# Bonus Tutorial: Planning with Monte Carlo

## Contents

# Bonus Tutorial: Planning with Monte Carlo¶

**Week 3, Day 5: Reinforcement Learning for Games**

**By Neuromatch Academy**

**Content creators:** Mandana Samiei, Raymond Chua, Tim Lilicrap, Blake Richards

**Content reviewers:** Arush Tagade, Lily Cheng, Melvin Selim Atay, Kelson Shilling-Scrivo

**Content editors:** Melvin Selim Atay, Spiros Chavlis, Gunnar Blohm

**Production editors:** Namrata Bafna, Gagana B, Spiros Chavlis

# Tutorial Objectives¶

In this tutorial, you will learn how to implement a game loop and improve the performance of a random player.

The specific objectives for this tutorial:

Understand the format of two-players games

Learn about value network and policy network

In the Bonus sections you will learn about Monte Carlo Tree Search (MCTS) and compare its performance to policy-based and value-based players.

# Setup¶

## Install dependencies¶

```
# @title Install dependencies
!pip install coloredlogs --quiet
!pip install git+https://github.com/NeuromatchAcademy/evaltools --quiet
from evaltools.airtable import AirtableForm
# generate airtable form
atform = AirtableForm('appn7VdPRseSoMXEG', 'W3D5_T4', '95651a47-083f-406e-a6cd-8af24670c5bc')
```

```
# Imports
import os
import math
import time
import torch
import random
import logging
import coloredlogs
import numpy as np
import torch.nn as nn
import torch.optim as optim
import torch.nn.functional as F
from tqdm.notebook import tqdm
log = logging.getLogger(__name__)
coloredlogs.install(level='INFO') # Change this to DEBUG to see more info.
```

## Set random seed¶

Executing `set_seed(seed=seed)`

you are setting the seed

```
# @title Set random seed
# @markdown Executing `set_seed(seed=seed)` you are setting the seed
# For DL its critical to set the random seed so that students can have a
# baseline to compare their results to expected results.
# Read more here: https://pytorch.org/docs/stable/notes/randomness.html
# Call `set_seed` function in the exercises to ensure reproducibility.
import random
import torch
def set_seed(seed=None, seed_torch=True):
"""
Function that controls randomness. NumPy and random modules must be imported.
Args:
seed : Integer
A non-negative integer that defines the random state. Default is `None`.
seed_torch : Boolean
If `True` sets the random seed for pytorch tensors, so pytorch module
must be imported. Default is `True`.
Returns:
Nothing.
"""
if seed is None:
seed = np.random.choice(2 ** 32)
random.seed(seed)
np.random.seed(seed)
if seed_torch:
torch.manual_seed(seed)
torch.cuda.manual_seed_all(seed)
torch.cuda.manual_seed(seed)
torch.backends.cudnn.benchmark = False
torch.backends.cudnn.deterministic = True
print(f'Random seed {seed} has been set.')
# In case that `DataLoader` is used
def seed_worker(worker_id):
"""
DataLoader will reseed workers following randomness in
multi-process data loading algorithm.
Args:
worker_id: integer
ID of subprocess to seed. 0 means that
the data will be loaded in the main process
Refer: https://pytorch.org/docs/stable/data.html#data-loading-randomness for more details
Returns:
Nothing
"""
worker_seed = torch.initial_seed() % 2**32
np.random.seed(worker_seed)
random.seed(worker_seed)
```

## Set device (GPU or CPU). Execute `set_device()`

¶

```
# @title Set device (GPU or CPU). Execute `set_device()`
# especially if torch modules used.
# Inform the user if the notebook uses GPU or CPU.
def set_device():
"""
Set the device. CUDA if available, CPU otherwise
Args:
None
Returns:
Nothing
"""
device = "cuda" if torch.cuda.is_available() else "cpu"
if device != "cuda":
print("WARNING: For this notebook to perform best, "
"if possible, in the menu under `Runtime` -> "
"`Change runtime type.` select `GPU` ")
else:
print("GPU is enabled in this notebook.")
return device
```

```
SEED = 2021
set_seed(seed=SEED)
DEVICE = set_device()
```

```
Random seed 2021 has been set.
WARNING: For this notebook to perform best, if possible, in the menu under `Runtime` -> `Change runtime type.` select `GPU`
```

## Download the modules¶

```
# @title Download the modules
# @markdown Run this cell!
# @markdown Download from OSF. The original repo is https://github.com/raymondchua/nma_rl_games.git
import os, io, sys, shutil, zipfile
from urllib.request import urlopen
# download from github repo directly
#!git clone git://github.com/raymondchua/nma_rl_games.git --quiet
REPO_PATH = 'nma_rl_games'
if os.path.exists(REPO_PATH):
download_string = "Redownloading"
shutil.rmtree(REPO_PATH)
else:
download_string = "Downloading"
zipurl = 'https://osf.io/kf4p9/download'
print(f"{download_string} and unzipping the file... Please wait.")
with urlopen(zipurl) as zipresp:
with zipfile.ZipFile(io.BytesIO(zipresp.read())) as zfile:
zfile.extractall()
print("Download completed.")
print(f"Add the {REPO_PATH} in the path and import the modules.")
# add the repo in the path
sys.path.append('nma_rl_games/alpha-zero')
# @markdown Import modules designed for use in this notebook
import Arena
from utils import *
from Game import Game
from MCTS import MCTS
from NeuralNet import NeuralNet
# from othello.OthelloPlayers import *
from othello.OthelloLogic import Board
# from othello.OthelloGame import OthelloGame
from othello.pytorch.NNet import NNetWrapper as NNet
```

```
Redownloading and unzipping the file... Please wait.
```

```
Download completed.
Add the nma_rl_games in the path and import the modules.
```

