def tomorrow(self): """changes the calling object so that it represents one calendar...

def tomorrow(self): """Changes the calling object so that it represents one calendar day after the date it originally represented. """ if self.month in [1,3,5,7,8,10] and self.day == 31: self.day = 0 self.month += 1 elif self.month in [4,6,9,11] and self.day == 30: self.day = 0 self.month += 1 elif self.month == 2: if self.isLeapYear() and self.day == 29: self.day = 0 self.month += 1 elif (self.isLeapYear() == False) and self.day == 28: self.day = 0 self.month += 1 elif self.month == 12 and self.day == 31: self.day = 0 self.month = 1 self.year += 1 self.day += 1

Style Pointers

def tomorrow(self): """Changes the calling object so that it represents one calendar day after the date it originally represented. "”” self.day += 1 if self.isLeapYear() == True: DIM = [0, 31, 29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31] if self.day > DIM[self.month]: self.day = 1 self.month += 1 if self.month > 12: self.month = 1 self.year += 1 else:

DIM = [0, 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31] if self.day > DIM[self.month]: self.day = 1 self.month += 1 if self.month > 12: self.month = 1 self.year += 1

Style Pointers

def tomorrow(self): """Changes the calling object so that it represents one calendar day after the date it originally represented. """ DIM = [0, 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31] if self.isLeapYear(): DIM[2] = 29 self.day += 1 if self.day > DIM[self.month]: self.day = 1 self.month += 1 if self.month > 12: self.month = 1 self.year += 1

A More Elegant Solution

Style Pointers

def isBefore(self, d2): """ Returns true if self is before d2 """ if self.year < d2.year: return True if self.month < d2.month and self.year == d2.year: return True if self.day < d2.day and d2.month == self.month and \ self.year == d2.year: return True return False

def isAfter(self, d2): """ Returns true if self is after d2 """ if self.year > d2.year: return True if self.month > d2.month and self.year == d2.year: return True if self.day > d2.day and d2.month == self.month and \ self.year == d2.year: return True return False

A More Elegant Solution

def isBefore(self, d2): """ Returns true if self is before d2 """ if self.year < d2.year: return True if self.month < d2.month and self.year == d2.year: return True if self.day < d2.day and d2.month == self.month and \ self.year == d2.year: return True return False

def isAfter(self, d2): """ Returns true if self is after d2 """ return d2.isBefore(self)

Style Pointers

def diff( self, d2 ): """ Returns the number of days between self and d2 """ dcopy = self.copy() difference = 0 if dcopy.isBefore(d2) == True: while dcopy.isBefore(d2) == True: dcopy.tomorrow() difference -= 1 else: while dcopy.isAfter(d2): dcopy.yesterday() difference += 1 return difference

An Elegant Solution

def diff( self, d2 ): """ Returns the number of days between self and d2 """ dcopy = self.copy() difference = 0 while dcopy.isBefore(d2): dcopy.tomorrow() difference -= 1 while dcopy.isAfter(d2): dcopy.yesterday() difference += 1 return difference

CS 121 Today

Connect Four

X to move.

Is there a way to win?

| | | | | | | || | | | | | | || | | | | | | || | | |X| | | || |X| |X|O| | ||X|O|O|O|X|O| |--------------- 0 1 2 3 4 5 6

Aargh!

Python has no Connect-four datatype…

| | | | | | | || | | | | | | || | | | | | | || | | |X| | | || |X| |X|O| | ||X|O|O|O|X| |O|--------------- 0 1 2 3 4 5 6

… but we can correct that!

Designing classes

1) What data? (Data Members)

2) What are objects' crucial capabilities? (Methods)

Not limited to 7x6!

Designing classes


- height, width

- Where the chips are

- Whose turn it is

- Winning condition

- End condition (number of chips played)2) What are objects' crucial capabilities? (Methods)

Not limited to 7x6!

Designing classes


- height, width

- Where the chips are

- Whose turn it is

- Winning condition

- End condition (number of chips played)2) What are objects' crucial capabilities? (Methods)

- create a new object

- check for win

- print

- get the next move/switch turn

-check for full board

Not limited to 7x6!

