Fractional Hex

[From Edward Jackman conversations] Speaking of Hex, here's another idea to address it's first-player advantage that may not have been explored much. I found it in the Mudcrack Y and Poly Y book, but it applies to Hex as well. The first player draws a line connecting the midpoints of the opposite sides of one cell, dividing it half, creating two 5 sided cells. She plays her opening move to one of the two halves. The fewer sides a cell has, the weaker a move there is. You might even require that the line divides the cell into a 4 and a 6 sided cell and the move goes in the smaller cell -- that would be a very weak move, even in the center of the board.

Standard move, filling entire cell:
        +---+    
       /     \
  +---+       +---+
 /     \     /     \ 
+       +---+       +
 \     /xxxxx\     /
  +---+xxxxxxx+---+
 /     \xxxxx/     \ 
+       +---+       +
 \     /     \     /
  +---+       +---+
       \     /
        +---+

Half move:
        +---+    
       /     \
  +---+       +---+
 /     \     /     \ 
+       +-+-+       +
 \     /  |xx\     /
  +---+   |xxx+---+
 /     \  |xx/     \ 
+       +-+-+       +
 \     /     \     /
  +---+       +---+
       \     /
        +---+

One third move:
        +---+    
       /     \
  +---+       +---+
 /     \     /     \ 
+       +---+       +
 \     /    ,+     /
  +---+    /xx+---+
 /     \  |xx/     \ 
+       +-+-+       +
 \     /     \     /
  +---+       +---+
       \     /
        +---+