General rules

Tafl rules
Hagbard
Posts: 405
Joined: Sat Mar 14, 2015 6:07 pm

General rules

Post by Hagbard » Wed Jun 24, 2015 11:01 pm

Through experience from thousands of tafl games some general rules for all tafl variants have emerged.

Board.
Always quadratic, the width an uneven number of squares. Used are 7x7, 9x9, 11x11, 13x13, 15x15 and perhaps 19x19.

Pieces.
Always one king, and number of attackers = 2 * number of defenders.
The usual number of tafl game pieces is the Walker number p = 6w - 29, where p is the number of pieces and w is the width of the board in squares (hat tip: Damian Walker).

Initial ordering.
The king is on the centre square, surrounded by his defenders.
The attackers occupy the central edge squares.
The ordering is rotationally symmetrical.

Three types of king:
Armed king, captured from 4 sides (strong king).
Armed king, captured from 2 sides (weak king).
Unarmed king, captured from 4 sides (sea battle cargo ship).

Forbidden squares.
A sea battle board has no forbidden squares.
Only the king can stop on a forbidden square, but all pieces can pass through it.
If the king wins in corner, then the board has four forbidden corner squares. If the king wins on edge, there are no forbidden corner squares.
A forbidden square is hostile against all pieces, but if it's occupied by the king, it's hostile only against attackers.
If the board has a throne (forbidden centre square), then the king must always be captured by 4 attackers when he is on the throne. And by 3 attackers + throne when he is on one of the four neighbouring squares to the throne.

Capturing.
All pieces except the king are captured from 2 sides by custodian capture.
Forbidden squares are hostile and take part in custodian captures.
A weak king is captured from 2 sides like all other pieces, except if he is on or next to a throne.
A strong king is captured from 4 sides everywhere on the board. An unarmed king (sea battle) likewise.

Attackers win.
Attackers win by capturing the king.
The attackers can also win by encircling all defenders.

Defenders win.
Defenders win when the king escapes. In some variants he escapes to a corner, in other variants he escapes to the edge.

Repetition forbidden.
Perpetual repetitions are forbidden. If the overall board position is repeated three times, the player who maintains the situation ("the threatening player") must find another move to break the repetitions, or else he loses the game.
The player who does the side stepping with a piece in order to find an open path to break through, is the threatening player who must find another move. The other player brings his piece in line with the threatening piece in order to block the open path and is the blocking player.

Compulsory move.
If a player can't move, he loses the game.


These general rules actually cover it all for all game variants used here (except for a few specials: Copenhagen, Fetlar, Berserk and Magpie).
Left is only one varying parameter: the precise initial ordering of each game variant. Thus the initial ordering is the parameter, which tunes the balance of the game.
Last edited by Hagbard on Fri Aug 14, 2015 12:13 pm, edited 5 times in total.

crust
Posts: 127
Joined: Sat Mar 21, 2015 9:29 am

Re: General rules

Post by crust » Fri Jun 26, 2015 12:26 am

Excellent summary Hagbard. I can't think of anything to add except maybe that the starting position always has the king in the centre, surrounded by the defenders, and the attackers always occupy the central edge squares. The position is rotationally symmetrical, and usually cruciform, but there is some room for experimentation in the placement of both attackers and defenders, particularly with the larger boards.

Also, in Brandubh at Dragonheelslair, the King may be captured on two sides even when he is occupying the throne square, which is not hostile. I strongly prefer your version of Brandubh.

I like Damian's equation for the ratio of pieces to board size - I guess Ard Ri is no good because it violates this principle.

Hagbard
Posts: 405
Joined: Sat Mar 14, 2015 6:07 pm

Re: General rules

Post by Hagbard » Sat Jun 27, 2015 12:11 pm

Yes, a section about ordering is missing; could be:

Initial ordering.
The king is on the centre square, surrounded by his defenders.
The attackers occupy the central edge squares.
The ordering is rotationally symmetrical.

crust
Posts: 127
Joined: Sat Mar 21, 2015 9:29 am

Re: General rules

Post by crust » Sat Jun 27, 2015 5:40 pm

Yes, sounds good! This is a good general description of the Tafl family of games.

