Python: How do I get a while loop to continue within another while statement?

I am trying to learn how while statements work in Python. I am trying to create a code that continues multiplying num1 and num2 until either rounds <= 10 or till num1 > num2. If num1 is bigger than num2 before 10 rounds, the loop closes and num1 is the winner, otherwise, the winner is num2.

My output only prints the first round fully and then 'Round = #' over and over again. I want the output to look like this:

Initiate Math Competition:
Round = 1
1 = #
1 = #
2 = #
2 = #
2 = #
Round = 2
1 = #
1 = #
2 = #
2 = #
2 = #
...
Math Competition Closed
Winner = 1

Note: I cannot change the main program. Also, I understand one of the problems of this code is that the inner loops are complete before moving on preventing the code to check whether or not num1 has overtaken num2 but I do not know how to go about fixing it.

def math_competition(num1, multiply1, max_repitition_1, num2, multiply2, max_repitition_2):
    """
    -------------------------------------------------------
    Returns Winner of Math Competition.
    Use: winner = math_competition(num1, multiply1, max_repitition_1, num2, multiply2, max_repitition_2)
    -------------------------------------------------------
    Parameters:
        num1:  first value (int)
        multiply1: first multiplying factor (int)
        max_repitition_1: max repetition for the first value (int)
        num2: second value (int)
        multiply2: second multiplying factor (int)
        max_repitition_2: second repetition factor (int)
    Returns:
        winner - Winner of Math Competition 
    -------------------------------------------------------
    """
    print('Initiate Math Competition:')
    rounds = 1
    first_counter = 0
    second_counter = 0
    winner = ''
    while rounds <= 10 and num1 < num2: 
        print('Round = {}'.format(rounds))
        while first_counter != max_repitition_1:
            num1 = num1 * multiply1
            print('1 = {}'.format(num1))
            first_counter += 1
        while second_counter != max_repitition_2:
            num2 = num2 * multiply2
            print('2 = {}'.format(num2))
            second_counter += 1
        if num1 > num2:
            winner = '1'
            break
        elif rounds <= 10 and num2 > num1:
            rounds += 1
            continue
        else:
            winner = '2'
    print('Math Competition Closed')
    return winner

#-------------------------MAIN PROGRAM---------------------------#
cases = [[20, -8, 4, 30, 2, 3], [15, 2, 2, 18, 5, 3], [12, 4, 2, 3400, 1, 5]]
for c in cases:
    winner = math_competition(c[0],c[1],c[2],c[3],c[4],c[5])
    print('Winner is: {}'.format(winner))