It's a power in the corner of the board.

David Norman (david@ellought.demon.co.uk)

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What do you mean, you can't have that short an article???

OK then... Take 2.

This question recently came up while discussing Diplomacy AIs, and how to analyse a map before play begins. All Diplomacy players with any experience know that England and Turkey are corner powers, and Germany and Austria are central powers. And we all know that as a corner power, England and Turkey can pretty much choose to attack whichever neighbour they like, while Germany and Austria cannot — if they attack each other, it's suicidal, and it's not much better if Germany attacks Russia, or Austria attacks Italy.

But if an AI (or indeed a human player) is going to play on a non-standard map, then before the game, they need to work out which are the corner powers, which are the centre powers, and for the centre powers, which powers can they afford to fight with.

But what is a corner power? What is it that gives England and Turkey this freedom, and takes it away from Germany and Austria.

To understand the problem a little more, take a look at this map:

(Has your head stopped hurting yet???)

This is the Standard map, but redrawn. The grey rectangle in the centre is "Edge of the board". The outside edge of the map is Switzerland. Only five provinces touch the edge of the map — from the top left blue supply centre going clockwise, Marseilles, Piedmont, Tyrolia, Munich and Burgundy — the five provinces that normally touch Switzerland. The whole map is inside out!

The effects of this are Austria, Germany, Italy are now edge powers, while Turkey, England and Russia are centre powers. And yet all the provinces, supply centres and adjacencies are the same — if you played on this map (and your head didn't explode), you'd have exactly the same game as on a Standard map. So clearly it's not just being in a corner that makes it a corner power.

Further analysis of the Standard map (or the inside out map if you prefer!) shows something else that is actually a far better indication. A corner power is a power that can enclose a relatively large number of centres with a relatively small number of provinces. Taking England first, using just four provinces — NWG, NTH, ENG and MAO, it can enclose three centres.

And Turkey can do even better. With just five provinces — Sev, Rum, Ser, Alb, ION, it can enclose five centres.

Note further, that the "enclosed" centres are not including those on the boundary province. This is for two reasons. Firstly, by having the boundary outside the centres, it shows a defensive position where the enemy has to push the corner power back, and then make further progress in order to get to the rewards. This makes the attack a far less attractive proposition. Secondly, including the centres could give misleading results — e.g. Tri-Vie-Bud-Rum-Ser is five provinces enclosing five centres! However, to enclose the centres without using those provinces requires eleven provinces — which is what makes Austria a centre power.

There are other groups of centres that could be considered for Austria, but all of them have a number of border provinces which greatly exceed the number of enclosed centres.

So how do these central powers cope with this huge border? They do it by creating fake edges — DMZs. Germany is a good example of this. The best border for Germany is Bur-Bel-NTH-SKA-Swe, which encloses five centres with five provinces. However, this leaves a huge gap through BAL-Pru-Sil-Boh-Tyr. But fortunately in most games, these provinces are agreed DMZs with Russia and Austria.

But the obvious question is, why is it this way around? Why not have the DMZs with England and France in Bur-Bel-NTH-SKA-Swe, and the border provinces as BAL-Pru-Sil-Boh-TYr?

Russia and Austria also need a fake edge — a DMZ, while England and France don't. We've already seen that England is a corner power. It doesn't need any more edge to protect it, so trying to agree to a DMZ while Germany turns his back is very unlikely to be adhered to by England.

France does need a DMZ. However, it is much more natural for it to arrange one with Italy than with Germany. France, like Germany, needs to defend his border with England, and having set up that part of a line, it is much more effective to continue the defensive line around onto the German border than to have a second, completely separate border with Italy while DMZing the German border. Also, there is a lot bigger space between France and Italy than between France and Germany, so it's a lot harder for Italy to mount a surprise attack on France through the DMZ than it is for Germany.

On the other hand, we've already seen how long a border Austria has to try and work with, so anything which shortens this edge is much appreciated by Austria, and so it will readily accept and adhere to such an agreement. Equally, Russia also has a very long border compared to the number of centres it has, and so it also welcomes any DMZ it can get. This makes Russia and Austria much better candidates for a DMZ than France.

DMZs also work far better when they use non-supply-centres. The edge with England and France is running through neutral supply centres, which if Germany wants any involvement in, is quickly going to bring it into contact with France and Germany. The edge with Austria and Russia on the other hand, are all non-supply centres, so there is nothing to gain by entering the DMZ, either power would have to cross through the DMZ and out the other side in order to make any gains from it.

So having established what makes a corner power, let's have a look at a variant. The following is the African map. This is a six power variant — Ivory Coast (Purple), Libya (Green), Saudi Arabia (Yellow), Ethiopia (Blue), South Africa (Red) and Zaire (Brown).

Examining the map, we find two of these powers are definitely corner powers. Ivory Coast has seven border provinces enclosing eight centres, and South Africa also has six border provinces enclosing six centres. Saudi Arabia can do almost as well, it has six border provinces enclosing five centres.

Saudi Arabia, Ethiopia, and Zaire are definitely centre powers. It is therefore clear that Ethiopia and Zaire must not attack each other. They are the only two powers that need to get a DMZ from somewhere, and so much agree one with each other.

Libya has seven border provinces containing six centres.

However, it has some issues with both Saudi Arabia and Ivory Coast, as it's optimal enclosed centres include optimal enclosed centres from both the others! Without these, it is far more like a centre power — seven provinces enclosing three centres.

It should therefore probably also set up DMZs with Ethiopia and Zaire, which suggests that this variant may regularly be three centre powers allied against three outer powers. Unfortunately for Libya, this doesn't help it much, as its borders with Ethiopia and Zaire are very short. It also suggests that Libya needs to fight Ivory Coast early, in order to gain a more stable position, although fortunately it can reach both Morocco and Spain before Ivory Coast can, so it should reach this more stable position, although this still only gives it seven border provinces to hold five centres.

So with the DMZs set up, we now have Zaire holding eight centres with eight border provinces, Ethiopia holding four centres with five border provinces, and Libya holding five centres with seven border provinces.

All together, this would suggest that Libya is probably the weakest power in this variant. Without enough centres to hold a border, and without any natural DMZs, it is always going to be vulnerable to an attack by someone who has no reason not to do so.

In summary, when presented with a new variant (or when trying to write a Diplomacy AI), first work out which are the centre and which are the corner powers. From this, work out which powers need for form DMZs, and this should then lead to working out which powers can ally which are likely to fight, and which have common enemies.

David Norman (david@ellought.demon.co.uk)

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