==========[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
