Dots-and-Boxes Perfect 4x4 Game

In this game each player has chosen a best move--giving the opponent as few good choices as possible. The suffix v means player A must make the next loony move; ^ means player B must.

       Player A to move                   Player B to move

  +  0^	+  0^ +	 0^ +  0^ +	     +	2v +  2^ +  2^ +  2^ +

  0^	0^    0^    0^	  0^	     2v	   2^	 2^    2^    2^

  +  0^	+  0^ +	 0^ +  0^ +	     +	2^ +-----+  2^ +  2^ +

  0^	0^    0	    0^	  0^	     2^	   2^	 0^    2^    2^

  +  0^	+  0  +	 0  +  0^ +	     +	2^ +  0^ +  2  +  2^ +

  0^	0^    0	    0^	  0^	     2^	   2^	 2     2^    2^

  +  0^	+  0^ +	 0^ +  0^ +	     +	2^ +  2^ +  2^ +  2^ +

  0^	0^    0^    0^	  0^	     2^	   2^	 2^    2^    2v

  +  0^	+  0^ +	 0^ +  0^ +	     +	2^ +  2^ +  2^ +  2v +



  +  0^	+  0^ +	 0v +  0^ +	     +	2^ +  2^ +  2^ +  2^ +

  0^	0     0	    0^	  0^	     2^	   2^	 2^    2^    2^

  +  0	+-----#	 0^ +  0^ +	     +	2^ +-----+  4  +  2^ +
	      |					 |
  0^	0     |	    0^	  0^	     2^	   4^	 |     4^    2^
	      |					 |
  +  0v	+  0  #	 0^ +  0^ +	     +	2^ +  4^ +  2^ +  2^ +

  0^	0^    0v    0^	  0^	     2^	   4^	 0^    2^    2^

  +  0^	+  0^ +	 0v +  0^ +	     +	2^ #-----#  4  +  4^ +

  0^	0^    0	    0^	  0^	     2^	   2^	 2^    2^    2^

  +  0^	+  0^ +	 0^ +  0^ +	     +	2^ +  2^ +  2^ +  2^ +



  +  0v	+  0v +	 0v +  0v +	     +	0^ #-----#  2v +  0^ +

  0v	0v    0v    0v	  0v	     0^	   2v	 2v    2v    0^

  +  0v	+-----+	 0v +  0  +	     +	0^ +-----+  0^ +  0^ +
	      |					 |
  0v   -2v    |	    0^	  0v	     0^	   4^	 |     2v    0^
	      |					 |
  +  0v	+ -2^ #	 0^ +  0v +	     +	0v +  4^ +  0^ +  0^ +
	      |					 |
  0v   -2v    |	    0^	  0v	     0^	   4^	 |     0^    0^
	      |					 |
  +  0v	+-----#	 0v +  0  +	     +	0^ +-----+  0^ +  0^ +

  0v	0v    0v    0v	  0v	     0^	   0^	 0^    0^    0^

  +  0v	+  0v +	 0v +  0v +	     +	0^ +  0^ +  0^ +  0^ +



  +  0v	+-----+	 0v +  0v +	     +	2v +-----#-----#  2^ +

  0v   -2    -2	    0v	  0v	     2v	   0	 0     2^    2^

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

  0v	0v    0v   -2^	  0v	     0v	   0^	 0     0     0v

  +  0v	+  0v +	-2^ +  0v +	     +	0v +  0v +  0v +  0v +



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

 -2v   -2v   -2v   -4v	 -2v	     2^	   2^	 2v    2^    2^

  #-----#-----+	 0v + -2v +	     +-----+-----#-----#  2^ +
	      |					 |
 -2v   -2v    |	   -2v	 -4v	     4^	   4^	 |     2v    0v
	      |					 |
  +-----+ -2v +	-2v + -2v +	     +-----+  4^ +  2v +  0^ +
	      |					 |
 -2v   -2v    |	   -2v	 -4^	     0v	   4^	 |     0^    0^
	      |					 |
  +  0v	+-----+	-2v + -2v +	     +	0^ +-----+  0v +  0^ +

 -2v   -2v   -2v   -2v	 -2v	     0^	   0^	 0v    0^    0^

  + -2v	+ -2v +	-2v + -2v +	     +	0^ +  0^ +  0v +  0^ +



  + -2v	+-----+-----+ -4v +	     +	2^ +-----+-----+  2^ +

 -2v   -4v   -4v   -4v	 -4v	     2^	   2^	 2v    2^    2^

  +-----+-----+-----+  0v #	     +-----+-----+-----#-----#
	      |		  |			 |	     |
 -2v   -2v    |	   -2v	  |	     4^	   4^	 |     4v    |
	      |		  |			 |	     |
  +-----+ -2v +	-2v + -4v #	     +-----+  4^ +  4^ +  4^ +
	      |					 |
 -2v   -2v    |	   -4v	 -2v	     0v	   4^	 |     2^    0^
	      |					 |
  +  0v	+-----+	-4v + -2v +	     +	0^ +-----+  0^ +  0^ +

