Daldøs



Daldøs [dal'dø s ] is a running-fight board game only known from a few coastal locations in Scandinavia, where its history can be traced back to around 1800. The game is notable for its unusual four-sided rolling-pin style dice (stick or barrel dice). In Denmark it is known as daldøs in Northern and Western Jutland (Mors, Thisted and Fanø), and possibly as daldos on Bornholm. In Norway it is known under the name of daldøsa from Jæren, where, unlike in Denmark, a continuous tradition of the daldøs game exists. A rather similar game called sáhkku, using virtually identical dice, is known in a number of variants from the Sea Sami in Northern Norway, Finland and Russia. Otherwise, the closest relatives of this game appear to be the tâb games from Northern Africa and South-western Asia, possibly apart from one unlabelled diagram in a codex from Southern England.

Typical materials
Board

The board is boat-shaped and has three parallel rows of holes, two of which (A and B) have 16 holes each, while the middle row (C) has an extra hole in the prow of the ship.

Pieces

Each player has 16 spatula-shaped pieces with a bottom end fitting into the holes of the board. One player has pieces that are rather wide and thin; where as the other player's pieces are more obelisk-shaped. At the beginning of the game, player A's pieces are placed in the holes of row A so that the spatulas are perpendicular to the row (un-dalled), and equivalently for player B. Later in the game, the pieces will be turned (fordallede, or dalled) so that the spatula is parallel to the rows.

Dice

Two special dice are used. Each die is a four-sided rolling pin (or stick die) with pyramidal or rounded ends, preventing the rolling pin from standing on end. They may be about 2 by 2 cm in cross section, and 4 cm long. The four sides are marked A (with the value 1, called dallen, i.e. the dal), II (2, probably called døs), III (3) and IIII (4). According to some sources, the dal is opposite to III.

Rules


Starting the game

Both players throw the dice; the highest throw (adding the dice, the dal counting as 1) begins the game.

Dalling

Pieces cannot move until they have been dalled. A die showing the dal allows the player to dal one piece, which means to turn it parallel to its row and move it one position ahead. With the first dal, only the piece closest to the stern can be dalled, and then it goes into row C. With no dalled pieces, a throw with no dals is a lost move.

Moves

The dalled pieces move according to dice throws. Each player's pieces move first through the home row to the stern, then through row C towards the prow, then into the enemy row back towards the stern. From here it moves into row C again, etc., never returning to the home row. The showings of the two dice may be either added and used to move one piece, or used separately for two different pieces. E.g., a throw of a dal and a three allows the player (i) to dal one piece (moving it one position) and then move another dalled piece three positions; (ii) to dal one piece and move it a total of four positions; (iii) to move two dalled pieces, one three positions and the other one position; or (iv) to move one dalled piece four positions. The showings of both dice must be used in a move. If that is not possible, the showing of one of the dice must be used. If that is not possible either, the move is lost. A throw of dal-dal (two dals) always gives the right to an extra throw.

Object

The object of the game is to remove all enemy pieces from the board. An enemy piece is removed when another piece ends at the same position. When the dice are added, only an enemy piece at the final position can be removed. Enemy pieces can be jumped, but are not removed thereby. Friendly pieces cannot be jumped at all. (Whether pieces jumped or at the final position are dalled or not is irrelevant here.) The game ends when one player has no pieces left.

Variations
The shape of the board, the pieces and the dice vary. E.g., the dal marked A in Denmark is marked X in Norway, and I in some modern reconstructions.

In the rules supplied with some reconstructions of the game, the direction of the moves is reversed (prow-to-stern in row C instead of stern-to-prow). However, this difference has no real consequences.

In some reconstructions, the pieces are cylindrical with one end painted black for player A and white for player B. Undalled pieces are turned with the painted end down.

Some sources specify that only a player's undalled piece closest to the stern may be dalled. With this rule, the pieces need not be designed so that one can see whether a piece is dalled or not; instead the next piece to be dalled can be indicated by a marker.

Also, some sources indicate that when the dice are added and used to move one piece, enemy pieces at the intermediate position as well as at the final position are removed.

The end game can be tedious, so it has been suggested to agree that the first player to have only one piece left loses. Also, the players may agree to declare the game a draw.

