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.
I can't follow how you get 30 combinations, you have 2 matches per journey each of the 2 matches can result in 5 different attributions, so you get 5*5 = 25 different attribution per match. At each journey there are 3 possibilities to make 2 matches. So the result would be 25/3 + 25/3 + 25/3 = 25 different point attributions.
Did I got something wrong?

You want to calculate how many different point attributions there are after n journeys and the probabilities to make a match are the same for every combination at every journey?