 -2v   -2v   -2v   -2v	 -2v	     0^	   0^	 0v    0^    0^

  + -2v	+ -2v +	-2v + -2v +	     +	0^ +  0^ +  0^ +  0^ +



  +  0v	+-----+-----+  0v +	     #-----#-----+-----+  2^ +

  0v   -4v   -4v   -4v	  0v	     4^	   4^	 4^    4^    2^

  +-----+-----+-----+-----+	     +-----+-----+-----+-----+
	      |		  |			 |	     |
 -6v   -6v    |	   -2v	  |	     4^	   4^	 |     2v    |
	      |		  |			 |	     |
  #-----+ -6v +	-2v + -2v +	     +-----+  4^ +  2^ +  2^ +
  |	      |			     |		 |
  |    -6v    |	   -2v	 -2v	     |	   4^	 |     2^    0^
  |	      |			     |		 |
  # -6v	+-----+	 0v +  0v +	     +	4^ +-----+  0v +  2^ +

  0v	0v    0v   -2^	  0v	     0^	   2^	 2^    2^    2^

  +  0v	+ -2v +	 0v +  0v +	     +	0^ +  0v +  0^ +  2^ +



  +-----+-----+-----+  0v +	     +-----+-----+-----+  0^ +

 -2v   -2v   -2v   -2v	  0v	     2^	   2^	 2^    2^    0^

  +-----+-----+-----+-----+	     +-----+-----+-----+-----+
	      |		  |			 |	     |
 -8v   -8v    |	   -4v	  |	     2^	   2^	 |     2^    |
	      |		  |			 |	     |
  +-----+ -8v +	-4v + -4v +	     +-----+  2^ +  2^ +  2^ +
  |	      |			     |		 |
  |    -8v    |	   -2v	 -2v	     |	   2^	 |     2^    0v
  |	      |			     |		 |
  + -8v	+-----+	-2v + -2v +	     +	2^ #-----+  0v +  2^ +
					   |	 |
 -2v	0v    0v   -2v	 -2v	     0^	   |  B	 |     2^    2^
					   |	 |
  + -2v	#-----#	-2v + -2v +	     +	0^ #-----+  0v +  2^ +



  +-----+-----+-----+  0v +	     +-----+-----+-----+  4^ +

 -4v   -4v   -4v   -4v	  0v	     2^	   2^	 2^    2^    4^

  +-----+-----+-----+-----+	     +-----+-----+-----+-----+
	      |		  |			 |	     |
 -6v   -6v    |	   -4v	  |	     2^	   2^	 |     4^    |
	      |		  |			 |	     |
  +-----+ -6v +	-4v + -4v +	     +-----+  2^ +  4^ +  4^ +
  |	      |			     |		 |
  |    -6v    |	   -2v	 -2v	     |	   2^	 |     4^    0v
  |	      |			     |		 |
  + -6v	+-----+	-2v +  0v +	     +	2^ +-----+  0v #-----#
	|     |				   |	 |
  0v	|  B  |	   -2v	 -2v	     4^	   |  B	 |     0v    4^
	|     |				   |	 |
  +  0v	+-----#-----# -2v +	     +	4^ +-----+-----+  4^ +



  +-----+-----+-----+  0v +	     +-----+-----+-----+  0v +

 -2v   -2v   -2v   -2v	  0v	     4^	   4^	 4^    4^    0v

  +-----+-----+-----+-----+	     +-----+-----+-----+-----+
	      |		  |			 |	     |
 -4v   -4v    |	   -8v	  |	     4^	   4^	 |     4^    |
	      |		  |			 |	     |
  +-----+ -4v +	-8v + -8v +	     +-----+  4^ +  4^ +  4^ +
  |	      |			     |		 |
  |    -4v    |	   -8v	  0v	     |	   4^	 |     4^    0v
  |	      |			     |		 |
  + -4v	+-----#-----#-----+	     #	4^ +-----+-----+-----+
	|     |	    |		     |	   |	 |     |
  0v	|  B  |	 A  |	 -2v	     |	   |  B	 |  A  |     0v
	|     |	    |		     |	   |	 |     |
  +  0v	+-----+-----+ -2v +	     #	4^ +-----+-----+  0v +