## Helper functions from previous tutorials¶

```
# @title Helper functions from previous tutorials
class OthelloGame(Game):
"""
Instantiate Othello Game
"""
square_content = {
-1: "X",
+0: "-",
+1: "O"
}
@staticmethod
def getSquarePiece(piece):
return OthelloGame.square_content[piece]
def __init__(self, n):
self.n = n
def getInitBoard(self):
# Return initial board (numpy board)
b = Board(self.n)
return np.array(b.pieces)
def getBoardSize(self):
# (a,b) tuple
return (self.n, self.n)
def getActionSize(self):
# Return number of actions, n is the board size and +1 is for no-op action
return self.n*self.n + 1
def getCanonicalForm(self, board, player):
# Return state if player==1, else return -state if player==-1
return player*board
def stringRepresentation(self, board):
return board.tobytes()
def stringRepresentationReadable(self, board):
board_s = "".join(self.square_content[square] for row in board for square in row)
return board_s
def getScore(self, board, player):
b = Board(self.n)
b.pieces = np.copy(board)
return b.countDiff(player)
@staticmethod
def display(board):
n = board.shape[0]
print(" ", end="")
for y in range(n):
print(y, end=" ")
print("")
print("-----------------------")
for y in range(n):
print(y, "|", end="") # Print the row
for x in range(n):
piece = board[y][x] # Get the piece to print
print(OthelloGame.square_content[piece], end=" ")
print("|")
print("-----------------------")
@staticmethod
def displayValidMoves(moves):
# Display possible moves
A=np.reshape(moves[0:-1], board.shape)
n = board.shape[0]
print(" ")
print("possible moves")
print(" ", end="")
for y in range(n):
print(y, end=" ")
print("")
print("-----------------------")
for y in range(n):
print(y, "|", end="") # Print the row
for x in range(n):
piece = A[y][x] # Get the piece to print
print(OthelloGame.square_content[piece], end=" ")
print("|")
print("-----------------------")
def getNextState(self, board, player, action):
"""
Helper function to make valid move
If player takes action on board, return next (board,player)
and action must be a valid move
Args:
board: np.ndarray
Board of size n x n [6x6 in this case]
player: Integer
ID of current player
action: np.ndarray
Space of actions
Returns:
(board,player) tuple signifying next state
"""
if action == self.n*self.n:
return (board, -player)
b = Board(self.n)
b.pieces = np.copy(board)
move = (int(action/self.n), action%self.n)
b.execute_move(move, player)
return (b.pieces, -player)
def getValidMoves(self, board, player):
"""
Helper function to make valid move
If player takes action on board, return next (board,player)
and action must be a valid move
Args:
board: np.ndarray
Board of size n x n [6x6 in this case]
player: Integer
ID of current player
action: np.ndarray
Space of action
Returns:
valids: np.ndarray
Returns a fixed size binary vector
"""
valids = [0]*self.getActionSize()
b = Board(self.n)
b.pieces = np.copy(board)
legalMoves = b.get_legal_moves(player)
if len(legalMoves)==0:
valids[-1]=1
return np.array(valids)
for x, y in legalMoves:
valids[self.n*x+y]=1
return np.array(valids)
def getGameEnded(self, board, player):
"""
Helper function to signify if game has ended
Args:
board: np.ndarray
Board of size n x n [6x6 in this case]
player: Integer
ID of current player
Returns:
0 if not ended, 1 if player 1 won, -1 if player 1 lost
"""
b = Board(self.n)
b.pieces = np.copy(board)
if b.has_legal_moves(player):
return 0
if b.has_legal_moves(-player):
return 0
if b.countDiff(player) > 0:
return 1
return -1
def getSymmetries(self, board, pi):
"""
Get mirror/rotational configurations of board
Args:
board: np.ndarray
Board of size n x n [6x6 in this case]
pi: np.ndarray
Dimension of board
Returns:
l: list
90 degree of board, 90 degree of pi_board
"""
assert(len(pi) == self.n**2+1) # 1 for pass
pi_board = np.reshape(pi[:-1], (self.n, self.n))
l = []
for i in range(1, 5):
for j in [True, False]:
newB = np.rot90(board, i)
newPi = np.rot90(pi_board, i)
if j:
newB = np.fliplr(newB)
newPi = np.fliplr(newPi)
l += [(newB, list(newPi.ravel()) + [pi[-1]])]
return l
class RandomPlayer():
"""
Simulates Random Player
"""
def __init__(self, game):
self.game = game
def play(self, board):
"""
Simulates game play
Args:
board: np.ndarray
Board of size n x n [6x6 in this case]
Returns:
a: int
Randomly chosen move
"""
# Compute the valid moves using getValidMoves()
valids = self.game.getValidMoves(board, 1)
# Compute the probability of each move being played (random player means this should
# be uniform for valid moves, 0 for others)
prob = valids/valids.sum()
# Pick an action based on the probabilities (hint: np.choice is useful)
a = np.random.choice(self.game.getActionSize(), p=prob)
return a
class OthelloNNet(nn.Module):
"""
Instantiate Othello Neural Net with following configuration
nn.Conv2d(1, args.num_channels, 3, stride=1, padding=1) # Convolutional Layer 1
nn.Conv2d(args.num_channels, args.num_channels, 3, stride=1, padding=1) # Convolutional Layer 2
nn.Conv2d(args.num_channels, args.num_channels, 3, stride=1) # Convolutional Layer 3
nn.Conv2d(args.num_channels, args.num_channels, 3, stride=1) # Convolutional Layer 4
nn.BatchNorm2d(args.num_channels) X 4
nn.Linear(args.num_channels * (self.board_x - 4) * (self.board_y - 4), 1024) # Fully-connected Layer 1
nn.Linear(1024, 512) # Fully-connected Layer 2
nn.Linear(512, self.action_size) # Fully-connected Layer 3
nn.Linear(512, 1) # Fully-connected Layer 4
"""
def __init__(self, game, args):
"""
Initialise game parameters
Args:
game: OthelloGame instance
Instance of the OthelloGame class above;
args: dictionary
Instantiates number of iterations and episodes, controls temperature threshold, queue length,
arena, checkpointing, and neural network parameters:
learning-rate: 0.001, dropout: 0.3, epochs: 10, batch_size: 64,
num_channels: 512
Returns:
Nothing
"""
self.board_x, self.board_y = game.getBoardSize()
self.action_size = game.getActionSize()
self.args = args
super(OthelloNNet, self).__init__()
self.conv1 = nn.Conv2d(1, args.num_channels, 3, stride=1, padding=1)
self.conv2 = nn.Conv2d(args.num_channels, args.num_channels, 3, stride=1,
padding=1)
self.conv3 = nn.Conv2d(args.num_channels, args.num_channels, 3, stride=1)
self.conv4 = nn.Conv2d(args.num_channels, args.num_channels, 3, stride=1)
self.bn1 = nn.BatchNorm2d(args.num_channels)
self.bn2 = nn.BatchNorm2d(args.num_channels)
self.bn3 = nn.BatchNorm2d(args.num_channels)
self.bn4 = nn.BatchNorm2d(args.num_channels)
self.fc1 = nn.Linear(args.num_channels * (self.board_x - 4) * (self.board_y - 4), 1024)
self.fc_bn1 = nn.BatchNorm1d(1024)
self.fc2 = nn.Linear(1024, 512)
self.fc_bn2 = nn.BatchNorm1d(512)
self.fc3 = nn.Linear(512, self.action_size)
self.fc4 = nn.Linear(512, 1)
def forward(self, s):
"""
Controls forward pass of OthelloNNet
Args:
s: np.ndarray
Array of size (batch_size x board_x x board_y)
Returns:
Probability distribution over actions at the current state and the value of the current state.
"""
s = s.view(-1, 1, self.board_x, self.board_y) # batch_size x 1 x board_x x board_y
s = F.relu(self.bn1(self.conv1(s))) # batch_size x num_channels x board_x x board_y
s = F.relu(self.bn2(self.conv2(s))) # batch_size x num_channels x board_x x board_y
s = F.relu(self.bn3(self.conv3(s))) # batch_size x num_channels x (board_x-2) x (board_y-2)
s = F.relu(self.bn4(self.conv4(s))) # batch_size x num_channels x (board_x-4) x (board_y-4)
s = s.view(-1, self.args.num_channels * (self.board_x - 4) * (self.board_y - 4)) # reshaping of
s = F.dropout(F.relu(self.fc_bn1(self.fc1(s))), p=self.args.dropout, training=self.training) # batch_size x 1024
s = F.dropout(F.relu(self.fc_bn2(self.fc2(s))), p=self.args.dropout, training=self.training) # batch_size x 512
pi = self.fc3(s) # batch_size x action_size
v = self.fc4(s) # batch_size x 1
# Returns probability distribution over actions at the current state and the value of the current state.
return F.log_softmax(pi, dim=1), torch.tanh(v)
class ValueBasedPlayer():
"""
Simulate Value Based Player
"""
def __init__(self, game, vnet):
"""
Initialise value based player parameters
Args:
game: OthelloGame instance
Instance of the OthelloGame class above;
vnet: Value Network instance
Instance of the Value Network class above;
Returns:
Nothing
"""
self.game = game
self.vnet = vnet
def play(self, board):
"""
Simulate game play
Args:
board: np.ndarray
Board of size n x n [6x6 in this case]
Returns:
candidates: List
Collection of tuples describing action and values of future predicted states
"""
valids = self.game.getValidMoves(board, 1)
candidates = []
max_num_actions = 4
va = np.where(valids)[0]
va_list = va.tolist()
random.shuffle(va_list)
for a in va_list:
# Return next board state using getNextState() function
nextBoard, _ = self.game.getNextState(board, 1, a)
# Predict the value of next state using value network
value = self.vnet.predict(nextBoard)
# Add the value and the action as a tuple to the candidate lists, note that you might need to change the sign of the value based on the player
candidates += [(-value, a)]
