  Before chess came to Northern Europe there was Tafl, a family of asymmetric
strategy board games associated strongly with the Vikings. The purpose of this
paper is to study the combinatorial state-space complexity of an Irish
variation of Tafl called Brandubh. Brandubh was chosen because of its
asymmetric goals for the two players, but also its overall complexity well
below that of chess, which should make it tractable for strong solving.
Brandubh's rules and characteristics are used to gain an understanding of the
overall state-space complexity of the game. State-spaces will consider valid
piece positions, a generalized rule set, and accepted final state conditions.
From these states the upper bound for the complexity of strongly solving
Brandubh is derived. Great effort has been placed on thoroughly accounting for
all potential states and excluding invalid ones for the game. Overall, the
upper bound complexity for solving the game is around 10^14 states, between
that of connect four and draughts (checkers).
