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# This is a very simple implementation of the UCT Monte Carlo Tree Search algorithm in Python 2.7. # The function UCT(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. # # Example GameState classes for Nim, OXO and Othello are included to give some idea of how you # can write your own GameState use UCT in your 2-player game. Change the game to be played in # the UCTPlayGame() function at the bottom of the code. # # Written by Peter Cowling, Ed Powley, Daniel Whitehouse (University of York, UK) September 2012. # # 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 www.mcts.ai from math import * import random class GameState: """ A state of the game, i.e. the game board. These are the only functions which are absolutely necessary to implement UCT in any 2-player complete information deterministic zero-sum game, although they can 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 and 2. """ def __init__(self): self.playerJustMoved = 2 # At the root pretend the player just moved is player 2 - player 1 has the first move def Clone(self): """ Create a deep clone of this game state. """ st = GameState() st.playerJustMoved = self.playerJustMoved return st def DoMove(self, move): """ Update a state by carrying out the given move. Must update playerJustMoved. """ self.playerJustMoved = 3 - self.playerJustMoved def GetMoves(self): """ Get all possible moves from this state. """ def GetResult(self, playerjm): """ Get the game result from the viewpoint of playerjm. """ def __repr__(self): """ Don't need this - but good style. """ pass class NimState: """ A state of the game Nim. In Nim, players alternately take 1,2 or 3 chips with the winner being the player to take the last chip. In Nim any initial state of the form 4n+k for k = 1,2,3 is a win for player 1 (by choosing k) chips. Any initial state of the form 4n is a win for player 2. """ def __init__(self, ch): self.playerJustMoved = 2 # At the root pretend the player just moved is p2 - p1 has the first move self.chips = ch def Clone(self): """ Create a deep clone of this game state. """ st = NimState(self.chips) st.playerJustMoved = self.playerJustMoved return st def DoMove(self, move): """ Update a state by carrying out the given move. Must update playerJustMoved. """ assert move >= 1 and move <= 3 and move == int(move) self.chips -= move self.playerJustMoved = 3 - self.playerJustMoved def GetMoves(self): """ Get all possible moves from this state. """ return range(1,min([4, self.chips + 1])) def GetResult(self, playerjm): """ Get the game result from the viewpoint of playerjm. """ assert self.chips == 0 if self.playerJustMoved == playerjm: return 1.0 # playerjm took the last chip and has won else: return 0.0 # playerjm's opponent took the last chip and has won def __repr__(self): s = "Chips:" + str(self.chips) + " JustPlayed:" + str(self.playerJustMoved) return s class OXOState: """ A state of the game, i.e. the game board. Squares in the board are in this arrangement 012 345 678 where 0 = empty, 1 = player 1 (X), 2 = player 2 (O) """ def __init__(self): self.playerJustMoved = 2 # At the root pretend the player just moved is p2 - p1 has the first move self.board = [0,0,0,0,0,0,0,0,0] # 0 = empty, 1 = player 1, 2 = player 2 def Clone(self): """ Create a deep clone of this game state. """ st = OXOState() st.playerJustMoved = self.playerJustMoved st.board = self.board[:] return st def DoMove(self, move): """ Update a state by carrying out the given move. Must update playerToMove. """ assert move >= 0 and move <= 8 and move == int(move) and self.board[move] == 0 self.playerJustMoved = 3 - self.playerJustMoved self.board[move] = self.playerJustMoved def GetMoves(self): """ Get all possible moves from this state. """ return [i for i in range(9) if self.board[i] == 0] def GetResult(self, playerjm): """ Get the game result from the viewpoint of playerjm. """ for (x,y,z) in [(0,1,2),(3,4,5),(6,7,8),(0,3,6),(1,4,7),(2,5,8),(0,4,8),(2,4,6)]: if self.board[x] == self.board[y] == self.board[z]: if self.board[x] == playerjm: return 1.0 else: return 