hope that some game designers did find this useful. I was mostly intuitively familiar with most of the concepts outlined here, but having written them up concisely actually clarified my thinking a bit.

Ingermanlandski Regiment

It's been a while but here's some stuff I painted again. This is the Russian Ingermanlandski Regiment of the Great Northern War.



The Ingermanlandski was a regiment raised in Ingria, the bit of Russia that Peter nicked from the Swedes and build St. Petersburg in. They were a high profile regiment, being paid to the same level as the Guard Regiments.

The figures are Musketeer Miniatures, the flag is scanned from a uniform book I own (for the nitpickers, yes, it's the 1712 pattern flag, so after the 'highlight' of the Great Northern War) and the flag tassel is from Front Rank Figurines.

Even though my focus is now shifting to Napoleonics, I do plan to occasionally paint some things for the Great Northern War, and this was one of them. One cannot have a Russian GNW army without the Ingermanlandski, and that oversight has now been corrected.

The battle of Holowczyn: scenario

Update February 2, 2016: Apparantly the link was broken to the document describing the scenario. This link is now restored.

We've fought this one twice now, and there's at least one more time to follow, so I think the scenario is as finished as it will get. Here's the battle of Holowczyn.

Big Joe and friends

And away West we go:



These will feature in the next 'big scenario game' at my place. Incidentally, I've come up with a name for these, with thanks to Eddy to suggest part of it. As of now, they will be called Command Post games. Playing with toy soldiers tends to involve commanding them, and I live above a post office -- hence the name :).

And now for something completely different ...

Just painted:

Shootist in 54mm

I recently tried my painting skills at some old 54mm Britains Deetails Old West cowboys. These figures have been in my collection for almost 40 years - I got them when I was a kid aged 5 or 6 as a ‘Sinterklaas’ gift (Belgians and Dutch wargamers will know what this means, and for all the others: it’s the original Santa Claus in the low countries). The original Britains figures are very crudely painted; they are toy soldiers after all. I completely repainted the figures, maintaining the original color schemes, but applied some layering to give the figure more depth. Since I also wanted to maintain the toy soldier look, I didn’t go overboard with painting too much detail. The sculpting of the figures don't really allow it either.

I couldn’t resist setting up some scenes using my old wooden fort (same Sinterklaas gift), adding some scenery items from my wargaming collection.

Shootout at the Oklahoma - Minneapolis crossroads. The roadsign is also over 40 years old and is part of my wooden fort set.

Two gunmen defending their hideout. The 'Dead Man's Gulch' sign is also from the Britains Deetail range.

Shootout in front of Fort Delaware.

Just for comparison, below you see a picture (ripped from the internet somewhere) showing original Britains Deetail figures - but in different color schemes. Apparently, there was a lot of variation to be found in the painting style when they were sold. Britains Deetail figures were apparantly sold mostly during the seventies.

A complete overview of the Britains Deetail range (Wild West figures) can be found here: http://www.angelfire.com/biz/toysoldierhq/Britwestd.html

I still have some Indians and US Infantry figures lying around as well, but I think I'll return to painting 28mm figures for now.

Update: In the mean time I discovered that the oval-shaped bases date from a later period, and that the square-based bases are the original early-seventies ones. So somehow, some 'newer' figures have entered the box in which everything was kept in the attic during all those years. Perhaps my younger brother acquired some figures during later years, and they were all tossed together. I also don't exclude the possibility I bought some additional figures myself when I already started wargaming, but I have no recollection of that. Fact remains, I did receive a wooden fort with some cowboys and indian figures when I was a 6-year old kid :-)