What is Swedish board?
On a Swedish board the whole outer border is drawn before the first move. Those lines belong to nobody and are not moves: the players draw only the inside lines, one per turn, as in the standard game. A player who completes the fourth side of a box scores it and draws another line, and when every line has been drawn the player with more boxes wins.
The border changes the shape of the game. A corner box already has two sides, so two more lines close it, and every other box along the edge already has one. Lines near the edge become dangerous from the first move, there are fewer safe lines to play before someone must give boxes away, and the long chains that decide Dots and Boxes run along the border from the start.
On the 4×4 board the 16 border lines are drawn, so the game has 24 moves instead of 40.
Rule changes
| Rule | Standard Dots & Boxes | Swedish board |
|---|---|---|
| Starting position | Standard Dots & BoxesOnly the dots. No line is drawn. | Swedish boardThe dots and every line on the outside of the board. |
| Moves | Standard Dots & BoxesDraw any undrawn line between two neighbouring dots, inside or on the edge. | Swedish boardThe same, but only inside lines are left: the border cannot be drawn again. |
| Border lines | Standard Dots & BoxesEvery line is drawn by one of the players. | Swedish boardThe border lines belong to nobody. A box still goes to the player who draws its last side. |
| Closing the first box | Standard Dots & BoxesEvery box needs four lines. | Swedish boardA corner box needs two more lines and any other edge box three more. |
| Game length | Standard Dots & BoxesOne move per line: 40 moves on 4×4. | Swedish boardOne move per inside line: 24 moves on 4×4. |
| Other options | Standard Dots & BoxesEvery board size and grid in the table setup can be used. | Swedish boardWorks on every board size, in Misère and on the triangle and hexagon grids, where the outside of the shape is drawn. A border that would close a cell by itself is left off. |
History
The version with the outer lines drawn is known in English writing on the game as the Swedish board. A board where only the left and bottom sides start drawn is called an Icelandic board; it is not offered here. Neither name comes with a known inventor or date.
Swedish boards appear in mathematical work on the game. In Narrow Misère Dots-and-Boxes, published in Games of No Chance 4 in 2015, Sébastien Collette, Erik Demaine, Martin Demaine and Stefan Langerman gave results for Swedish boards one box wide next to the open ones.