Dots-and-Boxes Perfect 3x5 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

 + -1v + -1v + -1v + -1v + -1v +	+ -1^ +	-1^ + -1v + -1^	+ -1^ +

-1v   -1v   -1v	  -1v	-1v   -1v      -1^   -1^    1v	  1v   -1^   -1^

 + -1v + -1v + -1v + -1v + -1v +	+ -1^ +	-1^ #  1v + -1^	+ -1^ +
						    |
-1v   -1v   -1v	  -1v	-1v   -1v	1v   -1v    |	 -1^   -1^   -1^
						    |
 + -1v + -1v + -1v + -1v + -1v +	+ -1^ +	-1^ #  1v + -1^	+ -1^ +

-1v   -1v   -1v	  -1v	-1v   -1v      -1^   -1^    1v	  1v   -1^   -1^

 + -1v + -1v + -1v + -1v + -1v +	+ -1^ +	-1^ + -1v + -1^	+ -1^ +



 + -1v + -3v #-----# -1v + -1v +	+  1^ +	 1v #-----+  1v	+  1v +
						    |
-1v   -3v   -1v	  -3^	-1v   -1v	1^    1v    |	  1v	1v    1v
						    |
 + -1v + -1v + -1v + -1v + -1v +	+  1^ +	-1v #  1v +  1v	+  1v +
	     |					    |
-1v   -1v    |	  -1v	-1v   -1v	1^   -1v    |	  1v	1v    1v
	     |					    |
 + -1v + -1v + -3^ + -1v + -1v +	+  1^ +	-1v +  1v +  1v	+  1v +

-1v   -3v   -1v	  -1v	-1v   -1v	1^    1v    1^	  1^	1v    1v

 + -1v + -3v + -1v + -1v + -1v +	+  1^ +	 1v +  1v +  1v	+  1v +



 + -1v + -3v +-----+ -3v + -1v +	+  3v +	 1v +-----+  1v	+  1v +
	     |					    |
-1v   -3v    |	  -3v	-1v   -1v	3v    1v    |	  1v	1v    1v
	     |					    |
 + -3  #-----# -3v + -1v + -1v +	+  1^ +-----+  1v + -1v	+  1v +
	     |					    |
-1v   -3v    |	  -3v	-1v   -1v	1^   -1v    |	  1v	1v    1v
	     |					    |
 + -1v + -3v + -1v + -1v + -1v +	+  3v +	-1v #  1v +  1v	+  1v +
						    |
-1v   -3v   -1v	  -3v	-1v   -1v	1^    1v    |	  1v	1v    1v
						    |
 + -1v + -3v + -3v + -1v + -1v +	+  1^ +	 1v #  1v +  1v	+  1v +



 + -1v + -3v +-----+ -3v + -3v +	#-----#	-1v +-----+  1v	+  1v +
	     |					    |
-1v   -3v    |	  -3v	-3v   -3v	3^   -1v    |	  1v	1v    1v
	     |					    |
 + -3v +-----+ -3v + -3v + -1v +	+ -1v +-----+  1v + -1v	+  1v +
       |     |				      |	    |
-3v    |  A  |	  -3v	-1v   -3v	3^    |	 A  |	  1v	1v    1v
       |     |				      |	    |
 + -3v #-----# -1v + -1v + -3v +	+  3^ +-----+  1^ +  1^	+  1v +
	     |					    |
-1v   -3v    |	  -1v	-3v   -3v	3^    1v    |	  1v	1v    1v
	     |					    |
 + -1v + -3v + -1v + -3v + -3v +	+  3^ +	 1v +  1v +  1v	+  1v +



 +-----+ -5v +-----+ -3v + -3v +	+-----+	 5^ +-----+  3^	+  3^ +
	     |					    |
-5v   -5v    |	  -3v	-3v   -3v	5^    5^    |	  5v	3^    3^
	     |					    |
 #-----#-----+ -3v + -3v + -1v +	+-----+-----+  5v +  5v	+  3^ +
       |     |				      |	    |
-5v    |  A  |	  -3v	-1v   -3v      -1v    |	 A  |	  3^	3^    3^
       |     |				      |	    |
 + -5v +-----+ -1v + -1v + -3v +	# -1v +-----+  3v +  3v	+  3^ +
	     |				|	    |
-1v   -5v    |	  -1v	-3v   -3v	|    -1v    |	  3^	3^    3^
	     |				|	    |
 + -1v + -5v + -1v + -3v + -3v +	#  5v +	-1v +  3^ +  3^	+  3^ +



