Further Enhance and add:

Positional Memory Learning: Recalls and prioritizes move sequences based on specific strategic patterns across games.
Dynamic Depth Control: Adjusts the search depth based on position complexity rather than uniform depth limits, making it faster in tactical situations and deeper in positional ones.
Endgame Navigator: Specialized logic that kicks in when only a few pieces remain, enabling it to navigate even the trickiest endings with precision.

Alpha-Beta Pruning with enhanced Monte Carlo Tree Search (MCTS) for selective deep dives into critical variations.
Positional Heuristics like Outpost Mastery and Weak Square Exploitation for high-level strategic understanding.
Rook-on-the-Seventh and Minor Piece Dominance special emphasis within endgame evaluation.

```
import chess
import chess.engine
import chess.pgn
import random
import io
import numpy as np
from functools import lru_cache
from time import time, perf_counter
from scipy.interpolate import interp1d
import math
import sys
import logging
import multiprocessing
from multiprocessing import Pool, cpu_count
import signal

# ======================== Configuration and Initialization ========================

# Constants and Paths
STOCKFISH_PATH = r'C:\Users\hp\Downloads\Stock\stockfish\Stocky.exe'  # Update this to your Stockfish executable path
ENGINE_SAMPLER = 0.05  # Time in seconds per analysis
TOP_M = 3  # Number of top moves to consider from Stockfish
MCTS_ITERATIONS = 50  # Number of iterations for MCTS
MOVE_TIME_LIMIT = 2.0  # Maximum time (in seconds) allowed per move

# Initialize Logging
logging.basicConfig(level=logging.INFO, format='%(asctime)s [%(levelname)s] %(message)s')

# Initialize Stockfish Engine
try:
    engine = chess.engine.SimpleEngine.popen_uci(STOCKFISH_PATH)
    logging.info("Stockfish engine successfully initialized.")
except FileNotFoundError:
    logging.error(f"Stockfish engine not found at {STOCKFISH_PATH}. Please check the path.")
    sys.exit(1)

# ======================== Utility Functions ========================

def approximate_table(x):
    """
    Utilizes cubic interpolation to approximate values based on predefined data points.
    This function simulates complex evaluations or parameter tuning within the engine.
    """
    x_points = np.array([1, 2, 3, 4, 5])
    y_points = np.array([0.714, 0.703, 0.704, 0.701, 0.700])
    interpolating_function = interp1d(x_points, y_points, kind='cubic', fill_value="extrapolate")
    return float(interpolating_function(x))

# ======================== Positional Heuristics ========================

class PositionalHeuristics:
    """
    Evaluates various strategic elements of the chessboard to assess positional advantages.
    """

    @staticmethod
    def evaluate(board: chess.Board):
        score = 0.0
        score += PositionalHeuristics.outpost_mastery(board)
        score += PositionalHeuristics.weak_square_exploitation(board)
        score += PositionalHeuristics.rook_on_seventh(board)
        score += PositionalHeuristics.minor_piece_dominance(board)
        score += PositionalHeuristics.pawn_structure(board)
        score += PositionalHeuristics.king_safety(board)
        score += PositionalHeuristics.space_control(board)
        return score

    @staticmethod
    def outpost_mastery(board: chess.Board):
        """
        Rewards advanced positioning of knights and bishops on outposts.
        """
        score = 0.0
        for piece_type in [chess.KNIGHT, chess.BISHOP]:
            for square in board.pieces(piece_type, chess.WHITE):
                if PositionalHeuristics.is_outpost(board, square, chess.WHITE):
                    score += 0.3  # Bonus for white outpost
            for square in board.pieces(piece_type, chess.BLACK):
                if PositionalHeuristics.is_outpost(board, square, chess.BLACK):
                    score -= 0.3  # Bonus for black outpost
        return score

    @staticmethod
    def is_outpost(board: chess.Board, square, color):
        """
        An outpost is defined as a square protected by a pawn and cannot be attacked by opposing pawns.
        """
        opponent_color = not color
        if board.is_attacked_by(opponent_color, square):
            return False

        # Check for pawn protection
        defending_pawns = board.pieces(chess.PAWN, color)
        for pawn in defending_pawns:
            if PositionalHeuristics.can_pawn_protect_square(board, pawn, square, color):
                return True
        return False

    @staticmethod
    def can_pawn_protect_square(board: chess.Board, pawn_square, target_square, color):
        """
        Determines if a pawn can protect a given target square.
