games.py

"""Games, or Adversarial Search (Chapter 5)"""

from collections import namedtuple
import random
import itertools
import copy
from utils import argmax, vector_add

infinity = float('inf')
GameState = namedtuple('GameState', 'to_move, utility, board, moves')
StochasticGameState = namedtuple('StochasticGameState', 'to_move, utility, board, moves, chance')

# ______________________________________________________________________________
# Minimax Search


def minimax_decision(state, game):
    """Given a state in a game, calculate the best move by searching
    forward all the way to the terminal states. [Figure 5.3]"""

    player = game.to_move(state)

    def max_value(state):
        if game.terminal_test(state):
            return game.utility(state, player)
        v = -infinity
        for a in game.actions(state):
            v = max(v, min_value(game.result(state, a)))
        return v

    def min_value(state):
        if game.terminal_test(state):
            return game.utility(state, player)
        v = infinity
        for a in game.actions(state):
            v = min(v, max_value(game.result(state, a)))
        return v

    # Body of minimax_decision:
    return argmax(game.actions(state),
                  key=lambda a: min_value(game.result(state, a)))

# ______________________________________________________________________________


def expectiminimax(state, game):
    """Return the best move for a player after dice are thrown. The game tree
	includes chance nodes along with min and max nodes. [Figure 5.11]"""
    player = game.to_move(state)

    def max_value(state):
        v = -infinity
        for a in game.actions(state):
            v = max(v, chance_node(state, a))
        return v

    def min_value(state):
        v = infinity
        for a in game.actions(state):
            v = min(v, chance_node(state, a))
        return v

    def chance_node(state, action):
        res_state = game.result(state, action)
        if game.terminal_test(res_state):
            return game.utility(res_state, player)
        sum_chances = 0
        num_chances = len(game.chances(res_state))
        for chance in game.chances(res_state):
            res_state = game.outcome(res_state, chance)
            util = 0
            if res_state.to_move == player:
                util = max_value(res_state)
            else:
                util = min_value(res_state)
            sum_chances += util * game.probability(chance)
        return sum_chances / num_chances

    # Body of expectiminimax:
    return argmax(game.actions(state),
                  key=lambda a: chance_node(state, a), default=None)


def alphabeta_search(state, game):
    """Search game to determine best action; use alpha-beta pruning.
    As in [Figure 5.7], this version searches all the way to the leaves."""

    player = game.to_move(state)

    # Functions used by alphabeta
    def max_value(state, alpha, beta):
        if game.terminal_test(state):
            return game.utility(state, player)
        v = -infinity
        for a in game.actions(state):
            v = max(v, min_value(game.result(state, a), alpha, beta))
            if v >= beta:
                return v
            alpha = max(alpha, v)
        return v

    def min_value(state, alpha, beta):
        if game.terminal_test(state):
            return game.utility(state, player)
        v = infinity
        for a in game.actions(state):
            v = min(v, max_value(game.result(state, a), alpha, beta))
            if v <= alpha:
                return v
            beta = min(beta, v)
        return v

    # Body of alphabeta_search:
    best_score = -infinity
    beta = infinity
    best_action = None
    for a in game.actions(state):
        v = min_value(game.result(state, a), best_score, beta)
        if v > best_score:
            best_score = v
            best_action = a
    return best_action


def alphabeta_cutoff_search(state, game, d=4, cutoff_test=None, eval_fn=None):
    """Search game to determine best action; use alpha-beta pruning.
    This version cuts off search and uses an evaluation function."""

    player = game.to_move(state)

    # Functions used by alphabeta
    def max_value(state, alpha, beta, depth):
        if cutoff_test(state, depth):
            return eval_fn(state)
        v = -infinity
        for a in game.actions(state):
            v = max(v, min_value(game.result(state, a),
                                 alpha, beta, depth + 1))
            if v >= beta:
                return v
            alpha = max(alpha, v)
        return v

    def min_value(state, alpha, beta, depth):
        if cutoff_test(state, depth):
            return eval_fn(state)
        v = infinity
        for a in game.actions(state):
            v = min(v, max_value(game.result(state, a),
                                 alpha, beta, depth + 1))
            if v <= alpha:
                return v
            beta = min(beta, v)
        return v

