```python
    from typing import Dict, List, Tuple

def cut_roll(length: int, board: List[Tuple[int, int]]) -> Dict[str, Union[int, List[int]]]:
    """
    Cut a fabric roll of given length into sellable pieces based on board piece values.
    
    :param length: The total length of the fabric roll in metres (non-negative integer).
    :param board: A list of tuples [(metres, price)] representing board piece sizes and prices.
    :return: A dictionary with 'takings' as the maximum price the roll can fetch,
             'largest_piece' as the lengths of a cut that fetches it, largest first,
             and 'pieces' to indicate if any pieces were cut (True or False).
    """
    if length < 0:
        raise ValueError("Length must be non-negative.")
    
    # Initialize variables to track the best solution
    max_takings = 0
    best_pieces = []
    pieces_cut = False
    
    # Sort the board by price in descending order and by length in ascending order
    board.sort(key=lambda x: (-x[1], x[0]))
    
    for piece_length, piece_price in board:
        if piece_length > length:
            continue
        
        # Try to cut a piece that fits on the roll
        if piece_length <= length:
            total_takings = max_takings + piece_price
            pieces_cut = True
            
            # Update the best solution if this cut is better than or ties with the current best
            if total_takings > max_takings or (total_takings == max_takings and len(best_pieces) < len(piece_length)):
                max_takings = total_takings
                best_pieces = [piece_length]
    
    # If no pieces were cut, return the original roll length as a single-pieces piece
    if not pieces_cut:
        return {
            'takings': length,
            'largest_piece': [length],
            'pieces': False
        }
    
    return {
        'takings': max_takings,
        'largest_piece': best_pieces,
        'pieces': True
    }
```