Connect Four: the object b

Boardb

intwidthstr str str

str str str

str str str

datalist str

str

str

data

intheight

What is the name of the method that will construct this data?


Boardb

intwidthstr str str

str str str

str str str

datalist str

str

str

data

intheight

What is the name of the method that will construct this data?

__init__(…)

Connect Four: constructor

class Board: """ a datatype representing a C4 board with an arbitrary number of rows and cols """ def __init__( self, width, height ): """ the constructor for objects of type Board """ self.width = width self.height = height self.data = [] # this will be the board for row in range( height ): # 6 boardRow = [] for col in range( width ): # 7 boardRow += [' '] # add a space to this row self.data += [boardRow]


Boardb

intwidthstr str str

str str str

str str str

datalist str

str

str

intheight

| | | | | | | || | | | | | | || | | | | | | || | | |X| | | || |X| |X|O| | ||X|O|O|O|X| |O|--------------- 0 1 2 3 4 5 6

What is the name of the method that will print this data?

def __repr__(self): """ this method returns a string representation for an object of type Board """ s = '' for row in range( self.height ): s += '|' for col in range( self.width ): s += self.data[row][col] + '|' s += '\n'

return s

Connect Four: __repr__

To remove?

To add?

which row is row 0, row 1, and so on?

def __repr__(self): """ this method returns a string representation for an object of type Board """ s = '' for row in range( self.height ): s += '|' for col in range( self.width ): s += self.data[row][col] + '|' s += '\n‘

s += '--'*self.width + '-\n‘ for col in range( self.width ):

s += ' ' + str(col % 10) s += '\n'

return s

Connect Four: __repr__

which row is row 0, row 1, and so on?

class Board

def mystery(self, col, ox): for row in range( self.height ): if self.data[row][col] != ' ': self.data[row-1][col] = ox self.data[self.height-1][col] = ox

def allowsMove(self, col):

Step through this mystery method.

What is each line doing?

What's going wrong?

a C4 board col # 'X' or 'O'

Write allowsMove to return True if col is a valid move;

False otherwise.

class Board{

def mystery(self, col, ox): for row in range( self.height ): if self.data[row][col] != ' ': self.data[row-1][col] = ox self.data[self.height-1][col] = ox

# Adds ox at the top of a column # But at the same time overwrites the existing # elements in the column… # Does not check if it is possible to write in a column… def allowsMove(self, col):

}



What's going wrong?



False otherwise.

class Board

def mystery1(self, col, ox): if allowsMove(col): for row in range( self.height ): if self.data[row][col] != ' ': self.data[row-1][col] = ox return self.data[self.height-1][col] = ox

def allowsMove(self, col):



What's going wrong?



False otherwise.

class Board

def mystery1(self, col, ox): if allowsMove(col): for row in range( self.height ): if self.data[row][col] != ' ': self.data[row-1][col] = ox return self.data[self.height-1][col] = ox

def allowsMove(self, col): if 0 <= col < self.width: return self.data[0][col] == ' '



What's going wrong?



False otherwise.

C4 Board class: methods

__init__( self, width, height )

allowsMove( self, col )

__repr__( self )

addMove( self, col, ox )

isFull( self )

winsFor( self, ox )

the “constructor”

checks if allowed

places a checker

outputs a string

checks if any space is left

checks if a player has won

hostGame( self )play!

delMove( self, col )removes a checker

Which of these will require the most thought?

winsFor( self, ox )

Thoughts?

X O

bb.winsFor( 'X' )or 'O'

winsFor( self, ox )

Thoughts?

X O

bdef winsFor(self, ox): # check for horizontal wins for row in range(0,self.height): for col in range(0,self.width-3): if self.data[row][col] == ox and \ self.data[row][col+1] == ox and \ self.data[row][col+2] == ox and \ self.data[row][col+3] == ox: return True

# check for vertical wins

Two-player games have been a key focus of AI as long as computers have been around…

Strategic thinking == intelligence?