  +-----+-----+-----#-----#	     +-----+-----+-----+-----+

 -4v   -4v   -4v   -4v	 -4v	     4^	   4^	 4^    4^    4^

  +-----+-----+-----+-----+	     +-----+-----+-----+-----+
	      |		  |			 |	     |
 -6v   -6v    |	   -8v	  |	     4^	   4^	 |     8^    |
	      |		  |			 |	     |
  +-----+ -6v +	-8v + -8v +	     +-----+  4^ +  8^ +  8^ #
  |	      |			     |		 |	     |
  |    -6v    |	   -8v	  0v	     |	   4^	 |     8^    |
  |	      |			     |		 |	     |
  + -6v	+-----+-----+-----+	     +	4^ +-----+-----+-----#
  |	|     |	    |		     |	   |	 |     |
  |	|  B  |	 A  |	 -2v	     |	   |  B	 |  A  |     0v
  |	|     |	    |		     |	   |	 |     |
  + -6v	+-----+-----+ -2v +	     +	4^ +-----+-----+  0v +



  +-----+-----+-----+-----+	     +-----+-----+-----+-----+

 -2v   -2v   -2v   -2v	 -2v

  +-----+-----+-----+-----+	     +-----+-----+-----#-----+
	      |		  |			 |     |     |
 -4v   -4v    |	    0v	  |			 |     |     |
	      |		  |			 |     |     |
  +-----+ -4v +	 0v +  0v +	     +-----+	 +  2^ #  2^ +
  |	      |		  |	     |		 |	     |
  |    -4v    |	    0v	  |	     |		 |     0v    |
  |	      |		  |	     |		 |	     |
  + -4v	+-----+-----+-----#	     +	   +-----+-----+-----+
  |	|     |	    |	  |	     |	   |	 |     |     |
  |	|  B  |	 A  |  A  |	     |	   |  B	 |  A  |  A  |
  |	|     |	    |	  |	     |	   |	 |     |     |
  + -4v	+-----+-----+-----#	     +	   +-----+-----+-----+



  +-----+-----+-----+-----+	     +-----+-----#-----+-----+
						 |     |     |
  0v	0v    0v    0v	  0v	     0v	   6^	 |  B  |  B  |
						 |     |     |
  +-----+-----+-----+-----+	     +-----+-----#-----+-----+
	      |	    |	  |			 |     |     |
  0v	0v    |	 A  |  A  |			 |  A  |  A  |
	      |	    |	  |			 |     |     |
  +-----+  0v +-----#-----+	     +-----+	 +-----+-----+
  |	      |	    |	  |	     |		 |     |     |
  |	0v    |	 A  |  A  |	     |		 |  A  |  A  |
  |	      |	    |	  |	     |		 |     |     |
  +  0v	+-----+-----#-----+	     +	   +-----+-----+-----+
  |	|     |	    |	  |	     |	   |	 |     |     |
  |	|  B  |	 A  |  A  |	     |	   |  B	 |  A  |  A  |
  |	|     |	    |	  |	     |	   |	 |     |     |
  +  0v	+-----+-----+-----+	     +	   +-----+-----+-----+



  #-----+-----+-----+-----+	     +-----+-----+-----+-----+
  |	|     |	    |	  |	     |	   |	 |     |     |
  |  A	|  A  |	 B  |  B  |	     |	A  |  A	 |  B  |  B  |
  |	|     |	    |	  |	     |	   |	 |     |     |
  #-----+-----+-----+-----+	     +-----#-----+-----+-----+
	      |	    |	  |	     |	   |	 |     |     |
  0v	0v    |	 A  |  A  |	     |	B  |  B	 |  A  |  A  |
	      |	    |	  |	     |	   |	 |     |     |
  +-----+  0v +-----+-----+	     +-----#-----+-----+-----+
  |	      |	    |	  |	     |	   |	 |     |     |
  |	0v    |	 A  |  A  |	     |	B  |  B	 |  A  |  A  |
  |	      |	    |	  |	     |	   |	 |     |     |
  +  0v	+-----+-----+-----+	     +-----+-----+-----+-----+
  |	|     |	    |	  |	     |	   |	 |     |     |
  |	|  B  |	 A  |  A  |	     |	B  |  B	 |  A  |  A  |
  |	|     |	    |	  |	     |	   |	 |     |     |
  +  0v	+-----+-----+-----+	     +-----+-----+-----+-----+

David Wilson / dwilson@cae.wisc.edu