In a previous tafl post, I remarked on the lack of pre-defined notations and mathematical resources for tafl games. In this one, I will remark on a more fundamental deficit: namely, this is the first article I can find on the Internet which will attempt to define a standard for timed tafl games.
Surprising? Well, yes and no. Competitive tafl games are rarely played in person. The only live tournament (in the modern era, anyway) put on to date was run by the Fetlar Hnefatafl Panel, and as tournaments go, it was a fairly casual affair—the games were untimed, with a gentleman’s agreement not to take an undue amount of time per move. The other major tafl tournaments are run at Aage Nielsen’s site, and are correspondence play: timed, but not in the sense we’re looking for here.
The Fetlar panel suggests using a regular chess clock, but that seems unappealing to me. Broadly speaking, tafl games are defined by two stages: an opening, where the two sides jockey for position and control in the corners, and an endgame, where the king has left his throne and is pushing to one corner. The length of the opening doesn’t vary much for a particular board size, and generally speaking, features thoughtful, cautious play. Once the king leaves the throne to start the endgame, the flavor of play changes dramatically. The king’s side must make bold, sweeping moves, and the besieging side must split its attention between putting out fires and shoring up its leaky positions. What was a game of edging around the opponent and building one’s own structure becomes a head-on conflict.
The similarity to battle is striking, and suggests a method of timing that mirrors the structure of the game. Go players among the readership will be familiar with the concept of byo-yomi, a kind of overtime comprising a number of periods of a given length. If you don’t use all of one of your byo-yomi periods, you get it back in full. If you do use it, you move onto your next one. I suggest a tafl timing scheme using a small amount of main time, and a relatively generous overtime allocation. My thinking is this: the main time ought to be used for the opening, and once the endgame begins, the players should be nearly out and into overtime. I don’t have good information on how tafl games play out yet, but as a rough starting point, I would suggest a main time of about ten minutes, and three to five overtime periods of one minute each. More generally, I propose this mutation from a single main-time chess clock: for a given chess clock length in minutes (say, 60), divide by six to get the tafl main time (10, in this case). Divide that by ten to get the length of the overtime periods. Depending on the desired difficulty and clock sensitivity, set the number of overtimes to somewhere between two and six.
Not only does this mirror the calm-to-intense structure of tafl games, it also serves a practical purpose. Although tafl games and chess appear to have similar distributions of game lengths1, I get the feeling that the most competitive chess games are clustered around the average more than the most competitive tafl games2 are. An adaptive time control like byo-yomi frees endgames from the tyranny of the clock. Some games will end up playing out more quickly, and won’t feel clock pressure at all; I don’t feel that this is an indictment of the scheme. Some games will end up playing out at around the average length, where the clock is set perfectly: players will feel some time pressure, but have sufficient main time to lay their plans for the endgame. Some games, finally, will end up running longer. With an ordinary chess clock, a longer game would end with increasingly desperate time pressure. With byo-yomi time, the clock remains a driving force, but doesn’t get much worse with time.
Although I do propose this system for general use, I plan on different time controls for the AI-vs-AI tournament: no main time, and three ten-second overtime periods. Quick-play tournaments are known to be as effective as long-play tournaments in sorting AIs by relative skill level, and a large number of five-minute games is a much easier task for yours truly than a large number of thirty-minute games.
In final news, you can find v0.1.7.1b here, which fixes a few bugs in 0.1.7 and adds threefold repetition rules.
- The standard deviation for game length in number of moves for chess comes in at about 25, based on correspondence games listed here, some eyeballing of graphs, and some math based on histogram values, and 11×11 tafl games come in at 23, taken in aggregate, from Aage Nielsen’s tafl tournament history. Neither of these figures are set in stone, for reasons I’ll go into when I write up my findings.
- Aage Nielsen’s tournament history, above, has a large number of games between top players in the vicinity of 40 moves, and a nearly equal number at 70 to 90 moves.