        """
        file_diff = chess.square_file(target_square) - chess.square_file(pawn_square)
        rank_diff = chess.square_rank(target_square) - chess.square_rank(pawn_square)
        if color == chess.WHITE:
            return rank_diff == 1 and abs(file_diff) == 1
        else:
            return rank_diff == -1 and abs(file_diff) == 1

    @staticmethod
    def weak_square_exploitation(board: chess.Board):
        """
        Rewards control over central weak squares while penalizing opponent control.
        """
        score = 0.0
        # Define central weak squares for both colors
        weak_squares = [chess.D4, chess.E4, chess.D5, chess.E5]
        for square in weak_squares:
            if board.is_attacked_by(chess.WHITE, square) and not board.is_attacked_by(chess.BLACK, square):
                score += 0.2  # Bonus for white controlling weak square
            if board.is_attacked_by(chess.BLACK, square) and not board.is_attacked_by(chess.WHITE, square):
                score -= 0.2  # Bonus for black controlling weak square
        return score

    @staticmethod
    def rook_on_seventh(board: chess.Board):
        """
        Rewards rooks that have penetrated into the opponent's seventh rank.
        """
        score = 0.0
        # White rooks on 7th rank (rank 7)
        for rook in board.pieces(chess.ROOK, chess.WHITE):
            if chess.square_rank(rook) == 6:  # 0-indexed ranks
                score += 0.4
        # Black rooks on 2nd rank (rank 2)
        for rook in board.pieces(chess.ROOK, chess.BLACK):
            if chess.square_rank(rook) == 1:
                score -= 0.4
        return score

    @staticmethod
    def minor_piece_dominance(board: chess.Board):
        """
        Incentivizes having a superior number of minor pieces (knights and bishops).
        """
        score = 0.0
        white_minors = len(board.pieces(chess.KNIGHT, chess.WHITE)) + len(board.pieces(chess.BISHOP, chess.WHITE))
        black_minors = len(board.pieces(chess.KNIGHT, chess.BLACK)) + len(board.pieces(chess.BISHOP, chess.BLACK))
        score += 0.1 * (white_minors - black_minors)
        return score

    @staticmethod
    def pawn_structure(board: chess.Board):
        """
        Evaluates the pawn structure, considering doubled pawns, isolated pawns, and passed pawns.
        """
        score = 0.0
        for color in [chess.WHITE, chess.BLACK]:
            pawns = board.pieces(chess.PAWN, color)
            files = [chess.square_file(p) for p in pawns]
            unique_files = set(files)
            for file in unique_files:
                count = files.count(file)
                if count > 1:
                    # Penalty for doubled pawns
                    score += (-0.2) * (count - 1) if color == chess.WHITE else 0.2 * (count - 1)
            # Isolated pawns
            isolated = PositionalHeuristics.count_isolated_pawns(board, color)
            score += (-0.1) * isolated if color == chess.WHITE else 0.1 * isolated
            # Passed pawns
            passed = PositionalHeuristics.count_passed_pawns(board, color)
            score += 0.3 * passed if color == chess.WHITE else -0.3 * passed
        return score

    @staticmethod
    def count_isolated_pawns(board: chess.Board, color):
        """
        Counts the number of isolated pawns for a given color.
        An isolated pawn has no friendly pawns on adjacent files.
        """
        pawns = board.pieces(chess.PAWN, color)
        files = sorted([chess.square_file(p) for p in pawns])
        isolated = 0
        for file in files:
            if (file - 1 not in files) and (file + 1 not in files):
                isolated += 1
        return isolated

    @staticmethod
    def count_passed_pawns(board: chess.Board, color):
        """
        Counts the number of passed pawns for a given color.
        A passed pawn has no opposing pawns that can block its advancement.
        """
        passed = 0
        direction = 1 if color == chess.WHITE else -1
        opponent_color = not color
        opponent_pawns = board.pieces(chess.PAWN, opponent_color)

        for pawn in board.pieces(chess.PAWN, color):
            file = chess.square_file(pawn)
            rank = chess.square_rank(pawn)
            is_passed = True
            for f in [file - 1, file, file + 1]:
                if 0 <= f <= 7:
                    for r in range(rank + direction, 8 if color == chess.WHITE else -1, direction):
                        sq = chess.square(f, r)
                        if sq in opponent_pawns:
                            is_passed = False
                            break
                if not is_passed:
                    break
            if is_passed:
                passed += 1
        return passed

    @staticmethod
    def king_safety(board: chess.Board):
        """
        Assesses the safety of the king based on pawn shields and nearby friendly pieces.
