0
$\begingroup$

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.

$\endgroup$
0
$\begingroup$

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?

| cite | improve this answer | |
$\endgroup$
  • $\begingroup$ No you are right indeed. As for what I want to achieve : my goal is to compute, at the end of all journeys, the probability (% of situation) of each possible rankings among the 4 teams, depending on the successive score attributions. $\endgroup$ – Beinje Feb 13 at 20:22
  • $\begingroup$ Actually, there are 6 different attributions per match, so a total of 36 combinations after a journey with 4 teams. I edited the post though this is not the core problem. $\endgroup$ – Beinje Feb 14 at 9:23
0
$\begingroup$

It is straightforward to write a program that enumerates all 36 different combinations, computes the probability of each, and aggregates them. Or, equivalently, you can think of this as creating the entire tree. A computer can do billions of operations in a second, so doing this for 36 different combinations should be completed so fast it is done before you are even aware it started.

If you're trying to do it by hand rather than with a computer, this isn't a question about computer science and it belongs on Math.SE rather than here.

| cite | improve this answer | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.