    # Body of alphabeta_cutoff_search starts here:
    # The default test cuts off at depth d or at a terminal state
    cutoff_test = (cutoff_test or
                   (lambda state, depth: depth > d or
                    game.terminal_test(state)))
    eval_fn = eval_fn or (lambda state: game.utility(state, player))
    best_score = -infinity
    beta = infinity
    best_action = None
    for a in game.actions(state):
        v = min_value(game.result(state, a), best_score, beta, 1)
        if v > best_score:
            best_score = v
            best_action = a
    return best_action

# ______________________________________________________________________________
# Players for Games


def query_player(game, state):
    """Make a move by querying standard input."""
    print("current state:")
    game.display(state)
    print("available moves: {}".format(game.actions(state)))
    print("")
    move = None
    if game.actions(state):
        move_string = input('Your move? ')
        try:
            move = eval(move_string)
        except NameError:
            move = move_string
    else:
        print('no legal moves: passing turn to next player')
    return move


def random_player(game, state):
    """A player that chooses a legal move at random."""
    return random.choice(game.actions(state)) if game.actions(state) else None

def alphabeta_player(game, state):
    return alphabeta_search(state, game)

def expectiminimax_player(game, state):
    return expectiminimax(state, game)


# ______________________________________________________________________________
# Some Sample Games


class Game:
    """A game is similar to a problem, but it has a utility for each
    state and a terminal test instead of a path cost and a goal
    test. To create a game, subclass this class and implement actions,
    result, utility, and terminal_test. You may override display and
    successors or you can inherit their default methods. You will also
    need to set the .initial attribute to the initial state; this can
    be done in the constructor."""

    def actions(self, state):
        """Return a list of the allowable moves at this point."""
        raise NotImplementedError

    def result(self, state, move):
        """Return the state that results from making a move from a state."""
        raise NotImplementedError

    def utility(self, state, player):
        """Return the value of this final state to player."""
        raise NotImplementedError

    def terminal_test(self, state):
        """Return True if this is a final state for the game."""
        return not self.actions(state)

    def to_move(self, state):
        """Return the player whose move it is in this state."""
        return state.to_move

    def display(self, state):
        """Print or otherwise display the state."""
        print(state)

    def __repr__(self):
        return '<{}>'.format(self.__class__.__name__)

    def play_game(self, *players):
        """Play an n-person, move-alternating game."""
        state = self.initial
        while True:
            for player in players:
                move = player(self, state)
                state = self.result(state, move)
                if self.terminal_test(state):
                    self.display(state)
                    return self.utility(state, self.to_move(self.initial))

class StochasticGame(Game):
    """A stochastic game includes uncertain events which influence
    the moves of players at each state. To create a stochastic game, subclass
    this class and implement chances and outcome along with the other
    unimplemented game class methods."""

    def chances(self, state):
        """Return a list of all possible uncertain events at a state."""
        raise NotImplementedError

    def outcome(self, state, chance):
        """Return the state which is the outcome of a chance trial."""
        raise NotImplementedError

    def probability(self, chance):
        """Return the probability of occurence of a chance."""
        raise NotImplementedError

    def play_game(self, *players):
        """Play an n-person, move-alternating stochastic game."""
        state = self.initial
        while True:
            for player in players:
                chance = random.choice(self.chances(state))
                state = self.outcome(state, chance)
                move = player(self, state)
                state = self.result(state, move)
                if self.terminal_test(state):
                    self.display(state)
                    return self.utility(state, self.to_move(self.initial))

class Fig52Game(Game):
    """The game represented in [Figure 5.2]. Serves as a simple test case."""

    succs = dict(A=dict(a1='B', a2='C', a3='D'),
                 B=dict(b1='B1', b2='B2', b3='B3'),
                 C=dict(c1='C1', c2='C2', c3='C3'),
                 D=dict(d1='D1', d2='D2', d3='D3'))
    utils = dict(B1=3, B2=12, B3=8, C1=2, C2=4, C3=6, D1=14, D2=5, D3=2)
    initial = 'A'

    def actions(self, state):
        return list(self.succs.get(state, {}).keys())

    def result(self, state, move):
        return self.succs[state][move]

    def utility(self, state, player):
        if player == 'MAX':
            return self.utils[state]
        else:
            return -self.utils[state]

    def terminal_test(self, state):
        return state not in ('A', 'B', 'C', 'D')

    def to_move(self, state):
        return 'MIN' if state in 'BCD' else 'MAX'


class Fig52Extended(Game):
    """Similar to Fig52Game but bigger. Useful for visualisation"""

    succs = {i:dict(l=i*3+1, m=i*3+2, r=i*3+3) for i in range(13)}
    utils = dict()