 +-----+ -5v +-----+ -3v + -3v +	+-----+	 3^ +-----+  3^	+ -1v +
	     |					    |
-5v   -5v    |	  -3v	-3v   -3v	3^    1v    |	  1v	3^   -1v
	     |					    |
 #-----+-----+ -3v + -3v + -1v +	+-----+-----+  1v + -1v	#  1v +
 |     |     |				|     |	    |		|
 |  A  |  A  |	  -3v	-1v   -3v	|  A  |	 A  |	 -1v	|    -1v
 |     |     |				|     |	    |		|
 #-----+-----+ -1v + -1v + -3v +	+-----+-----+  3^ +  3^	# -1  +
 |	     |				|	    |
 |    -5v    |	  -1v	-3v   -3v	|     1v    |	  1v	1^   -1
 |	     |				|	    |
 + -5v + -5v + -1v + -3v + -3v +	+  3^ +	 3^ +  1^ +  1^	+ -1  +



 +-----+ -5v +-----+ -3v + -3v +	+-----+	 3^ +-----+ -1v	+ -1v +
	     |					    |
-5v   -5v    |	  -3v	-3v   -3v	3^    1v    |	  3^   -1v   -1v
	     |					    |
 +-----+-----+ -3v # -3v + -1v +	+-----+-----+  1  +  1v	#-----#
 |     |     |	   |	 |		|     |	    |	  |	|
 |  A  |  A  |	   |	 |    -3v	|  A  |	 A  |	  |	|     1v
 |     |     |	   |	 |		|     |	    |	  |	|
 +-----+-----+ -3v # -3v + -3v +	+-----+-----+  3^ +  1v	+  1v +
 |	     |				|	    |
 |    -5v    |	  -3v	-3v   -3v	|     1v    |	 -1v	1v   -1v
 |	     |				|	    |
 + -5v + -5v + -1v + -3v + -3v +	+  3^ +	 3^ + -1v +  1v	+ -1v +



 +-----+ -7v +-----+ -3v + -3v +	+-----+	 1^ +-----+ -1v	+ -1v +
	     |					    |
-7v   -7v    |	  -3v	-3v   -3v	1^    1v    |	  3^   -1v   -1v
	     |					    |
 +-----+-----+ -3v + -1v +-----+	+-----+-----+  3^ #-----#-----+
 |     |     |	   |	 |		|     |	    |	  |	|
 |  A  |  A  |	   |	 |    -5v	|  A  |	 A  |	  |  B	|    -1v
 |     |     |	   |	 |		|     |	    |	  |	|
 +-----+-----+ -3v # -1v + -5v +	+-----+-----+  3^ +-----+ -1v +
 |	     |	   |			|	    |	  |
 |    -7v    |	   |	-3v   -3v	|     1v    |	  |    -1v    3^
 |	     |	   |			|	    |	  |
 + -7v + -7v + -3v # -3v + -3v +	+  1^ +	 1^ +  3^ + -1v	+  3^ +



 +-----+ -5v +-----#-----# -1v +	+-----+	 5^ +-----+-----+  5^ +
	     |					    |
-5v   -5v    |	  -5v	-5v   -1v	5^    5^    |	  3^	3^    5^
	     |					    |
 +-----+-----+ -5v +-----+-----+	+-----+-----+  3^ +-----+-----+
 |     |     |	   |	 |		|     |	    |	  |	|
 |  A  |  A  |	   |  B	 |    -3v	|  A  |	 A  |	  |  B	|    -1v
 |     |     |	   |	 |		|     |	    |	  |	|
 +-----+-----+ -5v +-----+ -3v +	+-----+-----+  3^ +-----+ -1v #
 |	     |	   |			|	    |	  |	      |
 |    -5v    |	   |	-3v   -1v	|     5^    |	  |    -1v    |
 |	     |	   |			|	    |	  |	      |
 + -5v + -5v + -5v + -3v + -1v +	+  5^ +	 5^ +  3^ + -1v	+  5^ #



 +-----+ -5v +-----+-----+ -1v +	+-----+	 5^ +-----+-----#-----#
	     |					    |
-5v   -5v    |	  -3v	-3v   -1v	5^   -1v    |	  5^	5^    5^
	     |					    |
 +-----+-----+ -3v +-----+-----#	+-----+-----+  5^ +-----+-----+
 |     |     |	   |	 |     |	|     |	    |	  |	|     |
 |  A  |  A  |	   |  B	 |  A  |	|  A  |	 A  |	  |  B	|  A  |
 |     |     |	   |	 |     |	|     |	    |	  |	|     |
 +-----+-----+ -3v +-----+-----#	+-----+-----+  5^ +-----+-----+
 |	     |	   |	       |	|	    |	  |	      |
 |    -5v    |	   |	-5v    |	|    -1v    |	  |    -1v    |
 |	     |	   |	       |	|	    |	  |	      |
 + -5v + -5v + -3v + -5v + -5v +	+  5^ +	 5^ +  5^ +  5^	+  5^ +

Player A gets two of the short chains plus the three boxes s/he already has for a total of 7 boxes; player B gets one short chain, the long 5 box chain and the one box s/he already has for a total of 8 boxes.

David Wilson / dwilson@cae.wisc.edu