Dots-and-Boxes Board Notation Explanation

The dots are represented by plus signs. For example:

   +     +     +     +
                                  
                                  
                                  
   +     +     +     +
                                  
                                  
                                  
   +     +     +     +

Some people call this a 3x4 game because it's 3 dots by 4 dots. Others call it a 2x3 game because it's 2 boxes by 3 boxes. At this web site, I use the latter convention, calling this a 2x3 game.

Lines filled in are representd by ----- or three vertical bars (|). For the last move made, the plus signs around it are replaced with pound signs. For example:

   +     +     +     +
         |            
         |            
         |            
   +     #-----#     +
                     |
                     |
                     |
   +     +     +     +

To display analysis results, a number is placed in each open line showing the final score with subsequent perfect play following a move to that line. The final score is defined as the number of boxes the first player has at the end minus the number of boxes the second player has at the end. Thus, the first player is aiming for the most positive score and the second player is aiming for the most negative score. For example:

   +  0  +  0  + -2  +
         |            
   0     |     0    -2
         |            
   + -2  #-----# -2  +
                     |
  -2    -2     0     |
                     |
   + -2  + -2  + -2  +

Here, it is the second player's turn to move. S/he should select one of the moves marked -2 rather than one marked 0.

A "loony" move is a move that permits the opponent to sacrifice 2 (or, in a loop, 4) cells to, in effect, switch sides. For example, in:

   +-----+     +-----+
         |           |
         |           |
         |           |
   +     #-----#     +
   |           |     |
   |           |     |
   |           |     |
   +-----+     +     +

all moves are loony. The play might continue:

     Player A to move         Player B to move

   +-----#-----#-----+      +-----+-----+-----+
         |           |            |     |     |
         |           |            |  A  |     |
         |           |            |     |     |
   +     +-----+     +      +     +-----+     +
   |           |     |      |           |     |
   |           |     |      |           |     |
   |           |     |      |           |     |
   +-----+     +     +      +-----+     #-----#




   +-----+-----+-----+      +-----+-----+-----+
         |     |     |      |     |     |     |
         |  A  |  B  |      |  A  |  A  |  B  |
         |     |     |      |     |     |     |
   #-----#-----+-----+      +-----+-----+-----+
   |           |     |      |     |     |     |
   |           |  B  |      |  A  |  A  |  B  |
   |           |     |      |     |     |     |
   +-----+     +-----+      +-----#-----#-----+

By convention, the first player is called player A and the second player is called player B.

The analysis results displayed can optionally include a loony move analysis. The score is suffixed by ^ if player B can be forced to make the next loony move or by v if player A can be forced to make the next loony move. If neither can be forced to make a loony move, the suffix is omitted. For example:

    +  2v +-----#-----#  2^ +

    2v    0     0     2^    2^

    +  0v +-----+  0^ +  0v +
                |
    2v    6^    |     2^    2^
                |
    +-----+  6^ +  0^ +  0v +
                |
    0v    6^    |     2     0^
                |
    +  0v +-----+  0v +  0^ +

    0v    0^    0     0     0v

    +  0v +  0v +  0v +  0v +

For entering moves into the program or refering to various possible moves in the text, a lettered coordinate system is used. For example:

   a  b  c  d  e  f  g

a  +  0  +  0  + -2  +
         |            
b  0     |     0    -2  
         |            
c  + -2  #-----# -2  +
                     |
d -2    -2     0     |  
                     |
e  + -2  + -2  + -2  +

To get the coordinates for a move, first look to the left to get the letter for the row and then to the top to get the letter for the column. The row letter is given first. The good moves here are [af], [bg], [cb], [cf], [da], [dc], [eb], [ed] and [ef].

For the 3x3, 3x5 and 4x4 games, Dots-and-Boxes Analysis Results gives opening advice for both player A and player B. Underneath the scores for the moves the opponent can make are the coordinates of the moves you should make. For example:

   a  b  c  d  e  f  g

a  +-----+ -1v + -1v +
           gf    cf 
b -1v   -1v   -1v   -1v 
  be*   da    ba*   cf 
c  + -1v +-----+ -1  +
     ad  |       fg*  
d -1v    |     1    -1v 
  fg*    |   +gf*   cf 
e  + -1v +  1  + -1v +
     ba*  +gf*   cf 
f -1v   -1    -1v    1v 
  fc    gf    fc    gf*
g  + -1v + -1v +  1v +
     fc    fc    fg*  

Where you have a blue link, you can click on the link to see the resulting position if the opponent selects that move. If the move coordinates are followed by an *, the resulting position after you click is a symmetric (rotation and/or reflection) transformation of the original position. If the move coordinates are preceded by a +, you are suppose to capture available boxes before making the suggested move.

David Wilson / dwilson@cae.wisc.edu