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An example of Information Set Monte Carlo Tree Search from
# This is a very simple Python 2.7 implementation of the Information Set Monte Carlo Tree Search algorithm.
# The function ISMCTS(rootstate, itermax, verbose = False) is towards the bottom of the code.
# It aims to have the clearest and simplest possible code, and for the sake of clarity, the code
# is orders of magnitude less efficient than it could be made, particularly by using a
# state.GetRandomMove() or state.DoRandomRollout() function.
# An example GameState classes for Knockout Whist is included to give some idea of how you
# can write your own GameState to use ISMCTS in your hidden information game.
# Written by Peter Cowling, Edward Powley, Daniel Whitehouse (University of York, UK) September 2012 - August 2013.
# Licence is granted to freely use and distribute for any sensible/legal purpose so long as this comment
# remains in any distributed code.
# For more information about Monte Carlo Tree Search check out our web site at
# Also read the article accompanying this code at ***URL HERE***
from math import *
import random, sys
from copy import deepcopy
class GameState:
""" A state of the game, i.e. the game board. These are the only functions which are
absolutely necessary to implement ISMCTS in any imperfect information game,
although they could be enhanced and made quicker, for example by using a
GetRandomMove() function to generate a random move during rollout.
By convention the players are numbered 1, 2, ..., self.numberOfPlayers.
def __init__(self):
self.numberOfPlayers = 2
self.playerToMove = 1
def GetNextPlayer(self, p):
""" Return the player to the left of the specified player
return (p % self.numberOfPlayers) + 1
def Clone(self):
""" Create a deep clone of this game state.
st = GameState()
st.playerToMove = self.playerToMove
return st
def CloneAndRandomize(self, observer):
""" Create a deep clone of this game state, randomizing any information not visible to the specified observer player.
return self.Clone()
def DoMove(self, move):
""" Update a state by carrying out the given move.
Must update playerToMove.
self.playerToMove = self.GetNextPlayer(self.playerToMove)
def GetMoves(self):
""" Get all possible moves from this state.
raise NotImplementedException()
def GetResult(self, player):
""" Get the game result from the viewpoint of player.
raise NotImplementedException()
def __repr__(self):
""" Don't need this - but good style.
class Card:
""" A playing card, with rank and suit.
rank must be an integer between 2 and 14 inclusive (Jack=11, Queen=12, King=13, Ace=14)
suit must be a string of length 1, one of 'C' (Clubs), 'D' (Diamonds), 'H' (Hearts) or 'S' (Spades)
def __init__(self, rank, suit):
if rank not in range(2, 14+1):
raise Exception("Invalid rank")
if suit not in ['C', 'D', 'H', 'S']:
raise Exception("Invalid suit")
self.rank = rank
self.suit = suit
def __repr__(self):
return "??23456789TJQKA"[self.rank] + self.suit
def __eq__(self, other):
return self.rank == other.rank and self.suit == other.suit
def __ne__(self, other):
return self.rank != other.rank or self.suit != other.suit
class KnockoutWhistState(GameState):
""" A state of the game Knockout Whist.
See for a full description of the rules.
For simplicity of implementation, this version of the game does not include the "dog's life" rule
and the trump suit for each round is picked randomly rather than being chosen by one of the players.
def __init__(self, n):
""" Initialise the game state. n is the number of players (from 2 to 7).
self.numberOfPlayers = n
self.playerToMove = 1
self.tricksInRound = 7
self.playerHands = {p:[] for p in xrange(1, self.numberOfPlayers+1)}
self.discards = [] # Stores the cards that have been played already in this round
self.currentTrick = []
self.trumpSuit = None
self.tricksTaken = {} # Number of tricks taken by each player this round
self.knockedOut = {p:False for p in xrange(1, self.numberOfPlayers+1)}
def Clone(self):
""" Create a deep clone of this game state.
st = KnockoutWhistState(self.numberOfPlayers)
st.playerToMove = self.playerToMove
st.tricksInRound = self.tricksInRound
st.playerHands = deepcopy(self.playerHands)
st.discards = deepcopy(self.discards)
st.currentTrick = deepcopy(self.currentTrick)
st.trumpSuit = self.trumpSuit
st.tricksTaken = deepcopy(self.tricksTaken)
st.knockedOut = deepcopy(self.knockedOut)
return st
def CloneAndRandomize(self, observer):
""" Create a deep clone of this game state, randomizing any information not visible to the specified observer player.