if len(candidates) == max_num_actions:
break
# Sort by the values
candidates.sort()
# Return action associated with highest value
return candidates[0][1]
class ValueNetwork(NeuralNet):
"""
Initiates the Value Network
"""
def __init__(self, game):
"""
Initialise network parameters
Args:
game: OthelloGame instance
Instance of the OthelloGame class above;
Returns:
Nothing
"""
self.nnet = OthelloNNet(game, args)
self.board_x, self.board_y = game.getBoardSize()
self.action_size = game.getActionSize()
self.nnet.to(args.device)
def train(self, games):
"""
Function to train value network
Args:
games: list
List of examples with each example is of form (board, pi, v)
Returns:
Nothing
"""
optimizer = optim.Adam(self.nnet.parameters())
for examples in games:
for epoch in range(args.epochs):
print('EPOCH ::: ' + str(epoch + 1))
self.nnet.train()
v_losses = [] # To store the losses per epoch
batch_count = int(len(examples) / args.batch_size) # len(examples)=200, batch-size=64, batch_count=3
t = tqdm(range(batch_count), desc='Training Value Network')
for _ in t:
sample_ids = np.random.randint(len(examples), size=args.batch_size) # Read the ground truth information from MCTS simulation using the loaded examples
boards, pis, vs = list(zip(*[examples[i] for i in sample_ids])) # Length of boards, pis, vis = 64
boards = torch.FloatTensor(np.array(boards).astype(np.float64))
target_vs = torch.FloatTensor(np.array(vs).astype(np.float64))
# Predict
# To run on GPU if available
boards, target_vs = boards.contiguous().to(args.device), target_vs.contiguous().to(args.device)
# Compute output
_, out_v = self.nnet(boards)
l_v = self.loss_v(target_vs, out_v) # Total loss
# Record loss
v_losses.append(l_v.item())
t.set_postfix(Loss_v=l_v.item())
# Compute gradient and do SGD step
optimizer.zero_grad()
l_v.backward()
optimizer.step()
def predict(self, board):
"""
Function to perform prediction
Args:
board: np.ndarray
Board of size n x n [6x6 in this case]
Returns:
v: OthelloNet instance
Data of the OthelloNet class instance above;
"""
# Timing
start = time.time()
# Preparing input
board = torch.FloatTensor(board.astype(np.float64))
board = board.contiguous().to(args.device)
board = board.view(1, self.board_x, self.board_y)
self.nnet.eval()
with torch.no_grad():
_, v = self.nnet(board)
return v.data.cpu().numpy()[0]
def loss_v(self, targets, outputs):
"""
Calculates Mean squared error
Args:
targets: np.ndarray
Ground Truth variables corresponding to input
outputs: np.ndarray
Predictions of Network
Returns:
MSE Loss calculated as: square of the difference between your model's predictions
and the ground truth and average across the whole dataset
"""
# Mean squared error (MSE)
return torch.sum((targets - outputs.view(-1)) ** 2) / targets.size()[0]
def save_checkpoint(self, folder='checkpoint', filename='checkpoint.pth.tar'):
"""
Code Checkpointing
Args:
folder: string
Path specifying training examples
filename: string
File name of training examples
Returns:
Nothing
"""
filepath = os.path.join(folder, filename)
if not os.path.exists(folder):
print("Checkpoint Directory does not exist! Making directory {}".format(folder))
os.mkdir(folder)
else:
print("Checkpoint Directory exists! ")
torch.save({'state_dict': self.nnet.state_dict(),}, filepath)
print("Model saved! ")
def load_checkpoint(self, folder='checkpoint', filename='checkpoint.pth.tar'):
"""
Load code checkpoint
Args:
folder: string
Path specifying training examples
filename: string
File name of training examples
Returns:
Nothing
"""
# https://github.com/pytorch/examples/blob/master/imagenet/main.py#L98
filepath = os.path.join(folder, filename)
if not os.path.exists(filepath):
raise ("No model in path {}".format(filepath))
checkpoint = torch.load(filepath, map_location=args.device)
self.nnet.load_state_dict(checkpoint['state_dict'])
class PolicyBasedPlayer():
"""
Simulate Policy Based Player
"""
def __init__(self, game, pnet, greedy=True):
"""
Initialize Policy based player parameters
Args:
game: OthelloGame instance
Instance of the OthelloGame class above;
pnet: Policy Network instance
Instance of the Policy Network class above
greedy: Boolean
If true, implement greedy approach
Else, implement random sample policy based player
Returns:
Nothing
"""
self.game = game
self.pnet = pnet
self.greedy = greedy
def play(self, board):
"""
Simulate game play
Args:
board: np.ndarray
Board of size n x n [6x6 in this case]
Returns:
a: np.ndarray
If greedy, implement greedy policy player
Else, implement random sample policy based player
"""
valids = self.game.getValidMoves(board, 1)
action_probs = self.pnet.predict(board)
vap = action_probs*valids # Masking invalid moves
sum_vap = np.sum(vap)
if sum_vap > 0:
vap /= sum_vap # Renormalize
else:
# If all valid moves were masked we make all valid moves equally probable
print("All valid moves were masked, doing a workaround.")
vap = vap + valids
vap /= np.sum(vap)
if self.greedy:
# Greedy policy player
a = np.where(vap == np.max(vap))[0][0]
else:
# Sample-based policy player
a = np.random.choice(self.game.getActionSize(), p=vap)
return a
class PolicyNetwork(NeuralNet):
"""
Initialise Policy Network
"""
def __init__(self, game):
"""
Initalise policy network paramaters
Args:
game: OthelloGame instance
Instance of the OthelloGame class above;
Returns:
Nothing
"""
self.nnet = OthelloNNet(game, args)
self.board_x, self.board_y = game.getBoardSize()
self.action_size = game.getActionSize()
self.nnet.to(args.device)
def train(self, games):
"""
Function for Policy Network Training
Args:
games: list
List of examples where each example is of form (board, pi, v)
Return:
Nothing
"""
optimizer = optim.Adam(self.nnet.parameters())
for examples in games:
for epoch in range(args.epochs):
print('EPOCH ::: ' + str(epoch + 1))
self.nnet.train()
pi_losses = []
batch_count = int(len(examples) / args.batch_size)
t = tqdm(range(batch_count), desc='Training Policy Network')
for _ in t:
sample_ids = np.random.randint(len(examples), size=args.batch_size)
boards, pis, _ = list(zip(*[examples[i] for i in sample_ids]))
boards = torch.FloatTensor(np.array(boards).astype(np.float64))
target_pis = torch.FloatTensor(np.array(pis))
# Predict
boards, target_pis = boards.contiguous().to(args.device), target_pis.contiguous().to(args.device)
# Compute output
out_pi, _ = self.nnet(boards)
l_pi = self.loss_pi(target_pis, out_pi)
# Record loss
pi_losses.append(l_pi.item())
t.set_postfix(Loss_pi=l_pi.item())
# Compute gradient and do SGD step
optimizer.zero_grad()
l_pi.backward()
optimizer.step()
def predict(self, board):
"""
Function to perform prediction
Args:
board: np.ndarray
Board of size n x n [6x6 in this case]
Returns:
Data from the OthelloNet class instance above;
"""
# Timing
start = time.time()
# Preparing input
board = torch.FloatTensor(board.astype(np.float64))
board = board.contiguous().to(args.device)
board = board.view(1, self.board_x, self.board_y)
self.nnet.eval()
with torch.no_grad():
pi,_ = self.nnet(board)
return torch.exp(pi).data.cpu().numpy()[0]
def loss_pi(self, targets, outputs):
"""
Calculates Negative Log Likelihood(NLL) of Targets
Args:
targets: np.ndarray
Ground Truth variables corresponding to input
outputs: np.ndarray
Predictions of Network
Returns:
Negative Log Likelihood calculated as: When training a model, we aspire to find the minima of a
loss function given a set of parameters (in a neural network, these are the weights and biases).
Sum the loss function to all the correct classes. So, whenever the network assigns high confidence at
the correct class, the NLL is low, but when the network assigns low confidence at the correct class,
the NLL is high.
"""
## To implement the loss function, please compute and return the negative log likelihood of targets.
## For more information, here is a reference that connects the expression to the neg-log-prob: https://gombru.github.io/2018/05/23/cross_entropy_loss/
return -torch.sum(targets * outputs) / targets.size()[0]
def save_checkpoint(self, folder='checkpoint', filename='checkpoint.pth.tar'):
"""
Code Checkpointing
Args:
folder: string
Path specifying training examples
filename: string
File name of training examples
Returns:
Nothing
"""
filepath = os.path.join(folder, filename)
if not os.path.exists(folder):
print("Checkpoint Directory does not exist! Making directory {}".format(folder))
os.mkdir(folder)
else:
print("Checkpoint Directory exists! ")
torch.save({'state_dict': self.nnet.state_dict(),}, filepath)
print("Model saved! ")
def load_checkpoint(self, folder='checkpoint', filename='checkpoint.pth.tar'):
"""
Load code checkpoint
Args:
folder: string
Path specifying training examples
filename: string
File name of training examples
Returns:
Nothing
"""
# https://github.com/pytorch/examples/blob/master/imagenet/main.py#L98
filepath = os.path.join(folder, filename)
if not os.path.exists(filepath):
raise ("No model in path {}".format(filepath))
checkpoint = torch.load(filepath, map_location=args.device)
self.nnet.load_state_dict(checkpoint['state_dict'])
```

