Board Games Round the World

Sunday, 29th September 2013

I have two books in my collection aimed at schools, one of which covers hnefatafl. This is "Board Games Round the World: A Resource Book for Mathematical Investigators", written jointly by Robbie (a.k.a. R. C.) Bell and Michael Cornelius, and published in 1988. I've chosen this as my Sunday Read for this week.

Arranged a bit like the teacher's edition of a school text book, Board Games Round the World uses the games to stimulate mathematical investigation. It is split into main sections of games of position, mancala games, war games and race games. Each section gives the history and rules of the games, and then goes on to pose questions leading to mathematical and strategic investigation of the games. A final section contains a chapter of answers and comments on the questions.

Hnefatafl is covered in the form of tablut. The unbalanced rules of J. E. Smith and H. J. R. Murray are used, where the king reaches an edge to win, can capture other pieces, and is captured by being surrounded on all four sides. This does not stop the game from being popular with the pupils: the authors' experience was that the pupils enjoyed the game so much they neglected the theoretical study!

The questions posed range from the arithmetic to the strategic. The first question asks the number of opening moves available to each side, taking into account the symmetry of the board. It goes on to ask which are the best. The answer section gives only the numbers of moves and does not discuss the strategy at all.

The second question is an odd one: the number of moves in which each side could win, assuming that the opponent is an idiot. For instance, the king in tablut could win in three moves, but to do so would necessitate the attacker himself opening up a path. I am not sure what strategic value the question has, except for generally encouraging the pupils to investigate the game.

The third question is interesting and open ended, inviting the reader to consider altering the number of pieces on each side. It points out that the king with no defenders would easily win; his route to the edge would be too quick for the attackers to block. The conclusion in the comments section goes only part way towards an answer, pointing out that the game is finely balanced as reducing either side favours the king. However, it is apparent that the authors didn't consider increasing the number of pieces; studies of ard ri and other over-populated games shows that a crowded board would favour the attackers.

I don't know if such a book would fit the curriculum today, which teachers complain of being overly restricted. I was at school at the time the book was published, and would love to have worked from it. Perhaps it would have brought my interest in traditional board games forward by a decade and a half!