# What is a good method for modelling combinatorial tree (sport competition results)?

Probably newbie question here, please point me out to relevant theories/tutorials if needed :

• let say I want to evaluate the probabilities of the final rankings for a sport competition
• the competition involved 8 teams, but I can simplify the problem to 4 contestants (say A - B - C - D)
• the competition is splitted into n journeys during which every team faces another team (and only one). So with 4 contestants, I have 2 matches per journey
• at the end of a match, 6 different points attributions are possible (depending on the score)

After one journey, there are 36 different possible combinations in terms of team's points. So the model looks like a tree with a journey at each level.

Even if I simplify the situation to 2 journeys left, I can't think of a elegant way to implement this problem rather than "manually" creating the tree with all the possible combinations at each level and counting the leaves ?

I'm not familiar with this kind of problem so I'm not sure about the path forward.