The hyperparameters used throughout the notebook.

```
args = dotdict({
'numIters': 1, # In training, number of iterations = 1000 and num of episodes = 100
'numEps': 1, # Number of complete self-play games to simulate during a new iteration.
'tempThreshold': 15, # To control exploration and exploitation
'updateThreshold': 0.6, # During arena playoff, new neural net will be accepted if threshold or more of games are won.
'maxlenOfQueue': 200, # Number of game examples to train the neural networks.
'numMCTSSims': 15, # Number of games moves for MCTS to simulate.
'arenaCompare': 10, # Number of games to play during arena play to determine if new net will be accepted.
'cpuct': 1,
'maxDepth':5, # Maximum number of rollouts
'numMCsims': 5, # Number of monte carlo simulations
'mc_topk': 3, # Top k actions for monte carlo rollout
'checkpoint': './temp/',
'load_model': False,
'load_folder_file': ('/dev/models/8x100x50','best.pth.tar'),
'numItersForTrainExamplesHistory': 20,
# Define neural network arguments
'lr': 0.001, # learning rate
'dropout': 0.3,
'epochs': 10,
'batch_size': 64,
'device': DEVICE,
'num_channels': 512,
})
```

Load in trained value and policy networks

```
# @markdown Load in trained value and policy networks
model_save_name = 'ValueNetwork.pth.tar'
path = "nma_rl_games/alpha-zero/pretrained_models/models/"
set_seed(seed=SEED)
game = OthelloGame(6)
vnet = ValueNetwork(game)
vnet.load_checkpoint(folder=path, filename=model_save_name)
model_save_name = 'PolicyNetwork.pth.tar'
path = "nma_rl_games/alpha-zero/pretrained_models/models/"
set_seed(seed=SEED)
game = OthelloGame(6)
pnet = PolicyNetwork(game)
pnet.load_checkpoint(folder=path, filename=model_save_name)
# Alternative if the downloading of trained model didn't work (will train the model)
if not os.listdir('nma_rl_games/alpha-zero/pretrained_models/models/'):
path = "nma_rl_games/alpha-zero/pretrained_models/data/"
loaded_games = loadTrainExamples(folder=path, filename='checkpoint_1.pth.tar')
set_seed(seed=SEED)
game = OthelloGame(6)
vnet = ValueNetwork(game)
vnet.train(loaded_games)
set_seed(seed=SEED)
game = OthelloGame(6)
pnet = PolicyNetwork(game)
pnet.train(loaded_games)
```

```
Random seed 2021 has been set.
Random seed 2021 has been set.
```

