A cylindrical map would still have an up-down middle. For true middle-less-ness you need to get your hands on a toroid.

Mmmm, donut shaped universe...

Or if you're not a big nerd you could use a sphere.

The problem is that the cylinder would be relatively easy to implement, although it would still be pretty hard. Making the maps fit on a sphere or especially a toroid seems like it would be pretty tough.

On a toroid you could have more players, because the number of colors needed for the map would be greater. On a plane, cylinder, or sphere, four colors are sufficent for any two adjacent countries not to have the same color. On a toroid, eight colors would be needed. So that would suggest what? 14 players?

or just be able to attack any territory from any territory ;)

skrumgear i totally dont get your point. Why would there be a need for more or less colors?
What has that to do with the nature of the map being a plain cylinder sphere or toroid surface?

Anyhow i dont embrace the idea too much to be realised in any near future. its worth a thought though.

"Or if you're not a big nerd you could use a sphere."
A toroid is far easier to implement: connect the bottom with the top and left with right, et voila.

Anyway, it would be interesting to see maps without a middle, it would even out the chances more.

But it could take away from some of the strategy. A wise kdicer builds from the coasts. Having a middleless map would institute more luck and less strategy. Something that we all hate.

Madwilly: The more countries that can touch each country, the more ways connections can be made. Also, each country can have more attackers at the same time. Since there are more ways to connect, it would make sense to balance the game by having more potential attackers.

cylindrical... toroid....

Could we just start with a couple of east-west links?

A correction of my earlier post on toroidal maps. Seven colors are sufficient for a toroidal map. If indidivual countries are small, in a small area of a toroidal map there is no difference from an ordinary planar map. A maximum of four countries can touch all the others. But on a toroidal map there can be seven contiguous empires, all of which are touching all the others, while on a planar map there can be only four such empires while the other three players are sidelined.