It is possible to run the game in a Euclidean hex grid and compare. For example:
* In Euclidean open space, if you are attacked by two adjacent monsters at once, you cannot escape, because the monsters would just move in parallel lines. In hyperbolic, you can, because parallel lines do not work.
* In Euclidean open space, if you are ambushed by many (say, 12) monsters on all sides, you cannot escape. In hyperbolic, you can. There is always more directions than it seems.
* In Euclidean open space, if you are attacked by two adjacent monsters at once, you cannot escape, because the monsters would just move in parallel lines. In hyperbolic, you can, because parallel lines do not work.
* In Euclidean open space, if you are ambushed by many (say, 12) monsters on all sides, you cannot escape. In hyperbolic, you can. There is always more directions than it seems.
There is a land Hunting Grounds which teaches the tactics above. It simply does not work in Euclidean mode. There is also this article: http://zenorogue.blogspot.com/2012/03/hyperbolic-geometry-in...