What is Misère Dots and Boxes?
Misère Dots and Boxes keeps every rule of the standard game except the goal. Players take turns drawing one line between two neighbouring dots. A player who completes the fourth side of a box scores it and must draw another line. When every line has been drawn, the player with the fewest boxes wins. Equal scores are a draw.
The extra move is what makes the game hard. In the standard game it is a reward that lets you collect a whole chain of boxes. Here it can be a trap: closing a box forces you to draw again, and the line you must then draw may leave you worse off than before. Long chains, the prize of the standard game, become something both players try to leave to the other.
You cannot refuse a move. If every line left on the board closes a box or gives one away, you must draw one of them. The skill lies in counting the safe lines that are left and in leaving your opponent the last of them.
Rule changes
| Rule | Standard Dots & Boxes | Misère Dots and Boxes |
|---|---|---|
| How to win | Standard Dots & BoxesClose more boxes than your opponent. | Misère Dots and BoxesClose fewer boxes than your opponent. |
| Scoring | Standard Dots & BoxesEach box you close is one point for you. | Misère Dots and BoxesThe same. Each box you close still counts as yours, and the scores show who is closer to losing. |
| After closing a box | Standard Dots & BoxesYou draw another line: a reward, since it lets you take a whole chain. | Misère Dots and BoxesYou still draw another line. It is now a burden, because the next line may close yet another box. |
| Draws | Standard Dots & BoxesEqual scores at the end are a draw. | Misère Dots and BoxesEqual lowest scores are also a draw. |
| Other options | Standard Dots & BoxesEvery board size and grid in the table setup can be used. | Misère Dots and BoxesWorks on every board size, with the pre-drawn border and on the triangle and hexagon grids. With three or four players the fewest boxes win. |
History
Losing versions of games are called misère, a word borrowed from card games such as solo whist, where misère is a bid to take no tricks at all. Mathematicians who study combinatorial games look at the misère form of almost every game, and Dots and Boxes is no exception.
In 2015 Sébastien Collette, Erik Demaine, Martin Demaine and Stefan Langerman published Narrow Misère Dots-and-Boxes in the collection Games of No Chance 4. They worked out who wins on boards one box wide and gave a winning strategy for those boards, with first results for boards two boxes wide and for Swedish boards, whose border is drawn from the start. They noted that no winning strategy is known for larger boards, so the misère game on a full board remains open.