Python solution with simple steps
Everything we need to know  to answer if we can win this game the total tree size  and  left and right subtrees size, because we only have 3 options to choose t
Everything we need to know  to answer if we can win this game the total tree size  and  left and right subtrees size, because we only have 3 options to choose to win this game:\n\n1. The choice left  sub tree or red node, if left subtree more that whole tree \n1. The choice right sub tree or red node, if right subtree more that whole tree.\n1. The choice the parent node of red node, if  red is not root and red subtree include red node self is less  that whole tree.\n\nBTW, we do not need calculate  whole tree size because we got it from input parameters as `n` parameter. \n\n\n\n```\n# Definition for a binary tree node.\n# class TreeNode:\n#     def __init__(self, val=0, left=None, right=None):\n#         self.val = val\n#         self.left = left\n#         self.right = right\nclass Solution:\n    def btreeGameWinningMove(self, root: TreeNode, n: int, x: int) -> bool:\n        \n        def sub_tree_size(node ):\n            if node is None:\n                return 0    \n            return sub_tree_size(node.left) + sub_tree_size(node.right) + 1     \n        \n        def find_red(root, x):\n            q = [root]\n            while len(q):\n                node = q.pop()\n                if node.val == x:\n                    return node\n                if node.left is not None:\n                    q.append(node.left)\n                if node.right is not None:\n                    q.append(node.right)\n        \n        red_node = find_red(root,x)\n        l_tree_size = sub_tree_size(red_node.left)\n        r_tree_size = sub_tree_size(red_node.right)\n        red_size = l_tree_size + r_tree_size +1\n        is_red_root = red_node == root\n        \n        # use left\n        if n - l_tree_size <l_tree_size:\n            return True\n        # use right \n        if n - r_tree_size < r_tree_size:\n                return True\n        # use parent \n        if is_red_root !=True and  n - red_size >red_size:\n                return True     \n        return False        \n                \n```
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