Dots-and-Boxes Analysis Results

The numbers are the resulting score with best play if the player on the move selects the corresponding line. Positive numbers are wins for the first player to move (player A); negative numbers are wins for the second player to move (player B). If you have a position you'd like analyzed (or an analysis you'd like taken deeper), send me an e-mail message at: dwilson@cae.wisc.edu The analysis programs are available if you want to run your own analyses.


 + -3  + -3  + -3  +        3x3 game.  Page 9 of The Dots-and-Boxes Game describes how player B
                            can force a win by 1.  However, player B really should win by 3.  This
-3    -3    -3    -3        game is more interesting if a loss by 1 is considered a win for player A.
                            
 + -3  + -3  + -3  +        Next move

-3    -3    -3    -3        Player A opening advice

 + -3  + -3  + -3  +        Player B opening advice

-3    -3    -3    -3        Perfect game

 + -3  + -3  + -3  +        Play the game



 + -1  + -1  + -1  + -1  + -1  +        3x5 American game

-1    -1    -1    -1    -1    -1

 + -1  + -1  + -1  + -1  + -1  +        Next moves

-1    -1    -1    -1    -1    -1        Commentary

 + -1  + -1  + -1  + -1  + -1  +        Player A opening advice

-1    -1    -1    -1    -1    -1        Player B opening advice

 + -1  + -1  + -1  + -1  + -1  +        Perfect game



 +  0^ +  0^ +  0^ +  0^ +        4x4 game.  Unlike the other analyses on this
                                  page, this one includes a loony move analysis.
 0^    0^    0^    0^    0^       With best play, the game is tied.  However,
                                  the ^ means player B can be forced to make the
 +  0^ +  0^ +  0^ +  0^ +        first loony move.  Symmetric play loses for
                                  player B.
 0^    0^    0     0^    0^

 +  0^ +  0  +  0  +  0^ +        Next moves

 0^    0^    0     0^    0^       Commentary

 +  0^ +  0^ +  0^ +  0^ +        Player A opening advice; Player B opening advice

 0^    0^    0^    0^    0^       Analysis of all openings

 +  0^ +  0^ +  0^ +  0^ +        Perfect game and more complete games



 +-----+-----+-----+-----+-----+        3x5 Swedish game
 |                             |
 |    -1    -1    -1    -1     |
 |                             |
 + -1  +  3  +  1  +  3  + -1  +
 |                             |
 |     5     5     5     5     |        Next move
 |                             |
 + -1  +  3  +  1  +  3  + -1  +
 |                             |
 |    -1    -1    -1    -1     |
 |                             |
 +-----+-----+-----+-----+-----+



 +-----+-----+-----+-----+-----+-----+       4x6 Swedish game
 |                                   |
 |     2     0     0     0     2     |
 |                                   |
 +  2  +  2  +  2  +  2  +  2  +  2  +
 |                                   |
 |     2     2     0     2     2     |
 |                                   |
 +  0  +  0  +  0  +  0  +  0  +  0  +       Next move
 |                                   |
 |     2     2     0     2     2     |
 |                                   |
 +  2  +  2  +  2  +  2  +  2  +  2  +
 |                                   |
 |     2     0     0     0     2     |
 |                                   |
 +-----+-----+-----+-----+-----+-----+



 + -3  + -3  + -3  + -3  + -5  +        3x5 Icelandic game
 |
 |    -3    -5    -3    -3    -5
 |
 + -5  + -3  + -3  + -3  + -3  +
 |
 |    -5    -3    -1    -3    -3        Next move
 |
 + -5  + -5  + -5  + -5  + -3  +
 |
 |    -5    -3    -1    -3    -5
 |
 +-----+-----+-----+-----+-----+



 +  2  +  2  +  2  +  2  +       3x4 Icelandic game
 |
 |     4     0     2     2
 |
 +  0  +  0  +  2  +  4  +
 |
 |     4     0     2     2       Next move
 |
 +  2  +  4  +  4  +  2  +
 |
 |     2     0     0     2
 |
 +-----+-----+-----+-----+



  +  1  +  1  +  1  +  1  +  1  +       5x5 game
                                        Analyzed by William Fraser
  1     1     1     1     1     1       (bfraser at alumni dot ucsc dot edu)

  +  1  +  1  +  1  +  1  +  1  +
                    
  1     1     1     1     1     1
                    
  +  1  +  1  +  1  +  1  +  1  +
        
  1     1     1     1     1     1

  +  1  +  1  +  1  +  1  +  1  +

  1     1     1     1     1     1
                    
  +  1  +  1  +  1  +  1  +  1  +
                    
  1     1     1     1     1     1
                    
  +  1  +  1  +  1  +  1  +  1  +



  +  1  +  1  +  1  +  1  +  1  +       A common 5x5 position
                                        Analyzed by Kevin Buzzard
  1     1     1     1     1     1       (k dot buzzard at imperial dot ac dot uk)

  +  1  +  1  +-----+  1  + -1  +
                    |
  1     1    -3     |     1    -1
                    |
  +  1  + -3  + -3  + -1  +  1  +
        |           |
  1     |    -3     |    -1     1       Next move
        |           |
  +  1  +-----+-----+-----+-----+
                    |           |
  1     1    -1     |    -3     |
                    |           |
  +  1  +  1  + -1  + -3  + -3  +
                    |
  1    -1     1     |    -3     1
                    |
  +  1  + -1  +  1  +-----+  1  +



  + -1  + -3  + -3  + -3  + -1  +
  |                                     Analyzed by William Fraser
  |    -1    -1    -1    -1    -1
  |                              
  + -3  + -1  + -3  + -3  + -1  +
  |                              
  |    -1    -1    -1    -3    -3
  |                              
  + -1  + -1  + -1  + -1  + -1  +
  |                              
  |    -3    -3    -1    -3    -3
  |                              
  + -1  + -3  + -3  + -1  + -1  +
  |                              
  |    -3    -3    -1    -1    -3
  |                              
  + -3  + -3  + -3  + -1  + -1  +
  |                              
  |    -3    -1    -1    -3    -1
  |                              
  +-----+-----+-----+-----+-----+


  +-----+-----+-----+-----+-----+
  |                             |       Analyzed by William Fraser
  |    -3    -3    -3    -3     |
  |                             |
  + -3  + -3  + -3  + -3  + -3  +
  |                             |
  |    -3    -3    -3    -3     |
  |                             |
  + -3  + -3  + -3  + -3  + -3  +
  |                             |
  |    -3    -3    -3    -3     |
  |                             |
  + -3  + -3  + -3  + -3  + -3  +
  |                             |
  |    -3    -3    -3    -3     |
  |                             |
  + -3  + -3  + -3  + -3  + -3  +
  |                             |
  |    -3    -3    -3    -3     |
  |                             |
  +-----+-----+-----+-----+-----+

<- Parent Directory

David Wilson / dwilson@cae.wisc.edu