        """
        score = 0.0
        for color in [chess.WHITE, chess.BLACK]:
            king_square = board.king(color)
            if king_square is None:
                continue
            pawn_shield = PositionalHeuristics.count_pawn_shield(board, king_square, color)
            nearby_pieces = PositionalHeuristics.count_nearby_pieces(board, king_square, color)
            # Adjust scores based on pawn shield and nearby pieces
            score += 0.2 * pawn_shield if color == chess.WHITE else -0.2 * pawn_shield
            score += 0.1 * nearby_pieces if color == chess.WHITE else -0.1 * nearby_pieces
        return score

    @staticmethod
    def count_pawn_shield(board: chess.Board, king_square, color):
        """
        Counts the number of pawns in the immediate vicinity to shield the king.
        """
        file = chess.square_file(king_square)
        rank = chess.square_rank(king_square)
        shield = 0
        for shift in [-1, 0, 1]:
            f = file + shift
            if 0 <= f <= 7:
                # Determine the pawn's rank based on color
                rank_shift = 1 if color == chess.WHITE else -1
                sq = chess.square(f, rank + rank_shift)
                if 0 <= chess.square_rank(sq) <= 7:
                    piece = board.piece_at(sq)
                    if piece and piece.piece_type == chess.PAWN and piece.color == color:
                        shield += 1
        return shield

    @staticmethod
    def count_nearby_pieces(board: chess.Board, king_square, color):
        """
        Counts the number of friendly pieces within two squares of the king.
        """
        nearby = 0
        king_rank = chess.square_rank(king_square)
        king_file = chess.square_file(king_square)
        for square in chess.SQUARES:
            if board.piece_at(square) and board.piece_at(square).color == color:
                dist = chess.square_distance(square, king_square)
                if dist <= 2 and square != king_square:
                    nearby += 1
        return nearby

    @staticmethod
    def space_control(board: chess.Board):
        """
        Rewards control over central and expansive squares.
        """
        score = 0.0
        central_squares = [chess.D4, chess.E4, chess.D5, chess.E5]
        for square in central_squares:
            if board.is_attacked_by(chess.WHITE, square):
                score += 0.1
            if board.is_attacked_by(chess.BLACK, square):
                score -= 0.1
        return score

# ======================== Positional Memory Learning ========================

class PositionalMemory:
    """
    Remembers and scores moves based on past outcomes to prioritize strong moves in similar positions.
    """
    def __init__(self):
        self.memory = {}  # {fen: [move1, move2, ...]}
        self.move_scores = {}  # {fen: {move: score}}

    def recall(self, board_fen):
        """
        Retrieves the list of remembered moves for a given board position.
        """
        return self.memory.get(board_fen, [])

    def remember(self, board_fen, move, outcome):
        """
        Stores a move and updates its score based on the game outcome.
        """
        if board_fen not in self.memory:
            self.memory[board_fen] = []
            self.move_scores[board_fen] = {}
        self.memory[board_fen].append(move)
        if move not in self.move_scores[board_fen]:
            self.move_scores[board_fen][move] = 0
        # Update scores based on outcome
        if outcome == 'win':
            self.move_scores[board_fen][move] += 1
        elif outcome == 'loss':
            self.move_scores[board_fen][move] -= 1
        else:
            self.move_scores[board_fen][move] += 0.5  # For draws or neutral outcomes

    def prioritize_moves(self, board_fen, legal_moves):
        """
        Prioritizes moves based on historical performance in similar positions.
        """
        remembered_moves = self.memory.get(board_fen, [])
        if not remembered_moves:
            return list(legal_moves)
        # Assign scores to moves based on historical data
        move_scores = self.move_scores.get(board_fen, {})
        ranked_moves = sorted(legal_moves, key=lambda move: move_scores.get(move.uci(), 0), reverse=True)
        return ranked_moves

# ======================== Deep Reinforcement Learning Simulation ========================

class DeepReinforcementLearning:
    """
    Simulates a deep reinforcement learning model's evaluation of board positions.
    In a production environment, integrate an actual trained neural network model here.