A reminder of the network architecture

# Section 1: Plan using Monte Carlo Rollouts¶

*Time estimate: ~15mins*

**Goal**: Teach the students the core idea behind using simulated rollouts to understand the future and value actions.

**Exercise**:

Build a loop to run Monte Carlo simulations using the policy network.

Use this to obtain better estimates of the value of moves.

## Video 1: Play using Monte-Carlo rollouts¶

## Coding Exercise 1: `MonteCarlo`

¶

To recapitulate, the goal of the Monte Carlo algorithm here is to evaluate the outcome of different plans according to the policy used, i.e., what future Value function do we expect to end up with. So we will iterate the game forward in time (according to the game rules and with specific strategies) and return the Value function output at the end of that iteration.

Here, we will first set up the Monte Carlo planner.

**Note**: because we will be simulating different actions into the future (planning), we want to distinguish potential board positions from actual ones that are taken. Therefore, the current (actual) position of the board that is used as a starting point for Monte-Carlo simulations will be labeled “canonical board” to avoid confusion.

```
class MonteCarlo():
"""
Implementation of Monte Carlo Algorithm
"""
def __init__(self, game, nnet, args):
"""
Initialize Monte Carlo Parameters
Args:
game: OthelloGame instance
Instance of the OthelloGame class above;
nnet: OthelloNet instance
Instance of the OthelloNNet class above;
args: dictionary
Instantiates number of iterations and episodes, controls temperature threshold, queue length,
arena, checkpointing, and neural network parameters:
learning-rate: 0.001, dropout: 0.3, epochs: 10, batch_size: 64,
num_channels: 512
Returns:
Nothing
"""
self.game = game
self.nnet = nnet
self.args = args
self.Ps = {} # Stores initial policy (returned by neural net)
self.Es = {} # Stores game.getGameEnded ended for board s
# Call this rollout
def simulate(self, canonicalBoard):
"""
Helper function to simulate one Monte Carlo rollout
Args:
canonicalBoard: np.ndarray
Canonical Board of size n x n [6x6 in this case]
Returns:
temp_v:
Terminal State
"""
s = self.game.stringRepresentation(canonicalBoard)
init_start_state = s
temp_v = 0
isfirstAction = None
current_player = -1 # opponent's turn (the agent has already taken an action before the simulation)
self.Ps[s], _ = self.nnet.predict(canonicalBoard)
for i in range(self.args.maxDepth): # maxDepth
if s not in self.Es:
self.Es[s] = self.game.getGameEnded(canonicalBoard, 1)
if self.Es[s] != 0:
# Terminal state
temp_v = -self.Es[s] * current_player
break
self.Ps[s], v = self.nnet.predict(canonicalBoard)
valids = self.game.getValidMoves(canonicalBoard, 1)
self.Ps[s] = self.Ps[s] * valids # Masking invalid moves
sum_Ps_s = np.sum(self.Ps[s])
if sum_Ps_s > 0:
self.Ps[s] /= sum_Ps_s # Renormalize
else:
# If all valid moves were masked make all valid moves equally probable
# NB! All valid moves may be masked if either your NNet architecture is insufficient or you've get overfitting or something else.
# If you have got dozens or hundreds of these messages you should pay attention to your NNet and/or training process.
log.error("All valid moves were masked, doing a workaround.")
self.Ps[s] = self.Ps[s] + valids
self.Ps[s] /= np.sum(self.Ps[s])
##########################################################################
## TODO for students: Take a random action.
# 1. Take the random action.
# 2. Find the next state and the next player from the environment.
# 3. Get the canonical form of the next state.
# Fill out function and remove
raise NotImplementedError("Take the action, find the next state")
##########################################################################
# Take a random action
a = ...
# Find the next state and the next player
next_s, next_player = self.game.getNextState(..., ..., ...)
canonicalBoard = self.game.getCanonicalForm(..., ...)
s = self.game.stringRepresentation(next_s)
current_player *= -1
# Initial policy
self.Ps[s], v = self.nnet.predict(canonicalBoard)
temp_v = v
return temp_v
# Add event to airtable
atform.add_event('Coding Exercise 1: MonteCarlo')
```

# Section 2: Use Monte Carlo simulations to play games¶

*Time estimate: ~20mins*

**Goal:** Teach students how to use simple Monte Carlo planning to play games.

## Video 2: Play with planning¶

## Coding Exercise 2: Monte-Carlo simulations¶

Now we can run Monte-Carlo simulations. We essentially evaluate for a given action taken now what the potential future outcome will be. So we want to choose different future actions according to the policy (random vs. value-based vs. policy-based) and evaluate the outcomes. We will simulate potential future outcomes and compute their value and then average those values to get a sense of the averge value of our policy used for a given immediate (current) action. This iteration (rollout) can be expressed in the following pseudo-code:

for i in 1 to k:

Choose the ith ranked action \(a^i\) for the current state \(s_t\) according to our specific policy function.

Run N Monte Carlo rollouts from \(s_{t+1}\) following the application of \(a^i\), \(j\) steps into the future (depth)

Average the estimated values for each rollout to get: \(V_{i}^{AVG}\)

Build an array of \([V_{i}^{AVG}, a^i]\) pairs.

