A Risk board represents the map of the world, or of Europe. Thus, it implies some constraints for example on the connectedness of a territory.

I would like to explore how graph theory could help your strategies, and on which measure would a change of the node number and degree change them. Are there any variants of this game that are played on an arbitrary graph? (Yes, I realize that it wouldn't be in the spirit of a war game at that point.)


2 Answers 2


The computer game Lux is Risk, but with a huge number of custom maps and themes. You can also create your own maps using their map editor.

Many of the maps include additional rules, such as time-based continent values or starting positions.

If you're interested in Risk played on arbitrary graphs (nb. including directed graphs!) then I think this would be a great place to start investigating.


There are additional maps available for Risk. The most obvious is "Castle Risk" using just Europe. They don't substantially alter the play that much; sufficiently little that the other themed variants need other special rules to make them worth playing apart from the original world map.

That said, I've not seen any with a pure-grid topography. Not that it would be terribly hard to play it that way...

There is a variant with a regular pattern, but it's not a grid: Fleets. Fleets uses sectios of rings, in a clear pattern. It also uses a stacking limit of 1, so it has a very different feel.

I have played Fleets without the stacking limit; it turns out to be very much worse that way. Whomever gets the most territory early (a luck driven factor) wins the game as production is tightly linked to territory.

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .