Dots-and-Boxes American Game Analysis

The first player wins if s/he can achieve one of the following three positions (or a symmetric variation) after the first three moves:

   a  b  c  d  e  f  g  h  i  j  k

a  +  1  +  1  +  1  +  1  +  1  +
               |
b  1     1     |     1     1     1
               |
c  +  1  +  1  +  1  +  1  +  1  +
   |           |
d  |     1     |     1     1     1
   |           |
e  +  1  +  1  +  1  +  1  +  1  +

f  1     1     1     1     1     1

g  +  1  +  1  +  1  +  1  +  1  +



   a  b  c  d  e  f  g  h  i  j  k

a  +  1  +  1  +  1  +  1  +  1  +
               |
b  1     1     |     1     1     1
               |
c  +  1  +  1  +  1  +  1  +  1  +
               |
d  1     1     |     1     1     1
               |
e  +  1  +  1  +  1  +  1  +  1  +
               |
f  1     1     |     1     1     1
               |
g  +  1  +  1  +  1  +  1  +  1  +



   a  b  c  d  e  f  g  h  i  j  k

a  +  1  +  1  +  1  +  1  +  1  +
               |
b  1     1     |     1     1     1
               |
c  +  1  +  1  +-----+  1  +  1  +
                     |
d  1     1     1     |     1     1
                     |
e  +  1  +  1  +  1  +  1  +  1  +

f  1     1     1     1     1     1

g  +  1  +  1  +  1  +  1  +  1  +

The strongest opening move is:
 + -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  +
Of player B's possible responses the strongest is:
 + -1  + -3  #-----# -1  + -1  +

-1    -3    -1    -3    -1    -1

 + -1  + -1  + -1  + -1  + -1  +
             |
-1    -1     |    -1    -1    -1
             |
 + -1  + -1  + -3  + -1  + -1  +

-1    -3    -1    -1    -1    -1

 + -1  + -3  + -1  + -1  + -1  +

Another strong opening move is:
 + -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  +
This gives player B a nice variety of losing moves including three out of the four center moves.
Of player B's possible responses the strongest is:
 + -1  + -3  + -3  + -3  + -1  +
             |
-1    -3     |    -1    -1    -1
             |
 + -3  #-----# -3  + -3  + -1  +

-3    -3    -1    -1    -3    -1

 + -1  + -3  + -3  + -3  + -1  +

-1    -3    -3    -3    -3    -1

 + -1  + -3  + -3  + -3  + -1  +

David Wilson / dwilson@cae.wisc.edu