To act, choose the action associated with the highest average value, i.e., \(\underset{a^i}{\operatorname{argmax}}(V_{i}^{AVG})\). We will use \(k=3\), \(j=3\) and \(N=10\).

**Exercise**:

Incorporate Monte Carlo simulations into an agent.

Run the resulting player versus the random, value-based, and policy-based players.

```
# Load MC model from the repository
mc_model_save_name = 'MC.pth.tar'
path = "nma_rl_games/alpha-zero/pretrained_models/models/"
```

```
class MonteCarloBasedPlayer():
"""
Simulate Player based on Monte Carlo Algorithm
"""
def __init__(self, game, nnet, args):
"""
Initialize Monte Carlo Parameters
Args:
game: OthelloGame instance
Instance of the OthelloGame class above;
nnet: OthelloNet instance
Instance of the OthelloNNet class above;
args: dictionary
Instantiates number of iterations and episodes, controls temperature threshold, queue length,
arena, checkpointing, and neural network parameters:
learning-rate: 0.001, dropout: 0.3, epochs: 10, batch_size: 64,
num_channels: 512
Returns:
Nothing
"""
self.game = game
self.nnet = nnet
self.args = args
############################################################################
## TODO for students: Instantiate the Monte Carlo class.
# Fill out function and remove
raise NotImplementedError("Use Monte Carlo!")
############################################################################
self.mc = ...
self.K = self.args.mc_topk
def play(self, canonicalBoard):
"""
Simulate Play on Canonical Board
Args:
canonicalBoard: np.ndarray
Canonical Board of size n x n [6x6 in this case]
Returns:
best_action: tuple
(avg_value, action) i.e., Average value associated with corresponding action
i.e., Action with the highest topK probability
"""
self.qsa = []
s = self.game.stringRepresentation(canonicalBoard)
Ps, v = self.nnet.predict(canonicalBoard)
valids = self.game.getValidMoves(canonicalBoard, 1)
Ps = Ps * valids # Masking invalid moves
sum_Ps_s = np.sum(Ps)
if sum_Ps_s > 0:
Ps /= sum_Ps_s # Renormalize
else:
# If all valid moves were masked make all valid moves equally probable
# NB! All valid moves may be masked if either your NNet architecture is insufficient or you've get overfitting or something else.
# If you have got dozens or hundreds of these messages you should pay attention to your NNet and/or training process.
log = logging.getLogger(__name__)
log.error("All valid moves were masked, doing a workaround.")
Ps = Ps + valids
Ps /= np.sum(Ps)
num_valid_actions = np.shape(np.nonzero(Ps))[1]
if num_valid_actions < self.K:
top_k_actions = np.argpartition(Ps,-num_valid_actions)[-num_valid_actions:]
else:
top_k_actions = np.argpartition(Ps,-self.K)[-self.K:] # To get actions that belongs to top k prob
############################################################################
## TODO for students:
# 1. For each action in the top-k actions
# 2. Get the next state using getNextState() function.
# You can find the implementation of this function in Tutorial 1 in
# `OthelloGame()` class.
# 3. Get the canonical form of the getNextState().
# Fill out function and remove
raise NotImplementedError("Loop for the top actions")
############################################################################
for action in ...:
next_s, next_player = self.game.getNextState(..., ..., ...)
next_s = self.game.getCanonicalForm(..., ...)
values = []
# Do some rollouts
for rollout in range(self.args.numMCsims):
value = self.mc.simulate(canonicalBoard)
values.append(value)
# Average out values
avg_value = np.mean(values)
self.qsa.append((avg_value, action))
self.qsa.sort(key=lambda a: a[0])
self.qsa.reverse()
best_action = self.qsa[0][1]
return best_action
def getActionProb(self, canonicalBoard, temp=1):
"""
Helper function to get probabilities associated with each action
Args:
canonicalBoard: np.ndarray
Canonical Board of size n x n [6x6 in this case]
temp: Integer
Signifies if game is in terminal state
Returns:
action_probs: List
Probability associated with corresponding action
"""
if self.game.getGameEnded(canonicalBoard, 1) != 0:
return np.zeros((self.game.getActionSize()))
else:
action_probs = np.zeros((self.game.getActionSize()))
best_action = self.play(canonicalBoard)
action_probs[best_action] = 1
return action_probs
# Add event to airtable
atform.add_event('Coding Exercise 7: MonteCarlo siumulations')
set_seed(seed=SEED)
game = OthelloGame(6)
# Run the resulting player versus the random player
rp = RandomPlayer(game).play
num_games = 20 # Feel free to change this number
n1 = NNet(game) # nNet players
n1.load_checkpoint(folder=path, filename=mc_model_save_name)
args1 = dotdict({'numMCsims': 10, 'maxRollouts':5, 'maxDepth':5, 'mc_topk': 3})
## Uncomment below to check Monte Carlo agent!
# print('\n******MC player versus random player******')
# mc1 = MonteCarloBasedPlayer(game, n1, args1)
# n1p = lambda x: np.argmax(mc1.getActionProb(x))
# arena = Arena.Arena(n1p, rp, game, display=OthelloGame.display)
# MC_result = arena.playGames(num_games, verbose=False)
# print(f"\n\n{MC_result}")
# print(f"\nNumber of games won by player1 = {MC_result[0]}, "
# f"number of games won by player2 = {MC_result[1]}, out of {num_games} games")
# win_rate_player1 = MC_result[0]/num_games
# print(f"\nWin rate for player1 over {num_games} games: {round(win_rate_player1*100, 1)}%")
```

```
Random seed 2021 has been set.
```

```
Number of games won by player1 = 13, number of games won by player2 = 7, out of 20 games
Win rate for player1 over 20 games: 65.0%
```

**Note**: the Monte-Carlo player doesn’t seem to be doing much better than the random player… This is because training of a good MC player is VERY compute intensive and we have not done extensive training here. In Bonus 2 below, you can play with a Monte-Carlo Tree Search (MCTS) player that has been trained well and you’ll see that it performs much better!