    """
    def __init__(self):
        # Placeholder for a neural network model
        # In practice, load a trained model (e.g., using TensorFlow or PyTorch)
        pass

    def evaluate_position(self, board: chess.Board):
        """
        Combines material balance and mobility to simulate neural network evaluation.
        """
        material = self.material_evaluation(board)
        mobility = len(list(board.legal_moves))
        return material + 0.1 * mobility  # Weight mobility as a factor

    def material_evaluation(self, board: chess.Board):
        """
        Calculates the material balance of the board.
        """
        value = 0
        piece_values = {
            chess.PAWN: 100,
            chess.KNIGHT: 320,
            chess.BISHOP: 330,
            chess.ROOK: 500,
            chess.QUEEN: 900,
            chess.KING: 20000  # Essential piece
        }
        for piece in board.piece_map().values():
            v = piece_values.get(piece.piece_type, 0)
            if piece.color == chess.WHITE:
                value += v
            else:
                value -= v
        return value / 100  # Normalize (e.g., +3.20 means White has an advantage equivalent to a Knight)

# ======================== Alpha-Beta Pruning with Enhanced Move Ordering ========================

class AlphaBetaPruning:
    """
    Implements the Alpha-Beta pruning algorithm with enhanced move ordering based on positional memory and heuristics.
    """
    def __init__(self, engine, memory, sampler=ENGINE_SAMPLER):
        self.engine = engine
        self.memory = memory
        self.sampler = sampler
        self.lr = DeepReinforcementLearning()

    def get_best_move(self, board: chess.Board, depth: int):
        """
        Determines the best move using Alpha-Beta pruning with iterative deepening.
        """
        self.best_move = None
        alpha = -math.inf
        beta = math.inf

        logging.info(f"Alpha-Beta Pruning: Starting search at depth {depth}.")
        prioritized_moves = self.memory.prioritize_moves(board.fen(), list(board.legal_moves))
        prioritized_moves = sorted(prioritized_moves, key=lambda move: self.move_order(board, move), reverse=True)

        for move in prioritized_moves:
            board.push(move)
            score = self.alphabeta(board, depth - 1, alpha, beta, False)
            board.pop()
            logging.debug(f"Evaluated move {move.uci()} with Alpha-Beta score {score}.")
            if score > alpha:
                alpha = score
                self.best_move = move
                logging.debug(f"New best move updated to {move.uci()} with score {alpha}.")
            if alpha >= beta:
                logging.debug(f"Alpha ({alpha}) >= Beta ({beta}). Pruning remaining moves.")
                break  # Beta cut-off
        logging.info(f"Alpha-Beta Pruning: Best move determined as {self.best_move.uci()} with score {alpha}.")
        return self.best_move

    def alphabeta(self, board: chess.Board, depth: int, alpha: float, beta: float, maximizing_player: bool):
        """
        Recursively applies the Alpha-Beta pruning algorithm.
        """
        if depth == 0 or board.is_game_over():
            return self.evaluate(board)

        legal_moves = list(board.legal_moves)
        prioritized_moves = self.memory.prioritize_moves(board.fen(), legal_moves)
        prioritized_moves = sorted(prioritized_moves, key=lambda move: self.move_order(board, move), reverse=True)

        if maximizing_player:
            value = -math.inf
            for move in prioritized_moves:
                board.push(move)
                value = max(value, self.alphabeta(board, depth - 1, alpha, beta, False))
                board.pop()
                alpha = max(alpha, value)
                if alpha >= beta:
                    logging.debug(f"Pruning in maximizing player: Alpha ({alpha}) >= Beta ({beta}).")
                    break  # Beta cut-off
            return value
        else:
            value = math.inf
            for move in prioritized_moves:
                board.push(move)
                value = min(value, self.alphabeta(board, depth - 1, alpha, beta, True))
                board.pop()
                beta = min(beta, value)
                if beta <= alpha:
                    logging.debug(f"Pruning in minimizing player: Beta ({beta}) <= Alpha ({alpha}).")
                    break  # Alpha cut-off
            return value

    def evaluate(self, board: chess.Board):
        """
        Combines engine analysis, positional heuristics, and simulated deep RL evaluation.
