Bowling!

from itertools import count

values = dict(zip('-123456789X', count()))

def score(marks):
    """Return the score for only the first of a list of marks"""
    if marks[0] == '/':
        return 10 + values[marks[1]]
    elif marks[0] == 'X':
        return 10 + (10 if marks[2] == '/' else values[marks[1]] + values[marks[2]])
    elif marks[1] == '/':
        return 0
    else:
        return values[marks[0]]

def game(marks):
    """Return the game score for a list of marks

    >>> game("X-/X5-8/9-X811-4/X")
    137
    >>> game("9/8/9/8/9/8/9/8/9/81")
    175
    >>> game("9/8/9/8/9/8/9/8/9/8/9")
    185
    >>> game("XXXXXXXXXX9/")
    289
    >>> game("XXXXXXXXXXXX")
    300
    >>> game("--------------------")
    0
    >>> game("4/5-----------------")
    20
    >>> game("-------------------/1")
    11
    >>> game("-------------------X-1")
    11
    >>> game("1-1-1-1-1-1-1-1-1-1-")
    10
    >>> game("11111111111111111111")
    20
    """
    marks = list(marks + '-')
    tally = 0
    for frame in range(10):
        mark = marks.pop(0)
        tally += score([mark] + marks)
        if mark == 'X':
            continue
        tally += score([marks.pop(0)] + marks)
    return tally

if __name__ == '__main__':
    import doctest
    doctest.testmod()