Match_models.py

class Match(models.Model):

    WHITE = 'White',
    BLACK = 'Black',
    DRAW = 'Draw',
    UNDETERMINED = 'Undetermined'

    MATCH_RESULT_CHOICES = (
        (WHITE, 'White Won'),
        (BLACK, 'Black Won'),
        (DRAW, 'Draw'),
        (UNDETERMINED, 'Undetermined')
    )

    round = models.ForeignKey('Round')
    players = models.ManyToManyField('Player', through='PlayerColor')
    result = models.CharField(max_length=20, choices=MATCH_RESULT_CHOICES, default=UNDETERMINED)

    # def __str__(self):
    #     return "{} vs {} - {}".format(self.white_player, self.black_player, self.result)


class PlayerColor(models.Model):

    WHITE = 'White'
    BLACK = 'Black'

    COLOR_CHOICES = (
        (WHITE, 'White'),
        (BLACK, 'Black')
    )

    player = models.ForeignKey('Player')
    match = models.ForeignKey('Match')
    color = models.CharField(max_length=10, choices=COLOR_CHOICES)
    
    
# ALTERNATE CHOICE  

class Match(models.Model):
    ....
    white_player = models.ForeignKey('Player', related_name='match_as_white_player')
    black_player = models.ForeignKey('Player', related_name='match_as_black_player')
    ....