st = self.Clone()
# The observer can see his own hand and the cards in the current trick, and can remember the cards played in previous tricks
seenCards = st.playerHands[observer] + st.discards + [card for (player,card) in st.currentTrick]
# The observer can't see the rest of the deck
unseenCards = [card for card in st.GetCardDeck() if card not in seenCards]
# Deal the unseen cards to the other players
for p in xrange(1, st.numberOfPlayers+1):
if p != observer:
# Deal cards to player p
# Store the size of player p's hand
numCards = len(self.playerHands[p])
# Give player p the first numCards unseen cards
st.playerHands[p] = unseenCards[ : numCards]
# Remove those cards from unseenCards
unseenCards = unseenCards[numCards : ]
return st
def GetCardDeck(self):
""" Construct a standard deck of 52 cards.
return [Card(rank, suit) for rank in xrange(2, 14+1) for suit in ['C', 'D', 'H', 'S']]
def Deal(self):
""" Reset the game state for the beginning of a new round, and deal the cards.
self.discards = []
self.currentTrick = []
self.tricksTaken = {p:0 for p in xrange(1, self.numberOfPlayers+1)}
# Construct a deck, shuffle it, and deal it to the players
deck = self.GetCardDeck()
for p in xrange(1, self.numberOfPlayers+1):
self.playerHands[p] = deck[ : self.tricksInRound]
deck = deck[self.tricksInRound : ]
# Choose the trump suit for this round
self.trumpSuit = random.choice(['C', 'D', 'H', 'S'])
def GetNextPlayer(self, p):
""" Return the player to the left of the specified player, skipping players who have been knocked out
next = (p % self.numberOfPlayers) + 1
# Skip any knocked-out players
while next != p and self.knockedOut[next]:
next = (next % self.numberOfPlayers) + 1
return next
def DoMove(self, move):
""" Update a state by carrying out the given move.
Must update playerToMove.
# Store the played card in the current trick
self.currentTrick.append((self.playerToMove, move))
# Remove the card from the player's hand
# Find the next player
self.playerToMove = self.GetNextPlayer(self.playerToMove)
# If the next player has already played in this trick, then the trick is over
if any(True for (player, card) in self.currentTrick if player == self.playerToMove):
# Sort the plays in the trick: those that followed suit (in ascending rank order), then any trump plays (in ascending rank order)
(leader, leadCard) = self.currentTrick[0]
suitedPlays = [(player, card.rank) for (player, card) in self.currentTrick if card.suit == leadCard.suit]
trumpPlays = [(player, card.rank) for (player, card) in self.currentTrick if card.suit == self.trumpSuit]
sortedPlays = sorted(suitedPlays, key = lambda (player, rank) : rank) + sorted(trumpPlays, key = lambda (player, rank) : rank)
# The winning play is the last element in sortedPlays
trickWinner = sortedPlays[-1][0]
# Update the game state
self.tricksTaken[trickWinner] += 1
self.discards += [card for (player, card) in self.currentTrick]
self.currentTrick = []
self.playerToMove = trickWinner
# If the next player's hand is empty, this round is over
if self.playerHands[self.playerToMove] == []:
self.tricksInRound -= 1
self.knockedOut = {p:(self.knockedOut[p] or self.tricksTaken[p] == 0) for p in xrange(1, self.numberOfPlayers+1)}
# If all but one players are now knocked out, the game is over
if len([x for x in self.knockedOut.itervalues() if x == False]) <= 1:
self.tricksInRound = 0
def GetMoves(self):
""" Get all possible moves from this state.
hand = self.playerHands[self.playerToMove]
if self.currentTrick == []:
# May lead a trick with any card
return hand
(leader, leadCard) = self.currentTrick[0]
# Must follow suit if it is possible to do so
cardsInSuit = [card for card in hand if card.suit == leadCard.suit]
if cardsInSuit != []:
return cardsInSuit
# Can't follow suit, so can play any card
return hand
def GetResult(self, player):
""" Get the game result from the viewpoint of player.
return 0 if (self.knockedOut[player]) else 1
def __repr__(self):
""" Return a human-readable representation of the state
result = "Round %i" % self.tricksInRound
result += " | P%i: " % self.playerToMove
result += ",".join(str(card) for card in self.playerHands[self.playerToMove])
result += " | Tricks: %i" % self.tricksTaken[self.playerToMove]
result += " | Trump: %s" % self.trumpSuit
result += " | Trick: ["
result += ",".join(("%i:%s" % (player, card)) for (player, card) in self.currentTrick)
result += "]"
return result
class Node:
""" A node in the game tree. Note wins is always from the viewpoint of playerJustMoved.
def __init__(self, move = None, parent = None, playerJustMoved = None):
self.move = move # the move that got us to this node - "None" for the root node
self.parentNode = parent # "None" for the root node
self.childNodes = []
self.wins = 0
self.visits = 0
self.avails = 1
self.playerJustMoved = playerJustMoved # the only part of the state that the Node needs later
def GetUntriedMoves(self, legalMoves):
""" Return the elements of legalMoves for which this node does not have children.