### Monte-Carlo player against Value-based player¶

```
print('\n******MC player versus value-based player******')
set_seed(seed=SEED)
vp = ValueBasedPlayer(game, vnet).play # Value-based player
arena = Arena.Arena(n1p, vp, game, display=OthelloGame.display)
MC_result = arena.playGames(num_games, verbose=False)
print(f"\n\n{MC_result}")
print(f"\nNumber of games won by player1 = {MC_result[0]}, "
f"number of games won by player2 = {MC_result[1]}, out of {num_games} games")
win_rate_player1 = MC_result[0]/num_games
print(f"\nWin rate for player1 over {num_games} games: {round(win_rate_player1*100, 1)}%")
```

```
Number of games won by player1 = 9, number of games won by player2 = 11, out of 20 games
Win rate for player1 over 20 games: 45.0%
```

### Monte-Carlo player against Policy-based player¶

```
print('\n******MC player versus policy-based player******')
set_seed(seed=SEED)
pp = PolicyBasedPlayer(game, pnet).play # Policy player
arena = Arena.Arena(n1p, pp, game, display=OthelloGame.display)
MC_result = arena.playGames(num_games, verbose=False)
print(f"\n\n{MC_result}")
print(f"\nNumber of games won by player1 = {MC_result[0]}, "
f"number of games won by player2 = {MC_result[1]}, out of {num_games} games")
win_rate_player1 = MC_result[0]/num_games
print(f"\nWin rate for player1 over {num_games} games: {round(win_rate_player1*100, 1)}%")
```

```
Number of games won by player1 = 10, number of games won by player2 = 10, out of 20 games
Win rate for player1 over 20 games: 25.0%
```

# Summary¶

## Video 3: Outro¶

## Airtable Submission Link¶

```
# @title Airtable Submission Link
from IPython import display as IPydisplay
IPydisplay.HTML(
f"""
<div>
<a href= "{atform.url()}" target="_blank">
<img src="https://github.com/NeuromatchAcademy/course-content-dl/blob/main/tutorials/static/SurveyButton.png?raw=1"
alt="button link end of day Survey" style="width:410px"></a>
</div>""" )
```

# Bonus 1: Plan using Monte Carlo Tree Search (MCTS)¶

*Time estimate: ~30mins

**Goal:** Teach students to understand the core ideas behind Monte Carlo Tree Search (MCTS).

## Video 4: Plan with MCTS¶

## Bonus Coding Exercise 1: MCTS planner¶

In building the MCTS planner, we will focus on the action selection part, particularly the objective function used. MCTS will use a combination of the current action-value function \(Q\) and the policy prior as follows:

with \(u(s_t, a)=c_{puct} \cdot P(s,a) \cdot \frac{\sqrt{\sum_b N(s,b)}}{1+N(s,a)}\). This effectively implements an Upper Confidence bound applied to Trees (UCT). UCT balances exploration and exploitation by taking the values stored from the MCTS into account. The trade-off is parametrized by \(c_{puct}\).

**Note**: Polynomial Upper Confidence Trees (PUCT) is the technical term for the alorithm below in which we sequentially run MCTS and store/use information from previous runs to explore and find optimal actions).

**Exercise**:

Finish the MCTS planner by using UCT to select actions to build the tree.

Deploy the MCTS planner to build a tree search for a given board position, producing value estimates and action counts for that position.

```
class MCTS():
"""
This class handles MCTS (Monte Carlo Tree Search).
"""
def __init__(self, game, nnet, args):
"""
Initialize parameters of MCTS
Args:
game: OthelloGame instance
Instance of the OthelloGame class above;
nnet: OthelloNet instance
Instance of the OthelloNNet class above;
args: dictionary
Instantiates number of iterations and episodes, controls temperature threshold, queue length,
arena, checkpointing, and neural network parameters:
learning-rate: 0.001, dropout: 0.3, epochs: 10, batch_size: 64,
num_channels: 512
Returns:
Nothing
"""
self.game = game
self.nnet = nnet
self.args = args
self.Qsa = {} # Stores Q values for s,a (as defined in the paper)
self.Nsa = {} # Stores #times edge s,a was visited
self.Ns = {} # Stores #times board s was visited
self.Ps = {} # Stores initial policy (returned by neural net)
self.Es = {} # Stores game.getGameEnded ended for board s
self.Vs = {} # Stores game.getValidMoves for board s
def search(self, canonicalBoard):
"""
This function performs one iteration of MCTS. It is recursively called
till a leaf node is found. The action chosen at each node is one that
has the maximum upper confidence bound as in the paper.
Once a leaf node is found, the neural network is called to return an
initial policy P and a value v for the state. This value is propagated
up the search path. In case the leaf node is a terminal state, the
outcome is propagated up the search path. The values of Ns, Nsa, Qsa are
updated.
NOTE: the return values are the negative of the value of the current
state. This is done since v is in [-1,1] and if v is the value of a
state for the current player, then its value is -v for the other player.
Args:
canonicalBoard: np.ndarray
Canonical Board of size n x n [6x6 in this case]
Returns:
v: Float
The negative of the value of the current canonicalBoard
"""
s = self.game.stringRepresentation(canonicalBoard)
if s not in self.Es:
self.Es[s] = self.game.getGameEnded(canonicalBoard, 1)
if self.Es[s] != 0:
# Terminal node
return -self.Es[s]
if s not in self.Ps:
# Leaf node
self.Ps[s], v = self.nnet.predict(canonicalBoard)
valids = self.game.getValidMoves(canonicalBoard, 1)
self.Ps[s] = self.Ps[s] * valids # Masking invalid moves
sum_Ps_s = np.sum(self.Ps[s])
if sum_Ps_s > 0:
self.Ps[s] /= sum_Ps_s # Renormalize
else:
# If all valid moves were masked make all valid moves equally probable
# NB! All valid moves may be masked if either your NNet architecture is
# insufficient or you've get overfitting or something else.
# If you have got dozens or hundreds of these messages you should
# pay attention to your NNet and/or training process.
log = logging.getLogger(__name__)
log.error("All valid moves were masked, doing a workaround.")
self.Ps[s] = self.Ps[s] + valids
self.Ps[s] /= np.sum(self.Ps[s])
self.Vs[s] = valids
self.Ns[s] = 0
return -v
valids = self.Vs[s]
cur_best = -float('inf')
best_act = -1
############################################################################
## TODO for students:
# Implement the highest upper confidence bound depending whether we observed
# the state-action pair which is stored in self.Qsa[(s, a)].
# You can find the formula in the slide 52 in video 8 above.
# Fill out function and remove
raise NotImplementedError("Complete the for loop")
############################################################################
# Pick the action with the highest upper confidence bound
for a in range(self.game.getActionSize()):
if valids[a]:
if (s, a) in self.Qsa:
u = ... + ... * ... * math.sqrt(...) / (1 + ...)
else:
u = ... * ... * math.sqrt(... + 1e-8)
if u > cur_best:
cur_best = u
best_act = a
a = best_act
next_s, next_player = self.game.getNextState(canonicalBoard, 1, a)
next_s = self.game.getCanonicalForm(next_s, next_player)
v = self.search(next_s)
if (s, a) in self.Qsa:
self.Qsa[(s, a)] = (self.Nsa[(s, a)] * self.Qsa[(s, a)] + v) / (self.Nsa[(s, a)] + 1)
self.Nsa[(s, a)] += 1
else:
self.Qsa[(s, a)] = v
self.Nsa[(s, a)] = 1
self.Ns[s] += 1
return -v
def getNsa(self):
return self.Nsa
```

# Bonus 2: Use MCTS to play games¶

*Time estimate: ~10mins*

**Goal:** Learn how to use the results of MCTS to play games.

**Exercise:**

Plug the MCTS planner into an agent.