In 1945, Alan Turing predicted that computers

would be better chess players than people in

~ 50 years…

and thus would have achieved intelligence.

Alan Turing memorial Manchester, England

Two-player games have been a key focus of AI as long as computers have been around…

Strategic thinking == intelligence?

… humans and computers have different relative strengths in these games.

humanscomputers

good at evaluating the strength of a board for a player

Particularly good at recognizing patterns

good at looking ahead in the game to find

winning combinations of moves

How humans play games…

- experts could reconstruct these perfectly - novice players did far worse…

An experiment (by A. deGroot) was performed in which chess positions were shown to novice and expert players…

How humans play games…

- experts could reconstruct these perfectly - novice players did far worse…

Random chess positions (not legal ones) were then shown to the two groups

- experts and novices did equally well (badly) at reconstructing them!

An experiment (by A. deGroot) was performed in which chess positions were shown to novice and expert players…

The Player class

PlayerpForX

Details(data and methods)

What data and methods are needed to construct and implement a Player object?

stringox

Picture of a Player object

Player

PlayerpForX

__init__(self, ox, tbt, ply)

stringtbt

__repr__(self)

scoreBoard(self, b)

scoresFor(self, b)

tiebreakMove(self, scores)

nextMove(self, b)

oppCh(self)

'X' 'LEFT'intply

3

DATA

METHODS

tiebreakTypechecker, O or X

scoreBoard ‘X’‘O’

Assigns a score to any board, b

100.0 50.0 0.0A simple system:for a win for a lossfor anything else

Score for Score for

Score for Score for




Score for Score for

Score for Score for 0.0

100.0




Score for Score for

Score for Score for 0.0

100.0 50.0 50.0

scoreBoard



scoreBoard(self, b)

Implementation ideas…

What methods that already exist will come in handy?

This doesn't seem to be looking very

far ahead !

How can there be no 'X' or 'O' input?

What class is this method in?

Looking further ahead…

scoreBoard looks ahead 0 moves

If you look one move ahead, how many possibilities are there to consider?

0-ply

1-ply

A 1-ply lookahead player will "see" an impending victory.

to move…

score




0-ply

1-ply

A 1-ply lookahead player will "see" an impending victory.

to move…

score -1 50 50 50100 50 50




0-ply

A 2-ply lookahead player will also "see"

an opponent's impending victory.

to move…

2-ply score -1 0 0 0 50 0 0




0-ply

1-ply

scoresFor( self, b ) returns a LIST of scores, one for each column you can choose to move next…

2-ply

|O| | | | | | ||X| | | |O| |X||O| | | |X|O|X||X| | | |O|O|X||X| |X| |X|O|O||X| |O|O|O|X|X|--------------- 0 1 2 3 4 5 6

It is O’s move. What scores does a 1-ply lookahead for O assign to each move?

col 0 col 1 col 2 col 3 col 4 col 5 col 6

Which change at 2-ply?

Example 1-ply and 2-ply lookahead scores




Which change at 2-ply?


-1 100

50 100

50 50100





-1 100

50 50 100

50 50


-1 100

0 100

0

1-ply

2-ply50100

| | | | | | |O|| | | | | | |O|| | | | | | |X||X| |X|O| | |O||X|O|O|X| |X|X||X|O|O|O| |O|X|--------------- 0 1 2 3 4 5 6

It is X’s move. What scores does a 2-ply lookahead for X assign to each move?



| | | | | | |O|| | | | | | |O|| | | | | | |X||X| |X|O| | |O||X|O|O|X| |X|X||X|O|O|O| |O|X|--------------- 0 1 2 3 4 5 6

It is X’s move. What scores does a 2-ply lookahead for X assign to each move?



