==========[Example #1]==========

The full game tree is:

                o
           /    |    \
          o     o     o
         / \   / \   / \
        o   o o   o o   o
        |   | |   | |   |
        o   o o   o o   o


Branching factor: (3 + 3*2 + 3*2*1) / (1 + 3 + 3*2) = 15 / 10 = 1.5

If the middle branch is symmetric with one of it siblings.  The game tree becomes:

                o
           /         \
          o           o
         / \         / \
        o   o       o   o
        |   |       |   |
        o   o       o   o


Branching factor: (2 + 4 + 4) / (1 + 2 + 4) = 10 / 7 = 1.43 < 1.5

==========[Example #2]==========

The full game tree:

                                             o
             /                    /                     \                     \
            o                     o                     o                     o
       /    |    \           /    |    \           /    |    \           /    |    \
      o     o     o         o     o     o         o     o     o         o     o     o
     / \   / \   / \       / \   / \   / \       / \   / \   / \       / \   / \   / \
    o   o o   o o   o     o   o o   o o   o     o   o o   o o   o     o   o o   o o   o
    |   | |   | |   |     |   | |   | |   |     |   | |   | |   |     |   | |   | |   |
    o   o o   o o   o     o   o o   o o   o     o   o o   o o   o     o   o o   o o   o


Branching factor: (4 + 4*3 + 4*3*2 + 4*3*2*1) / (1 + 4 + 4*3 + 4*3*2) = 64 / 41 = 1.56

If the two branches on the right side are symmetric to their siblings, and a couple of the inner branches are symmetric to their siblings.  The game tree becomes:

                                             o
             /                    /                                                
            o                     o                                                    
       /         \           /    |    \                                               
      o           o         o     o     o                                              
     / \         / \       / \   /     /                                                 
    o   o       o   o     o   o o     o                                                    
    |   |       |   |     |   | |     |                                                   
    o   o       o   o     o   o o     o                                                


Branching factor: (2 + 5 + 8 + 8) / (1 + 2 + 5 + 8) = 23 / 16 = 1.44 < 1.56