    def actions(self, state):
        return sorted(list(self.succs.get(state, {}).keys()))

    def result(self, state, move):
        return self.succs[state][move]

    def utility(self, state, player):
        if player == 'MAX':
            return self.utils[state]
        else:
            return -self.utils[state]

    def terminal_test(self, state):
        return state not in range(13)

    def to_move(self, state):
        return 'MIN' if state in {1, 2, 3} else 'MAX'

class TicTacToe(Game):
    """Play TicTacToe on an h x v board, with Max (first player) playing 'X'.
    A state has the player to move, a cached utility, a list of moves in
    the form of a list of (x, y) positions, and a board, in the form of
    a dict of {(x, y): Player} entries, where Player is 'X' or 'O'."""

    def __init__(self, h=3, v=3, k=3):
        self.h = h
        self.v = v
        self.k = k
        moves = [(x, y) for x in range(1, h + 1)
                 for y in range(1, v + 1)]
        self.initial = GameState(to_move='X', utility=0, board={}, moves=moves)

    def actions(self, state):
        """Legal moves are any square not yet taken."""
        return state.moves

    def result(self, state, move):
        if move not in state.moves:
            return state  # Illegal move has no effect
        board = state.board.copy()
        board[move] = state.to_move
        moves = list(state.moves)
        moves.remove(move)
        return GameState(to_move=('O' if state.to_move == 'X' else 'X'),
                         utility=self.compute_utility(board, move, state.to_move),
                         board=board, moves=moves)

    def utility(self, state, player):
        """Return the value to player; 1 for win, -1 for loss, 0 otherwise."""
        return state.utility if player == 'X' else -state.utility

    def terminal_test(self, state):
        """A state is terminal if it is won or there are no empty squares."""
        return state.utility != 0 or len(state.moves) == 0

    def display(self, state):
        board = state.board
        for x in range(1, self.h + 1):
            for y in range(1, self.v + 1):
                print(board.get((x, y), '.'), end=' ')
            print()

    def compute_utility(self, board, move, player):
        """If 'X' wins with this move, return 1; if 'O' wins return -1; else return 0."""
        if (self.k_in_row(board, move, player, (0, 1)) or
                self.k_in_row(board, move, player, (1, 0)) or
                self.k_in_row(board, move, player, (1, -1)) or
                self.k_in_row(board, move, player, (1, 1))):
            return +1 if player == 'X' else -1
        else:
            return 0

    def k_in_row(self, board, move, player, delta_x_y):
        """Return true if there is a line through move on board for player."""
        (delta_x, delta_y) = delta_x_y
        x, y = move
        n = 0  # n is number of moves in row
        while board.get((x, y)) == player:
            n += 1
            x, y = x + delta_x, y + delta_y
        x, y = move
        while board.get((x, y)) == player:
            n += 1
            x, y = x - delta_x, y - delta_y
        n -= 1  # Because we counted move itself twice
        return n >= self.k


class ConnectFour(TicTacToe):
    """A TicTacToe-like game in which you can only make a move on the bottom
    row, or in a square directly above an occupied square.  Traditionally
    played on a 7x6 board and requiring 4 in a row."""

    def __init__(self, h=7, v=6, k=4):
        TicTacToe.__init__(self, h, v, k)

    def actions(self, state):
        return [(x, y) for (x, y) in state.moves
                if y == 1 or (x, y - 1) in state.board]


class Backgammon(StochasticGame):
    """A two player game where the goal of each player is to move all the
	checkers off the board. The moves for each state are determined by
	rolling a pair of dice."""

    def __init__(self):
        """Initial state of the game"""
        point = {'W' : 0, 'B' : 0}
        board = [point.copy() for index in range(24)]
        board[0]['B'] = board[23]['W'] = 2
        board[5]['W'] = board[18]['B'] = 5
        board[7]['W'] = board[16]['B'] = 3
        board[11]['B'] = board[12]['W'] = 5
        self.allow_bear_off = {'W' : False, 'B' : False}
        self.direction = {'W' : -1, 'B' : 1}
        self.initial = StochasticGameState(to_move='W',
                                           utility=0,
                                           board=board,
                                           moves=self.get_all_moves(board, 'W'), chance=None)

    def actions(self, state):
        """Return a list of legal moves for a state."""
        player = state.to_move
        moves = state.moves
        if len(moves) == 1 and len(moves[0]) == 1:
            return moves
        legal_moves = []
        for move in moves:
            board = copy.deepcopy(state.board)
            if self.is_legal_move(board, move, state.chance, player):
                legal_moves.append(move)
        return legal_moves