        """
        try:
            analysis = self.engine.analyse(board, chess.engine.Limit(time=self.sampler))
            engine_score = analysis["score"].white().score(mate_score=10000)
            if engine_score is None:
                engine_score = 0
            else:
                engine_score = engine_score / 100.0  # Normalize to match other scores
        except Exception as e:
            logging.error(f"Engine analysis failed: {e}")
            engine_score = 0
        positional_score = PositionalHeuristics.evaluate(board)
        rl_score = self.lr.evaluate_position(board)
        total_score = engine_score + positional_score + rl_score
        logging.debug(f"Evaluation - Engine: {engine_score}, Positional: {positional_score}, RL: {rl_score}, Total: {total_score}")
        return total_score

    def move_order(self, board: chess.Board, move: chess.Move):
        """
        Determines the order of move evaluation based on memory scores and additional heuristics.
        """
        board_fen = board.fen()
        move_score = 0
        # Incorporate historical performance
        move_score += self.memory.move_scores.get(board_fen, {}).get(move.uci(), 0)
        # Additional heuristics
        if board.is_capture(move):
            move_score += 0.5  # Prioritize captures
        if board.gives_check(move):
            move_score += 0.3  # Prioritize checks
        # Potential tactical motifs can be added here
        return move_score

# ======================== Monte Carlo Tree Search (MCTS) ========================

class MCTSNode:
    """
    Represents a node in the Monte Carlo Tree Search.
    """
    def __init__(self, board: chess.Board, parent=None, move=None):
        self.board = board.copy()
        self.parent = parent
        self.move = move
        self.children = {}
        self.visits = 0
        self.wins = 0
        self.untried_moves = list(board.legal_moves)

    def expand(self, memory):
        """
        Expands the node by adding a new child for an untried move.
        """
        move = self.untried_moves.pop()
        new_board = self.board.copy()
        new_board.push(move)
        child_node = MCTSNode(new_board, parent=self, move=move)
        self.children[move] = child_node
        logging.debug(f"MCTS Node expanded with move {move.uci()}.")
        return child_node

    def is_fully_expanded(self):
        """
        Checks if all possible moves from this node have been tried.
        """
        return len(self.untried_moves) == 0

    def best_child(self, c_param=1.4):
        """
        Selects the best child node based on the UCB1 formula.
        """
        choices_weights = [
            (child.wins / child.visits) + c_param * math.sqrt((2 * math.log(self.visits) / child.visits))
            for child in self.children.values()
        ]
        best = list(self.children.values())[choices_weights.index(max(choices_weights))]
        logging.debug(f"MCTS Best child selected with move {best.move.uci()}.")
        return best

def simulate_game(board: chess.Board):
    """
    Simulates a random playout from the current board position until the game ends.
    """
    simulation_board = board.copy()
    while not simulation_board.is_game_over():
        move = random.choice(list(simulation_board.legal_moves))
        simulation_board.push(move)
    result = simulation_board.result()
    logging.debug(f"Simulation completed with result: {result}")
    return result

def monte_carlo_tree_search(root: MCTSNode, iterations: int, memory: PositionalMemory):
    """
    Performs the Monte Carlo Tree Search algorithm to determine the best move.
    """
    for i in range(iterations):
        node = root
        # Selection
        while node.is_fully_expanded() and node.children:
            node = node.best_child()
        # Expansion
        if not node.is_fully_expanded():
            node = node.expand(memory)
        # Simulation
        result = simulate_game(node.board)
        # Backpropagation
        while node is not None:
            node.visits += 1
            if result == "1-0":
                node.wins += 1  # White wins
            elif result == "0-1":
                node.wins -= 1  # Black wins
            # Draws do not affect the score
            node = node.parent
        if (i+1) % 10 == 0:
            logging.debug(f"MCTS Iteration {i+1}/{iterations} completed.")
    # Return the move with the highest visit count
    if root.children:
        best_move = max(root.children.values(), key=lambda c: c.visits).move
        logging.info(f"MCTS selected move: {best_move.uci()} after {iterations} iterations.")
        return best_move
    return None

# ======================== Dynamic Depth Control ========================

def dynamic_depth_control(board: chess.Board):
    """
    Adjusts the search depth dynamically based on the complexity of the current position.
    """
    complexity = evaluate_complexity(board)
    if complexity > 40:
        depth = 4  # Deeper search for highly complex positions
    elif 25 < complexity <= 40:
        depth = 3  # Moderate search depth
    else:
        depth = 2  # Shallow search for simple positions
    logging.debug(f"Dynamic Depth Control set depth to: {depth} based on complexity: {complexity}")
    return depth

def evaluate_complexity(board: chess.Board):
    """
    Evaluates the complexity of the position based on legal moves and material balance.
