Most games are mostly mathematical. The mathematics might be probability, graph theory, logic, functions or any of dozens of other fields (one field of mathematics that has relatively little to do with traditional games is game theory – go figure).

Kruzno shares many mathematical features with chess and checkers such as a strong reliance on graph theory and logic, but Kruzno also has a couple of highly unusual features that give the game a unique dimension.

Intransitivity

Capturing in Kruzno is intransitive: bishops capture knights; knights capture rooks; rooks capture bishops. Intransitivity is extremely rare but real-life examples are not hard to find. Cases of intransitivity in voting have been widely studied. You can also demonstrate intransitivity in a probability problem with these special dice.

Permutation

Because a piece in Kruzno can jump over so many other pieces, not just those it can capture, the number of possible moves can be very large (often larger than in chess). As with most games, the number of possible sequences of moves tends to grow exponentially with the length of the sequence, but since Kruzno has so many possible moves each turn, the growth is unusually steep.