Modern Innovations: Altered Ratios

Saturday, 27th June 2015

One of the things that unites hnefatafl games is the ratio of attackers to defenders. In addition to the king, hnefatafl games will always have twice as many attackers as defenders at the start of the game. Well, nearly always. For people have experimented with this, too.

There's plenty of historical evidence that the ratio of attackers to defenders was a constant 2:1 regardless of the total number of pieces. Two Irish poems tell us that brandub had a king and four guards against eight enemies. Linnaeus tells us the exact makeup of a tablut game: a king and eight against sixteen, and the Ancient Laws of Wales describe a similar game. Robert ap Ifan tells us that later in Wales, a king and twelve defenders face 24 attackers. So far, all 2:1 ratios.

Archaeological evidence is much less firm, but has to account for the possibility that any set of pieces found is possibly incomplete. So at Scar there is a king and eight against thirteen. The magnificent set at Birka has a king and eight against seventeen: this could be explained either as a partial 37-piece set or a set with, for reasons unexplained, a spare attacker.

One set that has inspired some modern reconstructions is that at Gunnarshaug in Norway. The division of different piece types is of the ratio 1:4:12. The singleton is the largest, the quartet next in size and the twelve are the smallest. I've seen a couple of versions like this: one for sale and one as a (now sadly disappeared) set of rules on-line. Both use the 7x7 board.

A change in the ratio of the game would have to be accompanied by changes in the rules, to maintain the balance between the altered forces. A king with a reduced number of defenders may need to have some advantage conferred upon him to compensate for his loss of forces. This is not altogether certain, as a less congested board in itself favours the king.

Another alteration I've seen is to have a king and eight defenders against twelve attackers. Floyd & O'Flaherty's verion of brandubh, pictured, follows this pattern on a 7x7 board. They adjust the rules such that the king may move only to an adjacent square, until he reaches the edge of the board when he may move any distance along its edge.

A game called Break Away, part of the Hi Q collection by Gabriel, adopts the same 1:8:12 ratio of pieces but on a 9x9 board. As in Floyd & O'Flaherty's game, the king's movement is restricted to adjacent squares, this time with no exceptions. Gabriel did provide four extra attackers in the box to allow the standard tablut to be played, too.

A more recent game to adopt is Nuts, devised by the Formby hnefatafl club. While it is described as a new game "based on hnefatafl", the rules are close enough to be considered a hnefatafl variant. It adopts a ratio of one "acorn" (king) and eight red squirrels against 24 grey squirrels, playing on an 11x11 board. To compensate for the reduced defending force, the red squirrels are given safety on the central 3x3 section of the board, and the "acorn" has only to be escorted to the edge of the board (the forest), rather than the corner as in the hnefatafl games on which it is based.

Other descendant games have adopted their own ratios of pieces. Breakthru has twelve destroyers against twenty, and Thud! has eight trolls against 32 dwarfs. But their rules have been made different enough that their design would not be held back by the 2:1 ratio of hnefatafl pieces.

Before I finish the article, honourable mention should go to hnefatafl games like the one by Shannon games, which uses a king and six defenders against twelve attackers on a 7x7 board. While that adheres to the 2:1 ratio of attackers to defenders, it departs from a related characteristic that binds most hnefatafl games together: the fact that both of the forces are a multiple of four. The adoption of six defenders means that the board cannot be laid out in 4-way radial symmetry like other hnefatafl games.

As we have seen from this blog series, hnefatafl encompasses a broad variety of different combinations of rules. Ancient variants of the game had their differences, and so the modern ones are no less valid. For those who are not seeking pure historical authenticity, modern versions of the game provide an interesting and fresh variety of interest to players and game designers alike. This post concludes the series on modern innovations: if you think I've missed an obvious one, please get in touch!