Hagbard
Posts: 405
Joined: Sat Mar 14, 2015 6:07 pm

Re: General rules

Post by Hagbard » Sat Nov 07, 2015 11:01 pm

Yet some general reflections.

Balance.
It's often been claimed that game balance is not that crucial, because any size of unbalance can be overcome by always playing two games, one of each color.

Reductio ad absurdum, this argument would be equally valid for a perfectly unbalanced game: white always wins and black never. Playing two games, swapping colors, would always give one win to each player. And all players would come out equally strong. Though one could call such playing fair, no one would bother to play such a dull game. Fairness lies in the swap of colors, but the fun lies in the balance!


Catching.
Balance alone is not enough. Fx. test games show that The "Old Hnefatafl 11x11", which is described on multiple sites on the internet, has about the same balance as Fetlar 11x11. However it apparently by far doesn't catch the players' interest the same way as does Fetlar. For a year the "Old Hnefatafl" was the default game of this site (aagenielsen.dk), and through that period new players disappeared as quickly as they came. Somehow the game didn't catch them. I (and other players) suspect that the fault of Old Hnefatafl is the capturing of the king next to a corner by two attackers only. This makes it annoyingly difficult to get the king to a corner, and it inhibits many of the fierce and interesting corner fights you see in Fetlar.
Despite same balance, Fetlar is a catching game, and "Old Hnefatafl" apparently is not.


Throne or not throne.
Historical sources indicate that some tafl games (fx. tablut) have a throne (forbidden king's square in center) and others not (fx. tawlbwrdd).

The adding or not adding of a throne could've been used as simply a means to balance the game, when necessary. Especially the vulnerable tablut king, captured from two sides only, is well protected in center by a throne. Some test games indicate that adding a throne can shift the balance roughly +1, i.e. if the balance without a throne is fx. -1.8, it could be +1.2 with a throne added.


Test games and the internet.
On this site (aagenielsen.dk) we have till now tried 83 tafl variants, with emphasis on variants described in historical sources, described in important books and articles, used in commercial releases or used in reenactment milieus. (Hat tip Damian Walker, Sten Helmfrid and others).

Through test games via the internet the game balances of many variants have been measured . Till now about 600 players around the world did about 10,000 games of various tafl variants. The most accurate of the balance measurements is now based on 2800 games.

For comparison, a Canadian study of variants was based on 48 games done by a few fellow students. And the archaeologist behind the Skalk variant writes that he tested his ideas in games against a few colleagues.

I believe that a testing and study to the extent we're doing here, has not been done before. It's been possible thanks to the internet, since the 600 players are scattered over a large part of the world and the 10,000 games were done via the net.

crust
Posts: 127
Joined: Sat Mar 21, 2015 9:29 am

Re: General rules

Post by crust » Tue Nov 17, 2015 1:57 pm

That was a fascinating article, Hagbard, thanks so much for taking the time to write and post it.
Hagbard wrote:Test games and the internet.
On this site (aagenielsen.dk) we have till now tried 83 tafl variants, with emphasis on variants described in historical sources, described in important books and articles, used in commercial releases or used in reenactment milieus. (Hat tip Damian Walker, Sten Helmfrid and others).

Through test games via the internet the game balances of many variants have been measured . Till now about 600 players around the world did about 10,000 games of various tafl variants. The most accurate of the balance measurements is now based on 2800 games.

For comparison, a Canadian study of variants was based on 48 games done by a few fellow students. And the archaeologist behind the Skalk variant writes that he tested his ideas in games against a few colleagues.

