Tournament_Quiz.py

''' A tennis club invites 32 players of equal ability to compete in an elimination tournament.
    (Only the winner of the pair will stay for the next round)
    What is the probability that a particular pair of players will meet during the tournament?'''

import random

count = 0
def recursive_round(a):    # we create a recursive function to simulate the tournament where the argument is a list
        if len(a) == 1:
            return a[0]
        else:
            lista = []
            print()
            for i in range (1,int(len(a)/2 + 1)):
                    x = random.choice(a)
                    a.remove(x)
                    y = random.choice(a)
                    a.remove(y)
                    match = ("The {} match is: {} vs {}".format(i,x,y))
                    print(match)
                    if (x,y) == (1,2) or (x,y) == (2,1):      #every time that the couple (1,2) happens, we update the count.
                        global count
                        count += 1
                    winner1 = random.choice((x,y))
                    lista.append(winner1)
            return(recursive_round(lista))

N = 1000000              # montecarlo method
for i in range(N):       # we generate the tournament 1 million of times (it takes a lot of time)
    recursive_round([i for i in range (1,33)])                 # [i for i in range (1,33)] is the list of 32 players and this is the
                                                               # argument of our function

print()
print("The couple (1,2) happened {} times".format(count))
print()
print("Probability is: ", float(count / N))  # the result is around 1/16