class TreeNode:
    def __init__(self, value=0, left=None, right=None):
        self.value = value
        self.left = left
        self.right = right

def binary_tree_coloring_game_brute_force(root, number_of_nodes, first_player_choice):
    def count_colored_nodes(node, colored_nodes):
        if not node:
            return 0
        count = 0
        if node.value in colored_nodes:
            count += 1
        count += count_colored_nodes(node.left, colored_nodes)
        count += count_colored_nodes(node.right, colored_nodes)
        return count

    def find_node(root, target):
        if not root:
            return None
        if root.value == target:
            return root
        node = find_node(root.left, target)
        if node:
            return node
        return find_node(root.right, target)

    def check_win(first_player_nodes, second_player_nodes):
        first_player_count = 0
        second_player_count = 0

        first_player_count = count_colored_nodes(root, first_player_nodes)
        second_player_count = count_colored_nodes(root, second_player_nodes)

        return first_player_count > second_player_count

    def get_all_nodes(root):
        nodes = []
        if not root:
            return nodes
        nodes.append(root.value)
        nodes.extend(get_all_nodes(root.left))
        nodes.extend(get_all_nodes(root.right))
        return nodes

    def can_first_player_win(available_nodes, first_player_nodes, second_player_nodes, turn):
        if not available_nodes:
            return check_win(first_player_nodes, second_player_nodes)

        if turn == 0:
            # First player's turn.
            for node_choice in available_nodes:
                new_available_nodes = available_nodes[:]
                new_available_nodes.remove(node_choice)
                new_first_player_nodes = first_player_nodes[:]
                new_first_player_nodes.add(node_choice)

                # Recursively call the function to explore the next move
                if can_first_player_win(new_available_nodes, new_first_player_nodes, second_player_nodes, 1):
                    return True
            return False
        else:
            # Second player's turn.
            for node_choice in available_nodes:
                new_available_nodes = available_nodes[:]
                new_available_nodes.remove(node_choice)
                new_second_player_nodes = second_player_nodes[:]
                new_second_player_nodes.add(node_choice)

                # After second player's turn, it's first player's turn
                if not can_first_player_win(new_available_nodes, first_player_nodes, new_second_player_nodes, 0):
                    return False

            # Second player can always force a win
            return True

    # Get all the nodes in the tree to represent availble choices
    all_nodes_in_tree = get_all_nodes(root)
    available_nodes = set(all_nodes_in_tree)

    # Color the first player's choice and make it unavailable
    first_player_nodes = set()
    first_player_nodes.add(first_player_choice)
    available_nodes.remove(first_player_choice)

    # Represent second player's nodes
    second_player_nodes = set()

    # Check if first player can win
    return can_first_player_win(available_nodes, first_player_nodes, second_player_nodes, 1)

class TreeNode:
    def __init__(self, val=0, left=None, right=None):
        self.val = val
        self.left = left
        self.right = right

def binary_tree_coloring_game(root, number_of_nodes, node_chosen_by_player1):

    left_subtree_size = 0
    right_subtree_size = 0

    def count_subtree_nodes(node):
        if not node:
            return 0
        return 1 + count_subtree_nodes(node.left) + count_subtree_nodes(node.right)

    def find_node(node, target):
        if not node:
            return None
        if node.val == target:
            return node
        left_search = find_node(node.left, target)
        if left_search:
            return left_search
        return find_node(node.right, target)

    chosen_node = find_node(root, node_chosen_by_player1)

    # Count nodes in left subtree. 
    left_subtree_size = count_subtree_nodes(chosen_node.left)

    # Count nodes in right subtree.
    right_subtree_size = count_subtree_nodes(chosen_node.right)

    # Calculate size of the parent subtree
    parent_subtree_size = number_of_nodes - left_subtree_size - right_subtree_size - 1

    # Check if any subtree is larger than half the total nodes
    if left_subtree_size > number_of_nodes // 2 or \
       right_subtree_size > number_of_nodes // 2 or \
       parent_subtree_size > number_of_nodes // 2:
        return True
    else:
        return False