I believe that a testing and study to the extent we're doing here, has not been done before. It's been possible thanks to the internet, since the 600 players are scattered over a large part of the world and the 10,000 games were done via the net.
I am sure that is correct, that this research has never been done before in any depth; I really think we are pioneering the modern game, not just the rules and game balances, but the tactics and terminology too.
Hagbard wrote:Throne or not throne.Historical sources indicate that some tafl games (fx. tablut) have a throne (forbidden king's square in center) and others not (fx. tawlbwrdd).The adding or not adding of a throne could've been used as simply a means to balance the game, when necessary. Especially the vulnerable tablut king, captured from two sides only, is well protected in center by a throne. Some test games indicate that adding a throne can shift the balance roughly +1, i.e. if the balance without a throne is fx. -1.8, it could be +1.2 with a throne added.
That too is very interesting, I didn't know you were able to assign a balance value to the throne - another original piece of research!

crust
Posts: 127
Joined: Sat Mar 21, 2015 9:29 am

Re: General rules

Post by crust » Tue Feb 02, 2016 6:05 pm

09/10/2014 Adam wrote:
We could perhaps have a closing line stating that historical accuracy is important to us, but that playability in modern tournament settings is paramount. Also that the rule sets are under constant review and subject to development should new historical evidence come to light or if advances in strategy reveal flaws that make the game unplayable in tournaments.

09/10/2014 crust wrote:
That's really important. In the hnefatafl world, such as it is, we are the 'modernists', in that we want the best possible game that is still hnefatafl.

Hagbard
Posts: 405
Joined: Sat Mar 14, 2015 6:07 pm

Re: General rules

Post by Hagbard » Fri Apr 29, 2016 11:54 pm

Hagbard wrote:The usual number of tafl game pieces is the Walker number p = 6w - 29, where p is the number of pieces and w is the width of the board in squares (hat tip: Damian Walker).
crust wrote:I like Damian's equation for the ratio of pieces to board size - I guess Ard Ri is no good because it violates this principle.
Interestingly, it follows from the Walker formula that there can be no 5x5 tafl board.
Because a 5x5 board would use 6 * 5 - 29 = 1 piece only, that is only the king and no men.

Hagbard
Posts: 405
Joined: Sat Mar 14, 2015 6:07 pm

Re: General rules

Post by Hagbard » Mon Jul 18, 2016 10:37 am

When playing a pair of games white/black & black/white simultaneously, it's theoretically possible for a lower rated player to copy all the higher rated player's moves for his own moves. To avoid any risk or suspicion of that, when playing against higher rated players I usually as a common courtesy do first the game of black lower rated player (or a good part of it) and thereafter the other one.

Hagbard
Posts: 405
Joined: Sat Mar 14, 2015 6:07 pm

Re: General rules

Post by Hagbard » Mon Feb 13, 2017 2:44 pm

On preventing that a game is stuck in repetitions.

Repetitions were discussed at length in 2012. Here just a few comments.

If repetitions were to be counted as repetitions of full board positions, and the player to lose were to be he who first entered this particular board position, then this way of counting would suit well the computer, which can easily keep track of that.

For real players playing in real life, however, this would be a very inconvenient rule to handle.

The Foteviken Museum in Scone, Sweden, formulated this rule to break repetitions:
13. In certain situations the so-called perpetual moves may occur. This can happen both at exit and at encirclement. In order to break such a stalemate the aggressive party after a couple of repetitions has to make a different move. This rule can be explained by the following example:

The king threatens to exit and a muscovit is moved in between to block. The king then moves to another square and threatens to exit here as well. The same muscovit has to be employed to block this time too. The king moves back to the first square and the muscovit is also moved back to block. When the described moves are repeated a couple of times, he who plays the Swedes must make a different move, because it is he who is the aggressive party.
The "aggressive party" is always trying to break through, to find an open path, somewhere. The reacting player is always busy blocking those paths.

This way of counting repetitions and deciding which player loses the game, is a bit more difficult for the computer, but is very easy to handle for real players.

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