0.0 if self.GetMoves() == []: return 0.5 # draw assert False # Should not be possible to get here def __repr__(self): s= "" for i in range(9): s += ".XO"[self.board[i]] if i % 3 == 2: s += "\n" return s class OthelloState: """ A state of the game of Othello, i.e. the game board. The board is a 2D array where 0 = empty (.), 1 = player 1 (X), 2 = player 2 (O). In Othello players alternately place pieces on a square board - each piece played has to sandwich opponent pieces between the piece played and pieces already on the board. Sandwiched pieces are flipped. This implementation modifies the rules to allow variable sized square boards and terminates the game as soon as the player about to move cannot make a move (whereas the standard game allows for a pass move). """ def __init__(self,sz = 8): self.playerJustMoved = 2 # At the root pretend the player just moved is p2 - p1 has the first move self.board = [] # 0 = empty, 1 = player 1, 2 = player 2 self.size = sz assert sz == int(sz) and sz % 2 == 0 # size must be integral and even for y in range(sz): self.board.append([0]*sz) self.board[sz/2][sz/2] = self.board[sz/2-1][sz/2-1] = 1 self.board[sz/2][sz/2-1] = self.board[sz/2-1][sz/2] = 2 def Clone(self): """ Create a deep clone of this game state. """ st = OthelloState() st.playerJustMoved = self.playerJustMoved st.board = [self.board[i][:] for i in range(self.size)] st.size = self.size return st def DoMove(self, move): """ Update a state by carrying out the given move. Must update playerToMove. """ (x,y)=(move[0],move[1]) assert x == int(x) and y == int(y) and self.IsOnBoard(x,y) and self.board[x][y] == 0 m = self.GetAllSandwichedCounters(x,y) self.playerJustMoved = 3 - self.playerJustMoved self.board[x][y] = self.playerJustMoved for (a,b) in m: self.board[a][b] = self.playerJustMoved def GetMoves(self): """ Get all possible moves from this state. """ return [(x,y) for x in range(self.size) for y in range(self.size) if self.board[x][y] == 0 and self.ExistsSandwichedCounter(x,y)] def AdjacentToEnemy(self,x,y): """ Speeds up GetMoves by only considering squares which are adjacent to an enemy-occupied square. """ for (dx,dy) in [(0,+1),(+1,+1),(+1,0),(+1,-1),(0,-1),(-1,-1),(-1,0),(-1,+1)]: if self.IsOnBoard(x+dx,y+dy) and self.board[x+dx][y+dy] == self.playerJustMoved: return True return False def AdjacentEnemyDirections(self,x,y): """ Speeds up GetMoves by only considering squares which are adjacent to an enemy-occupied square. """ es = [] for (dx,dy) in [(0,+1),(+1,+1),(+1,0),(+1,-1),(0,-1),(-1,-1),(-1,0),(-1,+1)]: if self.IsOnBoard(x+dx,y+dy) and self.board[x+dx][y+dy] == self.playerJustMoved: es.append((dx,dy)) return es def ExistsSandwichedCounter(self,x,y): """ Does there exist at least one counter which would be flipped if my counter was placed at (x,y)? """ for (dx,dy) in self.AdjacentEnemyDirections(x,y): if len(self.SandwichedCounters(x,y,dx,dy)) > 0: return True return False def GetAllSandwichedCounters(self, x, y): """ Is (x,y) a possible move (i.e. opponent counters are sandwiched between (x,y) and my counter in some direction)? """ sandwiched = [] for (dx,dy) in self.AdjacentEnemyDirections(x,y): sandwiched.extend(self.SandwichedCounters(x,y,dx,dy)) return sandwiched def SandwichedCounters(self, x, y, dx, dy): """ Return the coordinates of all opponent counters sandwiched between (x,y) and my counter. """ x += dx y += dy sandwiched = [] while self.IsOnBoard(x,y) and self.board[x][y] == self.playerJustMoved: sandwiched.append((x,y)) x += dx y += dy if self.IsOnBoard(x,y) and self.board[x][y] == 3 - self.playerJustMoved: return sandwiched else: return [] # nothing sandwiched def IsOnBoard(self, x, y): return x >= 0 and x < self.size and y >= 0 and y < self.size def GetResult(self, playerjm): """ Get the game result from the viewpoint of playerjm. """ jmcount = len([(x,y) for x in range(self.size) for y in range(self.size) if self.board[x][y] == playerjm]) notjmcount = len([(x,y) for x in range(self.size) for y in range(self.size) if self.board[x][y] == 3 - playerjm]) if jmcount > notjmcount: return 1.0 elif notjmcount > jmcount: return 