    """
    legal_moves = len(list(board.legal_moves))
    material = sum([piece_value(p) for p in board.piece_map().values()])
    complexity = legal_moves + material / 100  # Combining factors
    logging.debug(f"Evaluating complexity: Legal Moves={legal_moves}, Material={material}, Complexity={complexity}")
    return complexity

def piece_value(piece):
    """
    Assigns a value to each piece type for material evaluation.
    """
    values = {
        chess.PAWN: 100,
        chess.KNIGHT: 320,
        chess.BISHOP: 330,
        chess.ROOK: 500,
        chess.QUEEN: 900,
        chess.KING: 20000  # Essential piece
    }
    return values.get(piece.piece_type, 0)

# ======================== Endgame Navigator ========================

def endgame_navigator(board: chess.Board):
    """
    Utilizes Stockfish's analysis to provide precise endgame moves.
    """
    material = sum([piece_value(p) for p in board.piece_map().values()])
    # Define endgame as having material below a certain threshold
    if material < 2000:
        try:
            analysis = engine.analyse(board, chess.engine.Limit(time=0.2))
            best_move = analysis["pv"][0]
            logging.info(f"Endgame Navigator selected move: {best_move.uci()}")
            return best_move
        except Exception as e:
            logging.error(f"Endgame analysis failed: {e}")
            return None
    return None

# ======================== Move Evaluation Helper ========================

def evaluate_move(args):
    """
    Evaluates a move in parallel using multiprocessing.
    Args:
        args (tuple): Contains (move, board_fen)
    Returns:
        tuple: (move, score)
    """
    move, board_fen = args
    board = chess.Board(board_fen)
    board.push(move)
    material = sum([piece_value(p) for p in board.piece_map().values()])
    mobility = len(list(board.legal_moves))
    score = material + 0.1 * mobility
    return (move, score)

# ======================== Alpha-Beta Pruning with Enhanced Move Ordering ========================

class AlphaBetaPruning:
    """
    Implements the Alpha-Beta pruning algorithm with enhanced move ordering based on positional memory and heuristics.
    """
    def __init__(self, engine, memory, sampler=ENGINE_SAMPLER):
        self.engine = engine
        self.memory = memory
        self.sampler = sampler
        self.lr = DeepReinforcementLearning()

    def get_best_move(self, board: chess.Board, depth: int):
        """
        Determines the best move using Alpha-Beta pruning with iterative deepening and time limits.
        """
        self.best_move = None
        alpha = -math.inf
        beta = math.inf
        start_time = perf_counter()
        time_limit = MOVE_TIME_LIMIT - 0.1  # Buffer to prevent overrunning

        prioritized_moves = self.memory.prioritize_moves(board.fen(), list(board.legal_moves))
        prioritized_moves = sorted(prioritized_moves, key=lambda move: self.move_order(board, move), reverse=True)

        logging.info(f"Alpha-Beta Pruning: Starting search at depth {depth} with {len(prioritized_moves)} prioritized moves.")

        for move in prioritized_moves:
            current_time = perf_counter()
            if current_time - start_time > time_limit:
                logging.warning("Alpha-Beta Pruning: Time limit exceeded during move evaluation.")
                break
            board.push(move)
            score = self.alphabeta(board, depth - 1, alpha, beta, False, start_time, time_limit)
            board.pop()
            logging.debug(f"Evaluated move {move.uci()} with Alpha-Beta score {score}.")
            if score > alpha:
                alpha = score
                self.best_move = move
                logging.debug(f"New best move updated to {move.uci()} with score {alpha}.")
            if alpha >= beta:
                logging.debug(f"Alpha ({alpha}) >= Beta ({beta}). Pruning remaining moves.")
                break  # Beta cut-off
        if self.best_move:
            logging.info(f"Alpha-Beta Pruning: Best move determined as {self.best_move.uci()} with score {alpha}.")
        else:
            logging.info("Alpha-Beta Pruning: No best move determined.")
        return self.best_move

    def alphabeta(self, board: chess.Board, depth: int, alpha: float, beta: float, maximizing_player: bool, start_time: float, time_limit: float):
        """
        Recursively applies the Alpha-Beta pruning algorithm with time checks.