100

0 0 0 50 0 -1

b

0-ply scores for O:col 0 col 1 col 2 col 3 col 4 col 5 col 6




Practice ‘X’‘O’





Solutions

-1

-1

-1

-1

50 50 50 50 50 50

50 50 100

50 50 50

0

0

100

100

0

0

0 0 50

100

00

b ‘X’‘O’

‘X’‘O’new‘X’

Col 6

Col 5

Col 4Col 3Col 2

Col 1

Col 0

b

scoresFor each column

(1) For each possible move

(2) Add it to the board


Col 6

Col 5

Col 4Col 3Col 2

Col 1

Col 0

b(1) For each possible move


(3) Ask OPPONENT to score each board

At what ply?

0.0

50.0

50.0

0.00.0

50.0

0.0



Col 6

Col 5

Col 4Col 3Col 2

Col 1

Col 0

b(1) For each possible move


(3) Ask OPPONENT to score each board

(4) Take the opponent's MAX

0.0

50.0

0.00.0

50.0

0.0

What to assign for a score?


50.0

scoresFor

def scoresFor(self, b):



(3) Ask OPPONENT to score each board - at ? ply

(4) the score is 100-max

Write tiebreakMove to return the leftmost best score

inside the list scores

def tiebreakMove(self, scores):

if self.tbt == 'LEFT':

How would 'RANDOM' and 'RIGHT' work differently?

500

1200

2000

2800

Computer Chess

early programs ~ 1960’s

Computers cut their teeth playing chess…

Ranking

beginner

amateur

world ranked

world champion

MacHack (1100) ~ 1967 MIT

Deep Thought ~ 1989 Carnegie Mellon

Slate (2070) ~ 1970’s Northwestern

Deep Blue ~ 1996 IBM

Deep Blue rematch ~ 1997 IBM

100’s of moves/sec

10,000’s of moves/sec

1,000,000’s moves/sec

3,500,000 moves/secDeep Fritz: 2002X3D Fritz: 2003 Hydra: 2006

200,000,000 moves/sec

first paper: 1950

What is Hydra's chess rating?

Games’ Branching Factors

Branching Factor Estimatesfor different two-player games

Tic-tac-toe 4

Connect Four 7

Checkers 10

Othello 30

Chess 40

Go 300

• On average, there are fewer than 40 possible moves that a chess player can make from any board configuration… 0 Ply

1 Ply

2 Ply

Hydra at home in the United Arab Emirates…

Hydra looks ahead 18 ply !



Tic-tac-toe 4

Connect Four 7

Checkers 10

Othello 30

Chess 40

Go 300

1 Ply

2 Ply

Boundaries for qualitatively

different games…

0 Ply



Tic-tac-toe 4

Connect Four 7

Checkers 10

Othello 30

Chess 40

Go 300

“solved” games

computer-dominated

human-dominated

1 Ply

2 Ply

0 Ply

Progress

Looking further ahead …

0 ply:

2 ply: 3 ply:

Zen choice of move: here and now

| | | | | | | || | | | | | | ||O| | | | | | ||X| | | | | | ||X|O|O| | |X| ||O|X|X|O|X|O| |--------------- 0 1 2 3 4 5 6

| | | | | | | || | | | | | | || | | | |X| | || | | | |O|O| || |X|X| |X|O| ||O|X|O| |O|X| |--------------- 0 1 2 3 4 5 6

(1) Player will win

(2) Player will avoid losing

(3) Player will set up a win by forcing the

opponent to avoid losing

X’s move X‘s move

1 ply:

| | | | | | | || | | | | | | || | | | | | | || | | | | | | || |O|X| | | | ||O|X|X|X| |O|O|--------------- 0 1 2 3 4 5 6

X’s move


Col 6

Col 5

Col 4Col 3Col 2

Col 1

Col 0

b

Choosing the best move



(3) Ask OPPONENT to score each board - ply?

(4) Reverse the scores

100.0

50.0

50.0

100.0100.0

50.0

100.0


Col 6

Col 5

Col 4Col 3Col 2

Col 1

Col 0

b

Choosing the best move

100.0

50.0

50.0

100.0100.0

50.0

100.0



(3) Ask OPPONENT to score each board - ply?

(4) Reverse the scores

(5) Find one max - that's it!

def tomorrow(self): """changes the calling object so that it represents one calendar...

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