Play games against other agents.

Explore the contributions of prior network, value function, number of simulations/time to play and explore/exploit parameters.

## Video 5: Play with MCTS¶

## Bonus Coding Exercise 2: Agent that uses an MCTS planner¶

Now we can use the MCTS planner and play the game! We will again let the MCTS planner play against players with other policies.

```
# Load MCTS model from the repository
mcts_model_save_name = 'MCTS.pth.tar'
path = "nma_rl_games/alpha-zero/pretrained_models/models/"
```

```
class MonteCarloTreeSearchBasedPlayer():
"""
Simulate Player based on MCTS
"""
def __init__(self, game, nnet, args):
"""
Initialize parameters of MCTS
Args:
game: OthelloGame instance
Instance of the OthelloGame class above;
nnet: OthelloNet instance
Instance of the OthelloNNet class above;
args: dictionary
Instantiates number of iterations and episodes, controls temperature threshold, queue length,
arena, checkpointing, and neural network parameters:
learning-rate: 0.001, dropout: 0.3, epochs: 10, batch_size: 64,
num_channels: 512
Returns:
Nothing
"""
self.game = game
self.nnet = nnet
self.args = args
self.mcts = MCTS(game, nnet, args)
def play(self, canonicalBoard, temp=1):
"""
Simulate Play on Canonical Board
Args:
canonicalBoard: np.ndarray
Canonical Board of size n x n [6x6 in this case]
temp: Integer
Signifies if game is in terminal state
Returns:
List of probabilities for all actions if temp is 0
Best action based on max probability otherwise
"""
for i in range(self.args.numMCTSSims):
##########################################################################
## TODO for students:
# Run MCTS search function.
# Fill out function and remove
raise NotImplementedError("Plug the planner")
##########################################################################
...
s = self.game.stringRepresentation(canonicalBoard)
############################################################################
## TODO for students:
# Call the Nsa function from MCTS class and store it in the self.Nsa
# Fill out function and remove
raise NotImplementedError("Compute Nsa (number of times edge s,a was visited)")
############################################################################
self.Nsa = ...
self.counts = [self.Nsa[(s, a)] if (s, a) in self.Nsa else 0 for a in range(self.game.getActionSize())]
if temp == 0:
bestAs = np.array(np.argwhere(self.counts == np.max(self.counts))).flatten()
bestA = np.random.choice(bestAs)
probs = [0] * len(self.counts)
probs[bestA] = 1
return probs
self.counts = [x ** (1. / temp) for x in self.counts]
self.counts_sum = float(sum(self.counts))
probs = [x / self.counts_sum for x in self.counts]
return np.argmax(probs)
def getActionProb(self, canonicalBoard, temp=1):
"""
Helper function to get probabilities associated with each action
Args:
canonicalBoard: np.ndarray
Canonical Board of size n x n [6x6 in this case]
temp: Integer
Signifies if game is in terminal state
Returns:
action_probs: List
Probability associated with corresponding action
"""
action_probs = np.zeros((self.game.getActionSize()))
best_action = self.play(canonicalBoard)
action_probs[best_action] = 1
return action_probs
set_seed(seed=SEED)
game = OthelloGame(6)
rp = RandomPlayer(game).play # All players
num_games = 20 # Games
n1 = NNet(game) # nnet players
n1.load_checkpoint(folder=path, filename=mcts_model_save_name)
args1 = dotdict({'numMCTSSims': 50, 'cpuct':1.0})
## Uncomment below to check your agent!
# print('\n******MCTS player versus random player******')
# mcts1 = MonteCarloTreeSearchBasedPlayer(game, n1, args1)
# n1p = lambda x: np.argmax(mcts1.getActionProb(x, temp=0))
# arena = Arena.Arena(n1p, rp, game, display=OthelloGame.display)
# MCTS_result = arena.playGames(num_games, verbose=False)
# print(f"\n\n{MCTS_result}")
# print(f"\nNumber of games won by player1 = {MCTS_result[0]}, "
# f"number of games won by player2 = {MCTS_result[1]}, out of {num_games} games")
# win_rate_player1 = MCTS_result[0]/num_games
# print(f"\nWin rate for player1 over {num_games} games: {round(win_rate_player1*100, 1)}%")
```

```
Random seed 2021 has been set.
```

```
Number of games won by player1 = 19, num of games won by player2 = 1, out of 20 games
Win rate for player1 over 20 games: 95.0%
```

### MCTS player against Value-based player¶

```
print('\n******MCTS player versus value-based player******')
set_seed(seed=SEED)
vp = ValueBasedPlayer(game, vnet).play # Value-based player
arena = Arena.Arena(n1p, vp, game, display=OthelloGame.display)
MC_result = arena.playGames(num_games, verbose=False)
print(f"\n\n{MC_result}")
print(f"\nNumber of games won by player1 = {MC_result[0]}, "
f"number of games won by player2 = {MC_result[1]}, out of {num_games} games")
win_rate_player1 = MC_result[0]/num_games
print(f"\nWin rate for player1 over {num_games} games: {round(win_rate_player1*100, 1)}%")
```

```
Number of games won by player1 = 14, number of games won by player2 = 6, out of 20 games
Win rate for player1 over 20 games: 70.0%
```

### MCTS player against Policy-based player¶

```
print('\n******MCTS player versus policy-based player******')
set_seed(seed=SEED)
pp = PolicyBasedPlayer(game, pnet).play # Policy-based player
arena = Arena.Arena(n1p, pp, game, display=OthelloGame.display)
MC_result = arena.playGames(num_games, verbose=False)
print(f"\n\n{MC_result}")
print(f"\nNumber of games won by player1 = {MC_result[0]}, "
f"number of games won by player2 = {MC_result[1]}, out of {num_games} games")
win_rate_player1 = MC_result[0]/num_games
print(f"\nWin rate for player1 over {num_games} games: {round(win_rate_player1*100, 1)}%")
```

```
Number of games won by player1 = 20, number of games won by player2 = 0, out of 20 games
Win rate for player1 over 20 games: 100.0%
```