def main_sequence_iter(game_tree):
    """Provide the 'leftmost' complete sequence of a Coarse_game_tree.

    game_tree -- Coarse_game_tree

    Returns an iterable of property maps.

    If the game has no variations, this provides the complete game. Otherwise,
    it chooses the first variation each time it has a choice.

    """
    while True:
        for properties in game_tree.sequence:
            yield properties
        if not game_tree.children:
            break
        game_tree = game_tree.children[0]
