Actually, if you take a look at the graph, you will notice that paths that direct to red leaves are almost all almost entirely red whereas there is a lot of paths to blue leaves that are mostly or even almost entirely red.
Or think another way. The largest number of states that can be blue and red still wins is 4. There isn't any combination of any combinations where 5 of selected states are blue and red can still win.
To calculate actual probability don't look at just the number of read leaves to number of blue leaves. You need to take into account probability of each of the state being blue or red. I am too lazy to calculate it but at first sight red outcome seems extremely unlikely.
I believe that the "direct" path of one color and "alternating" path are just a choice of the graphing and not dictated by the data. If you make different node selections, you could make the reverse. Same for the layout of the nicely ordered trees and those that seem more chaotic--it's just a matter of adjusting the layout of the nodes to determine the angles of the edges.
I don't mean the order, but the number of paths with given number of nodes of given color. This is independent on the chosen order or layout of the graph.
Or think another way. The largest number of states that can be blue and red still wins is 4. There isn't any combination of any combinations where 5 of selected states are blue and red can still win.
To calculate actual probability don't look at just the number of read leaves to number of blue leaves. You need to take into account probability of each of the state being blue or red. I am too lazy to calculate it but at first sight red outcome seems extremely unlikely.