The Length of a Hnefatafl Game

Saturday, 4th June 2016

One can always rely on Aage Nielsen for measurements and a good analysis of hnefatafl games.  The number of players on his site, and the sheer number of versions of hnefatafl that can be played there, make it a mine of statistical data.

Recently he published an interesting table that measures the length of games for different variants.  Alongside the simple mean average of moves per game, he has also calculated the moves for games that ended in victory for the king, and moves for games that ended in the king's loss.  And there are some interesting results.

Tablut, which is by far my preferred set of hnefatafl rules, gives the same average game length for both attacker wins and defender wins.  This is in keeping with its good balance in terms of victory for each side, which is approximately the same as that of chess.

The table overall shows some interesting patterns.  It shows generally that the bigger the game, the longer the attackers will take to achieve their victory: not just overall, which you'd expect for a bigger game, but in comparison to the defenders.  In Brandub, with its 7x7 board, the attackers on average win more quickly than the defenders.  At the other end of the table, the 11x11 Fetlar Hnefatafl game makes its attackers work nearly twice as long as the defenders to win a game.

So far, this makes sense.  The king can get from one end of the board to another in a single move.  Though he may have more defenders to clear out of the way before he escapes, the number of pieces shouldn't affect his strategy as much as it does the attackers, who have no quick single move to victory.

Another pattern is that corner exit games are even more extreme: Copenhagen and Fetlar Hnefatafl come bottom of the table for game length.  Both of these games have an 11x11 board, but they come below the 13x13 Sea Battle Tafl variant.  This I can't explain as easily.  I would have thought that a king who has to fight his way to a corner would have a longer battle to fight.

I'd be very interested to see a similar analysis on more variants.  The game Magpie has a slow king, who can move only one space at a time: does this affect his speed of victory in the manner one would expect?