Decision Trees in board games?
I don't know any games that use decision trees, at least not visually. The only game I can think of that lets you manipulate rules to reach a certain goal, is fluxx.

To keep with the visual decision trees, you could use a single card per node:


Cards could be decision nodes and terminal nodes, and you would need a starting node for each tree.

Alternatively
You could use concentric pie charts to visualize the type of directional graph you're describing:



Just start at the center and follow the labels.