# Find all moves for which this node *does* have children
triedMoves = [child.move for child in self.childNodes]
# Return all moves that are legal but have not been tried yet
return [move for move in legalMoves if move not in triedMoves]
def UCBSelectChild(self, legalMoves, exploration = 0.7):
""" Use the UCB1 formula to select a child node, filtered by the given list of legal moves.
exploration is a constant balancing between exploitation and exploration, with default value 0.7 (approximately sqrt(2) / 2)
# Filter the list of children by the list of legal moves
legalChildren = [child for child in self.childNodes if child.move in legalMoves]
# Get the child with the highest UCB score
s = max(legalChildren, key = lambda c: float(c.wins)/float(c.visits) + exploration * sqrt(log(c.avails)/float(c.visits)))
# Update availability counts -- it is easier to do this now than during backpropagation
for child in legalChildren:
child.avails += 1
# Return the child selected above
return s
def AddChild(self, m, p):
""" Add a new child node for the move m.
Return the added child node
n = Node(move = m, parent = self, playerJustMoved = p)
return n
def Update(self, terminalState):
""" Update this node - increment the visit count by one, and increase the win count by the result of terminalState for self.playerJustMoved.
self.visits += 1
if self.playerJustMoved is not None:
self.wins += terminalState.GetResult(self.playerJustMoved)
def __repr__(self):
return "[M:%s W/V/A: %4i/%4i/%4i]" % (self.move, self.wins, self.visits, self.avails)
def TreeToString(self, indent):
""" Represent the tree as a string, for debugging purposes.
s = self.IndentString(indent) + str(self)
for c in self.childNodes:
s += c.TreeToString(indent+1)
return s
def IndentString(self,indent):
s = "\n"
for i in range (1,indent+1):
s += "| "
return s
def ChildrenToString(self):
s = ""
for c in self.childNodes:
s += str(c) + "\n"
return s
def ISMCTS(rootstate, itermax, verbose = False):
""" Conduct an ISMCTS search for itermax iterations starting from rootstate.
Return the best move from the rootstate.
rootnode = Node()
for i in range(itermax):
node = rootnode
# Determinize
state = rootstate.CloneAndRandomize(rootstate.playerToMove)
# Select
while state.GetMoves() != [] and node.GetUntriedMoves(state.GetMoves()) == []: # node is fully expanded and non-terminal
node = node.UCBSelectChild(state.GetMoves())
# Expand
untriedMoves = node.GetUntriedMoves(state.GetMoves())
if untriedMoves != []: # if we can expand (i.e. state/node is non-terminal)
m = random.choice(untriedMoves)
player = state.playerToMove
node = node.AddChild(m, player) # add child and descend tree
# Simulate
while state.GetMoves() != []: # while state is non-terminal
# Backpropagate
while node != None: # backpropagate from the expanded node and work back to the root node
node = node.parentNode
# Output some information about the tree - can be omitted
if (verbose): print rootnode.TreeToString(0)
else: print rootnode.ChildrenToString()
return max(rootnode.childNodes, key = lambda c: c.visits).move # return the move that was most visited
def PlayGame():
""" Play a sample game between two ISMCTS players.
state = KnockoutWhistState(4)
while (state.GetMoves() != []):
print str(state)
# Use different numbers of iterations (simulations, tree nodes) for different players
if state.playerToMove == 1:
m = ISMCTS(rootstate = state, itermax = 1000, verbose = False)
m = ISMCTS(rootstate = state, itermax = 100, verbose = False)
print "Best Move: " + str(m) + "\n"
someoneWon = False
for p in xrange(1, state.numberOfPlayers + 1):
if state.GetResult(p) > 0:
print "Player " + str(p) + " wins!"
someoneWon = True
if not someoneWon:
print "Nobody wins!"
if __name__ == "__main__":
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