        """
        current_time = perf_counter()
        if current_time - start_time > time_limit:
            logging.warning("Alpha-Beta Pruning: Time limit exceeded during recursive search.")
            return 0  # Neutral score on timeout

        if depth == 0 or board.is_game_over():
            return self.evaluate(board)

        legal_moves = list(board.legal_moves)
        prioritized_moves = self.memory.prioritize_moves(board.fen(), legal_moves)
        prioritized_moves = sorted(prioritized_moves, key=lambda move: self.move_order(board, move), reverse=True)

        if maximizing_player:
            value = -math.inf
            for move in prioritized_moves:
                board.push(move)
                value = max(value, self.alphabeta(board, depth - 1, alpha, beta, False, start_time, time_limit))
                board.pop()
                alpha = max(alpha, value)
                if alpha >= beta:
                    logging.debug(f"Pruning in maximizing player: Alpha ({alpha}) >= Beta ({beta}).")
                    break  # Beta cut-off
            return value
        else:
            value = math.inf
            for move in prioritized_moves:
                board.push(move)
                value = min(value, self.alphabeta(board, depth - 1, alpha, beta, True, start_time, time_limit))
                board.pop()
                beta = min(beta, value)
                if beta <= alpha:
                    logging.debug(f"Pruning in minimizing player: Beta ({beta}) <= Alpha ({alpha}).")
                    break  # Alpha cut-off
            return value

    def evaluate(self, board: chess.Board):
        """
        Combines engine analysis, positional heuristics, and simulated deep RL evaluation.
        """
        try:
            analysis = self.engine.analyse(board, chess.engine.Limit(time=self.sampler))
            engine_score = analysis["score"].white().score(mate_score=10000)
            if engine_score is None:
                # If no mate score, categorize as 0
                engine_score = 0
            else:
                engine_score = engine_score / 100.0  # Normalize to match other scores
        except Exception as e:
            logging.error(f"Engine analysis failed: {e}")
            engine_score = 0
        positional_score = PositionalHeuristics.evaluate(board)
        rl_score = self.lr.evaluate_position(board)
        total_score = engine_score + positional_score + rl_score
        logging.debug(f"Evaluation - Engine: {engine_score}, Positional: {positional_score}, RL: {rl_score}, Total: {total_score}")
        return total_score

    def move_order(self, board: chess.Board, move: chess.Move):
        """
        Determines the order of move evaluation based on memory scores and additional heuristics.
        """
        board_fen = board.fen()
        move_score = 0
        # Incorporate historical performance
        move_score += self.memory.move_scores.get(board_fen, {}).get(move.uci(), 0)
        # Additional heuristics
        if board.is_capture(move):
            move_score += 0.5  # Prioritize captures
        if board.gives_check(move):
            move_score += 0.3  # Prioritize checks
        # Potential tactical motifs can be added here
        return move_score

# ======================== Monte Carlo Tree Search (MCTS) ========================

class MonteCarloTreeSearch:
    """
    Implements the Monte Carlo Tree Search algorithm with statistical backing.
    """
    def __init__(self, memory: PositionalMemory, iterations: int = MCTS_ITERATIONS):
        self.memory = memory
        self.iterations = iterations

    def search(self, board: chess.Board):
        """
        Performs MCTS to determine the best move from the current board position.
        """
        root = MCTSNode(board)
        logging.info(f"Starting MCTS with {self.iterations} iterations.")
        best_move = monte_carlo_tree_search(root, self.iterations, self.memory)
        return best_move

# ======================== DeepMaster Engine ========================

class DeepMasterEngine:
    """
    Integrates all components to manage game state and select optimal moves.
    """
    def __init__(self, engine, sampler=ENGINE_SAMPLER, top_m=TOP_M):
        self.board = chess.Board()
        self.memory = PositionalMemory()
        self.alphabeta = AlphaBetaPruning(engine, self.memory, sampler)
        self.top_m = top_m
        self.mcts_iterations = MCTS_ITERATIONS
        self.lr = DeepReinforcementLearning()
        self.mcts = MonteCarloTreeSearch(self.memory, self.mcts_iterations)

    def make_move(self, move_uci):
        """
        Applies a move to the board if it's legal.