0.0 else: return 0.5 # draw def __repr__(self): s= "" for y in range(self.size-1,-1,-1): for x in range(self.size): s += ".XO"[self.board[x][y]] s += "\n" return s class Node: """ A node in the game tree. Note wins is always from the viewpoint of playerJustMoved. Crashes if state not specified. """ def __init__(self, move = None, parent = None, state = 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.untriedMoves = state.GetMoves() # future child nodes self.playerJustMoved = state.playerJustMoved # the only part of the state that the Node needs later def UCTSelectChild(self): """ Use the UCB1 formula to select a child node. Often a constant UCTK is applied so we have lambda c: c.wins/c.visits + UCTK * sqrt(2*log(self.visits)/c.visits to vary the amount of exploration versus exploitation. """ s = sorted(self.childNodes, key = lambda c: c.wins/c.visits + sqrt(2*log(self.visits)/c.visits))[-1] return s def AddChild(self, m, s): """ Remove m from untriedMoves and add a new child node for this move. Return the added child node """ n = Node(move = m, parent = self, state = s) self.untriedMoves.remove(m) self.childNodes.append(n) return n def Update(self, result): """ Update this node - one additional visit and result additional wins. result must be from the viewpoint of playerJustmoved. """ self.visits += 1 self.wins += result def __repr__(self): return "[M:" + str(self.move) + " W/V:" + str(self.wins) + "/" + str(self.visits) + " U:" + str(self.untriedMoves) + "]" def TreeToString(self, indent): 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 UCT(rootstate, itermax, verbose = False): """ Conduct a UCT search for itermax iterations starting from rootstate. Return the best move from the rootstate. Assumes 2 alternating players (player 1 starts), with game results in the range [0.0, 1.0].""" rootnode = Node(state = rootstate) for i in range(itermax): node = rootnode state = rootstate.Clone() # Select while node.untriedMoves == [] and node.childNodes != []: # node is fully expanded and non-terminal node = node.UCTSelectChild() state.DoMove(node.move) # Expand if node.untriedMoves != []: # if we can expand (i.e. state/node is non-terminal) m = random.choice(node.untriedMoves) state.DoMove(m) node = node.AddChild(m,state) # add child and descend tree # Rollout - this can often be made orders of magnitude quicker using a state.GetRandomMove() function while state.GetMoves() != []: # while state is non-terminal state.DoMove(random.choice(state.GetMoves())) # Backpropagate while node != None: # backpropagate from the expanded node and work back to the root node node.Update(state.GetResult(node.playerJustMoved)) # state is terminal. Update node with result from POV of node.playerJustMoved node = node.parentNode # Output some information about the tree - can be omitted if (verbose): print rootnode.TreeToString(0) else: print rootnode.ChildrenToString() return sorted(rootnode.childNodes, key = lambda c: c.visits)[-1].move # return the move that was most visited def UCTPlayGame(): """ Play a sample game between two UCT players where each player gets a different number of UCT iterations (= simulations = tree nodes). """ # state = OthelloState(4) # uncomment to play Othello on a square board of the given size # state = OXOState() # uncomment to play OXO state = NimState(15) # uncomment to play Nim with the given number of starting chips while (state.GetMoves() != []): print str(state) if state.playerJustMoved == 1: m = UCT(rootstate = state, itermax = 1000, verbose = False) # play with values for itermax and verbose = True else: m = UCT(rootstate = state, itermax = 100, verbose = False) print "Best Move: " + str(m) + "\n" state.DoMove(m) if state.GetResult(state.playerJustMoved) == 1.0: print "Player " + str(state.playerJustMoved) + " wins!" elif state.GetResult(state.playerJustMoved) == 0.0: print "Player " + str(3 - state.playerJustMoved) + " wins!" else: print "Nobody wins!" if __name__ == "__main__": """ Play a single game to the end using UCT for both players. """ UCTPlayGame()

The complete Python code for this example can be downloaded here.