Computer-check 3x3 game in section 4.4

[amdw]

Use the engine to check the moves in this example game.

[amdw]

Session for the record:

   0 1 2
  + + + +
0        
  + + + +
1        
  + + + +
2        
  + + + +

eval
V(P) = -3, best move (0, 0) Top
(453.6 seconds)

1 2 b

   0 1 2
  + + + +
0        
  + + + +
1        
  + + + +
2        
  + +-+ +

eval
V(P) = 3, best move (0, 0) Top
(183.4 seconds)

0 2 r

   0 1 2
  + + + +
0        
  + + + +
1        
  + + + +
2   |    
  + +-+ +

eval
V(P) = -3, best move (0, 0) Top
(64.5 seconds)

1 1 t

   0 1 2
  + + + +
0        
  + +-+ +
1        
  + + + +
2   |    
  + +-+ +

eval
V(P) = 3, best move (2, 0) Top
(26.9 seconds)

0 0 b

   0 1 2
  + + + +
0        
  +-+-+ +
1        
  + + + +
2   |    
  + +-+ +

eval
V(P) = -3, best move (0, 0) Top
(9.3 seconds)

2 0 b

   0 1 2
  + + + +
0        
  +-+-+-+
1        
  + + + +
2   |    
  + +-+ +

eval
V(P) = 3, best move (1, 1) Right
(3.4 seconds)

1 0 r

   0 1 2
  + + + +
0     |  
  +-+-+-+
1        
  + + + +
2   |    
  + +-+ +

eval
V(P) = -1, best move (2, 1) Right
(1.1 seconds)

2 1 r

   0 1 2
  + + + +
0     |  
  +-+-+-+
1       |
  + + + +
2   |    
  + +-+ +

eval
V(P) = 1, best move (1, 1) Bottom
(0.5 seconds)

2 1 b 

   0 1 2
  + + + +
0     |  
  +-+-+-+
1       |
  + + +-+
2   |    
  + +-+ +

eval
V(P) = -1, best move (1, 1) Right
(0.1 seconds)

1 1 r

   0 1 2
  + + + +
0     |  
  +-+-+-+
1     | |
  + + +-+
2   |    
  + +-+ +

eval
V(P) = -2, best move (0, 1) Bottom
(0.2 seconds)

0 0 t

   0 1 2
  +-+ + +
0     |  
  +-+-+-+
1     | |
  + + +-+
2   |    
  + +-+ +

eval
V(P) = 4, best move (0, 1) Left

0 1 l

   0 1 2
  +-+ + +
0     |  
  +-+-+-+
1 |   | |
  + + +-+
2   |    
  + +-+ +

eval
V(P) = -4, best move (2, 0) Top

0 2 l

   0 1 2
  +-+ + +
0     |  
  +-+-+-+
1 |   | |
  + + +-+
2 | |    
  + +-+ +

eval
V(P) = 4, best move (2, 2) Bottom

2 2 b

   0 1 2
  +-+ + +
0     |  
  +-+-+-+
1 |   | |
  + + +-+
2 | |    
  + +-+-+

eval
V(P) = -4, best move (2, 0) Top

2 0 r

   0 1 2
  +-+ + +
0     | |
  +-+-+-+
1 |   | |
  + + +-+
2 | |    
  + +-+-+

eval
V(P) = 4, best move (2, 0) Top

2 0 t

   0 1 2
  +-+ +-+
0     | |
  +-+-+-+
1 |   | |
  + + +-+
2 | |    
  + +-+-+

eval
V(P) = 3, best move (0, 0) Right

0 0 r

   0 1 2
  +-+ +-+
0   | | |
  +-+-+-+
1 |   | |
  + + +-+
2 | |    
  + +-+-+

eval
V(P) = -3, best move (1, 0) Top

0 0 l

   0 1 2
  +-+ +-+
0 | | | |
  +-+-+-+
1 |   | |
  + + +-+
2 | |    
  + +-+-+

eval
V(P) = -4, best move (1, 0) Top

1 0 t

   0 1 2
  +-+-+-+
0 | | | |
  +-+-+-+
1 |   | |
  + + +-+
2 | |    
  + +-+-+

eval
V(P) = -5, best move (0, 1) Bottom

[amdw]

From this analysis, it appears the existing game has two mistakes, though neither changes the overall result.

The first is the sixth move, player B's (1,0) right. Playing (1,1) right instead would win by three squares instead of one square.

The second is the tenth move, player A's (0,0) top, which gives the two squares back to player B. Playing (0,1) bottom instead would keep the final score to 5-4 rather than 6-3.

[amdw]

Analysis of improvement:

   0 1 2
  + + + +
0        
  +-+-+-+
1     |  
  + + + +
2   |    
  + +-+ +

eval
V(P) = -3, best move (0, 0) Top
(1.2 seconds)

0 0 r

   0 1 2
  + + + +
0   |    
  +-+-+-+
1     |  
  + + + +
2   |    
  + +-+ +

eval
V(P) = 3, best move (0, 0) Top
(0.4 seconds)

2 0 t

   0 1 2
  + + +-+
0   |    
  +-+-+-+
1     |  
  + + + +
2   |    
  + +-+ +

eval
V(P) = -3, best move (0, 1) Bottom
(0.2 seconds)

0 1 b

   0 1 2
  + + +-+
0   |    
  +-+-+-+
1     |  
  +-+ + +
2   |    
  + +-+ +

eval
V(P) = 3, best move (0, 0) Top

2 2 b

   0 1 2
  + + +-+
0   |    
  +-+-+-+
1     |  
  +-+ + +
2   |    
  + +-+-+

eval
V(P) = -3, best move (0, 1) Left

2 2 r

   0 1 2
  + + +-+
0   |    
  +-+-+-+
1     |  
  +-+ + +
2   |   |
  + +-+-+

eval
V(P) = 3, best move (0, 0) Top

0 0 t

   0 1 2
  +-+ +-+
0   |    
  +-+-+-+
1     |  
  +-+ + +
2   |   |
  + +-+-+

0 0 l

   0 1 2
  +-+ +-+
0 | |    
  +-+-+-+
1     |  
  +-+ + +
2   |   |
  + +-+-+

eval
V(P) = -4, best move (0, 2) Left

0 2 l

   0 1 2
  +-+ +-+
0 | |    
  +-+-+-+
1     |  
  +-+ + +
2 | |   |
  + +-+-+

0 2 b

   0 1 2
  +-+ +-+
0 | |    
  +-+-+-+
1     |  
  +-+ + +
2 | |   |
  +-+-+-+

eval
V(P) = 3, best move (1, 0) Right

1 0 t 

   0 1 2
  +-+-+-+
0 | | |  
  +-+-+-+
1     |  
  +-+ + +
2 | |   |
  +-+-+-+

2 0 r

   0 1 2
  +-+-+-+
0 | | | |
  +-+-+-+
1     |  
  +-+ + +
2 | |   |
  +-+-+-+

eval
V(P) = -5, best move (0, 1) Left