    def result(self, state, move):
        board = copy.deepcopy(state.board)
        player = state.to_move
        self.move_checker(board, move[0], state.chance[0], player)
        if len(move) == 2:
            self.move_checker(board, move[1], state.chance[1], player)
        to_move = ('W' if player == 'B' else 'B')
        return StochasticGameState(to_move=to_move,
                                   utility=self.compute_utility(board, move, player),
                                   board=board,
                                   moves=self.get_all_moves(board, to_move), chance=None)

    def utility(self, state, player):
        """Return the value to player; 1 for win, -1 for loss, 0 otherwise."""
        return state.utility if player == 'W' else -state.utility

    def terminal_test(self, state):
        """A state is terminal if one player wins."""
        return state.utility != 0

    def get_all_moves(self, board, player):
        """All possible moves for a player i.e. all possible ways of
        choosing two checkers of a player from the board for a move
        at a given state."""
        all_points = board
        taken_points = [index for index, point in enumerate(all_points)
                        if point[player] > 0]
        if self.checkers_at_home(board, player) == 1:
            return [(taken_points[0], )]
        moves = list(itertools.permutations(taken_points, 2))
        moves = moves + [(index, index) for index, point in enumerate(all_points)
                         if point[player] >= 2]
        return moves

    def display(self, state):
        """Display state of the game."""
        board = state.board
        player = state.to_move
        print("current state : ")
        for index, point in enumerate(board):
            print("point : ", index, "	W : ", point['W'], "    B : ", point['B'])
        print("to play : ", player)

    def compute_utility(self, board, move, player):
        """If 'W' wins with this move, return 1; if 'B' wins return -1; else return 0."""
        util = {'W' : 1, 'B' : -1}
        for idx in range(0, 24):
            if board[idx][player] > 0:
                return 0
        return util[player]

    def checkers_at_home(self, board, player):
        """Return the no. of checkers at home for a player."""
        sum_range = range(0, 7) if player == 'W' else range(17, 24)
        count = 0
        for idx in sum_range:
            count = count + board[idx][player]
        return count

    def is_legal_move(self, board, start, steps, player):
        """Move is a tuple which contains starting points of checkers to be
		moved during a player's turn. An on-board move is legal if both the destinations
		are open. A bear-off move is the one where a checker is moved off-board.
        It is legal only after a player has moved all his checkers to his home."""
        dest1, dest2 = vector_add(start, steps)
        dest_range = range(0, 24)
        move1_legal = move2_legal = False
        if dest1 in dest_range:
            if self.is_point_open(player, board[dest1]):
                self.move_checker(board, start[0], steps[0], player)
                move1_legal = True
        else:
            if self.allow_bear_off[player]:
                self.move_checker(board, start[0], steps[0], player)
                move1_legal = True
        if not move1_legal:
            return False
        if dest2 in dest_range:
            if self.is_point_open(player, board[dest2]):
                move2_legal = True
        else:
            if self.allow_bear_off[player]:
                move2_legal = True
        return move1_legal and move2_legal

    def move_checker(self, board, start, steps, player):
        """Move a checker from starting point by a given number of steps"""
        dest = start + steps
        dest_range = range(0, 24)
        board[start][player] -= 1
        if dest in dest_range:
            board[dest][player] += 1
            if self.checkers_at_home(board, player) == 15:
                self.allow_bear_off[player] = True

    def is_point_open(self, player, point):
        """A point is open for a player if the no. of opponent's
        checkers already present on it is 0 or 1. A player can
        move a checker to a point only if it is open."""
        opponent = 'B' if player == 'W' else 'W'
        return point[opponent] <= 1

    def chances(self, state):
        """Return a list of all possible dice rolls at a state."""
        dice_rolls = list(itertools.combinations_with_replacement([1, 2, 3, 4, 5, 6], 2))
        return dice_rolls

    def outcome(self, state, chance):
        """Return the state which is the outcome of a dice roll."""
        dice = tuple(map((self.direction[state.to_move]).__mul__, chance))
        return StochasticGameState(to_move=state.to_move,
                                   utility=state.utility,
                                   board=state.board,
                                   moves=state.moves, chance=dice)

    def probability(self, chance):
        """Return the probability of occurence of a dice roll."""
        return 1/36 if chance[0] == chance[1] else 1/18