        """
        try:
            move = chess.Move.from_uci(move_uci)
            if move in self.board.legal_moves:
                self.board.push(move)
                logging.debug(f"User move applied: {move.uci()}")
                return True, ""
            else:
                logging.warning(f"Attempted illegal move: {move.uci()}")
                return False, "Illegal move."
        except ValueError:
            logging.warning(f"Invalid move format attempted: {move_uci}")
            return False, "Invalid move format."

    def get_deepmaster_move(self):
        """
        Determines and applies DeepMaster's move using integrated components.
        """
        # Check for endgame and use Endgame Navigator if applicable
        end_move = endgame_navigator(self.board)
        if end_move and end_move in self.board.legal_moves:
            self.board.push(end_move)
            outcome = 'win' if self.board.turn == chess.BLACK else 'loss'
            self.memory.remember(self.board.fen(), end_move.uci(), outcome)
            logging.info(f"DeepMaster (Endgame) execution: {end_move.uci()}")
            return end_move

        # Dynamic Depth Control
        depth = dynamic_depth_control(self.board)

        # Alpha-Beta Pruning to determine best move
        move = self.alphabeta.get_best_move(self.board, depth)
        if move:
            self.board.push(move)
            outcome = 'win'  # Assuming the engine's move is beneficial
            self.memory.remember(self.board.fen(), move.uci(), outcome)
            logging.info(f"DeepMaster (Alpha-Beta) move selected: {move.uci()}")
            return move

        # If Alpha-Beta fails or no move found, fallback to MCTS
        mcts_move = self.mcts.search(self.board)
        if mcts_move:
            if mcts_move in self.board.legal_moves:
                self.board.push(mcts_move)
                outcome = 'win'  # Assuming the engine's move is beneficial
                self.memory.remember(self.board.fen(), mcts_move.uci(), outcome)
                logging.info(f"DeepMaster (MCTS) move selected: {mcts_move.uci()}")
                return mcts_move

        # Fallback to random move
        if self.board.legal_moves:
            move = random.choice(list(self.board.legal_moves))
            self.board.push(move)
            outcome = 'draw'
            self.memory.remember(self.board.fen(), move.uci(), outcome)
            logging.info(f"DeepMaster (Random) move selected: {move.uci()}")
            return move
        else:
            logging.info("DeepMaster has no legal moves and resigns.")
            return None

    def play_engine_move(self):
        """
        Wrapper for selecting and executing DeepMaster's move.
        """
        move = self.get_deepmaster_move()
        return move

    def display_board(self):
        """
        Returns a string representation of the current board state.
        """
        return self.board.__str__()

    def is_game_over(self):
        """
        Checks if the game has concluded.
        """
        return self.board.is_game_over()

    def get_result(self):
        """
        Retrieves the result of the game.
        """
        return self.board.result()

# ======================== Master Function with Debugging and Logging ========================

def master_func():
    """
    Manages the game loop, handling user inputs and engine responses with debugging support.
    """
    try:
        deepmaster = DeepMasterEngine(engine)
        logging.info("DeepMaster Chess Engine Initialized.")
        print("Welcome to DeepMaster Chess Engine V.2!")
        print("Enter your moves in UCI format (e.g., e2e4) or type 'quit' to exit.")

        while not deepmaster.is_game_over():
            print("\nCurrent Board:")
            print(deepmaster.display_board())
            user_move = input("Your move: ").strip()
            if user_move.lower() == 'quit':
                logging.info("User terminated the game.")
                break
            success, message = deepmaster.make_move(user_move)
            if not success:
                print(f"Error: {message}")
                continue
            if deepmaster.is_game_over():
                break
            # DeepMaster's Move Selection
            move = deepmaster.play_engine_move()
            if move:
                print(f"DeepMaster move: {move.uci()}")
            else:
                print("DeepMaster resigns. No valid moves available.")
                logging.info("DeepMaster resigned due to no valid moves.")

        print("\nGame Over!")
        print(f"Result: {deepmaster.get_result()}")
        print(deepmaster.display_board())
        logging.info(f"Game concluded with result: {deepmaster.get_result()}")

    except KeyboardInterrupt:
        logging.info("Game interrupted by user.")
    except Exception as e:
        logging.exception(f"An unexpected error occurred: {e}")
    finally:
        engine.quit()
        logging.info("Stockfish engine process terminated.")

# ======================== Entry Point ========================

if __name__ == "__main__":
    master_func()