The number of holes in each row is rather arbitrary; instead of the 16+17+16 used in the Danish game, 12+13+12 are used in Norway, with 12 pieces for each player. In either case, there is no obvious reason for the extra hole in the middle row, other than to distinguish the two ends of the board, which is necessary to define the direction of play.

Strategy
The game is simple, and one will soon realise that it pays to have dalled pieces waiting in the home row close to the prow, and also in the enemy row behind all enemy pieces. Most dal throws are used to dal pieces rather than to move already dalled pieces.

Probabilities
It is often useful to have an idea of the probability that a given piece can be removed in the next round. Suppose player A has a piece a1, and player B has a piece b1 a few positions behind a1 with no other pieces in between. If it is B's turn, B's chances of being able to remove a1 using b1 in this turn depends on how many positions b1 is behind a1:



Note that the largest probability, two thirds, is found when b1 is four positions behind a1, and note the rapid decrease in the probabilities for larger distances. These values assume that B has sufficient possibilities to use part of the throw elsewhere on the board. E.g., with a distance of 2, B must either throw a dal-dal (probability 1/16), or one die must show 2 (probability 7/16), while B is able to use the other die to move another piece elsewhere on the board. The table row Use of dal-dal indicates how many positions B should move b1 at a throw of dal-dal in order to maximize the probability of removing a1, including the extra throw.

If B has an additional piece b2 behind b1, but no more than four positions behind a1, the first few probabilities are increased by including the possibility of jumping over a1 with b1 and then removing a1 using b2:

Note that now, the largest probability is three quarters, and is found when b1 is just one position behind a1.

History and sources
The origins of Daldøs are unknown, but it is strikingly similar to some games in the tâb group from Northern Africa and Western Asia, widely distributed during the Muslim expansion. One may conjecture that some sea-going trade contact has carried a tâb game to Scandinavia, either directly from the Arab world, or possibly via England, where a codex from Cerne Abbey, Dorset, from the second half of the thirteenth century (Folio 2v, MS 0.2.45, Trinity College Library, Cambridge) possibly shows a Daldøs board with 12+12+12 holes, after both players have made their first move. The game must have arrived in Scandinavia not much later than 1800, and quite possibly a few centuries before that. A connection involving the Swedish Vikings known as Varangians, mercenaries for the Byzantine Empire before 1100, has been suggested.

In a Danish historical novel "Fru Maria Grubbe" written in 1876 by J. P. Jacobsen, Maria plays daldøs with her husband in 1661. But most likely, Jacobsen knew the game from his childhood in Thisted in the 1850'es. In an article from 1927 by H. Billeskov Jansen [H. Billeskov Jansen: Daldøs, Danske Studier, Copenhagen 1927, pp. 96-100], the game is described in detail and the rules are given. The author had found one of the few surviving specimens from a farm near Thisted – a farm where Jacobsen used to come as a child. This game is now at Thisted Museum. Another game from Mors is now at Nationalmuseet (Brede). From Bornholm, no sources mention the game, but a local saying spilla daldōs (lit. playing daldøs), meaning to live beyond one's means, has been recorded in 1856. A similar meaning has been recorded in Jutland.

In Jæren in Norway, a game of unknown age is kept in Hå bygdemuseum, a part of Jærmuseet. Jæren had close trade connections with the Danish regions where daldøs was played, and also with Northern Norway, where sáhkku was played.

The name of the game
In the name daldøs, the first syllable refers to the throw dal. The marking A on the daldøs dice probably stands for ace or the like, but the etymology of the name dal remains a mystery. One theory connects dal to Medieval English daly, meaning die. Døs is probably a variant of a Nordic word traditionally used for the "two" on a die, related to old French doues, surviving in the Danish word sinkadus, originally meaning a dice throw of 5 and 2. Most of the tâb games and the Samít sáhkku game are likewise named after the dice throw "one", which is required to release the pieces so that they can start moving.

Danish

 * Peter Michaelsen: Daldøs og Sakku – to gamle nordiske spil med fjerne slægtninge. Ord & Sag 19, 1999, pp. 15-28
 * Peter Michaelsen: Daldøs – et gådefuldt gammelt brætspil. Historisk Årbog for Thy og Vester Han Herred, 2001