MokaMoka's blog

By MokaMoka, history, 6 years ago, In English

Hello guys,

I have a probability problem that might look easy for most of you mature and experienced programmers,

" For a football team which consist of 11 players, there's a player that's gonna retire.

the coach of that team decided to make a challenge among n young players to have that player's position, and he decided to make some 1-to-1 matches

the coach has some expectations for that matches, so he wrote down an n*n matrix that holds these expectations,

let's call that matrix with the name A, so for A[i][j], there's a value between 0 and 1 which denotes the probability of player i wins against player j according to the coach expectations. for sure that matrix is gonna be symmetric and A[j][i] = 1 — A[i][j]."

I need to find out each player's probability of holding that position according to the given information, to be real this problem is driving me nuts and for sure any help would be appreciated :"))

Forgive my bad English since I'm a non native speaker, and thank you guys :)

 
 
 
 
  • Vote: I like it
  • +11
  • Vote: I do not like it

»
6 years ago, # |
  Vote: I like it 0 Vote: I do not like it

Any help please :') ..

»
6 years ago, # |
  Vote: I like it +21 Vote: I do not like it

How is the player who takes the position determined? Do they play each versus each and the one with maximum score takes it? What happens with ties?

  • »
    »
    6 years ago, # ^ |
    Rev. 2   Vote: I like it -8 Vote: I do not like it

    The problem is not about determining the player who takes that position, it's to find each player's probability of taking that position according to the 1-to-1 matches expectations.

    Ex:

    for 2 players A and B, the coach wrote this expectation 2*2 matrix for 1-to-1 matches:

    0 0.5

    0.5 0

    which means that the probability of A wins against B is 0.5, same for B wins against A

    player can not play against himself so the probability of A wins against A is 0, same for B wins against B.

    what's the method we'll use to find each of A and B probability to take that position?

    • »
      »
      »
      6 years ago, # ^ |
        Vote: I like it +3 Vote: I do not like it

      I don't think I understand. I know the problem is to determine probabilities, but nevertheless we need to know how is the one taking the position chosen. What is the process the coach makes them go through with 1v1 matches. Who plays who.

      • »
        »
        »
        »
        6 years ago, # ^ |
          Vote: I like it 0 Vote: I do not like it

        Each player plays against all other players ..

        that's why it's an n*n matrix, which have a main diagonal of zeros

        given that matrix of the coach expectations, print n lines, the i'th of them denotes the probability of player's i takes that position

        clear now?

        • »
          »
          »
          »
          »
          6 years ago, # ^ |
            Vote: I like it 0 Vote: I do not like it

          Still not very clear. I assume the one with most points gets the title. In this case could you tell me the output for input:

          N=3

          0 1 0

          0 0 1

          1 0 0

          Each player would surely win exactly one match. What is the output in such case?

»
6 years ago, # |
  Vote: I like it 0 Vote: I do not like it

Up :D !

»
3 years ago, # |
  Vote: I like it 0 Vote: I do not like it

I think the problem is simple! you have a matrix of n*n elements. and you have to find out the probability to put elements in the upper triangular matrix(say upper), no of upper triangular matrix element is (n*n-n)/4. if I m correct. and the probability of putting them be 0.5. and on fixing any triangle fixes other elements as diagonal elements always not defined say it 0. therefore probability overall is 0.5*(n*n-n)*0.25.

hence answer is 0.125*(n*n-n)