PEMBUATAN GAME NIM MENGGUNAKAN

ALPHA-BETA PRUNING

ByMuhammad Arifin (7407 0300 45)

Supervisor :1. Entin Martiana Kusumaningtyas, S.Kom, M.Kom

2. Kholid Fathoni, S.Kom

Final Project Presentation

EEPIS-ITS, 2010

INTRODUCTION

BACKGROUND

In 1950 the scientists and researchers think about how that machine can do the job as can be done by humans.

Definition of Artificial Intelligence (AI)“Artificial Intelligence is a study of how to make computers do things which at present can be done better by humans.” Rich and Knight [1991] .

AI Methods :Graph, Tree, Expert System, Game Playing, dll.

BACKGROUND

Minimax ConceptJohn von Neumann in 1944, describes a search algorithm in the game, known as the Minimax, which maximizes the player's position and minimize the opponent's position

Alpha-beta Pruning Concept- Alpa-beta Pruning is an improvisation from Minimax.- Basic Idea

“If you have an idea that is surely bad, don’t take the time to see how truly awful it is.” (Pat Winston)

OBJECTIVE

This project purpose is to make intelligent machine that can play Game NIM against Human, using the Alpha-beta PruningMethod.

PROBLEMS

How to apply the Alpha-beta Pruning method into Game NIM ?

PROBLEMS LIMITATION

NIM Game was built using JAVA programming language.

The variant of NIM Game that used in these project is type Grundy's game

Number of objects in NIM Game is dynamic between 5 s/d 15 objects

BASIC THEORY

BASIC THEORY

1. Game Theory2. Game NIM Theory3. Artificial Intelligence4. Alpha-beta Pruning Method

GAME THEORY

The general characteristics of the game : Have two player Perfect information game The player knows all the information state of the

game The loss of a player is a benefit to other players Does not contain probabilistic like dice

NIM GAME THEORY

Begins with a single heap of objects Each player must be able to split a heap of

objects into two heaps of different sizes. The number of object in each heap must not be

the same and cannot be empty. The game ends when only heaps of size two

and smaller remain, none of which can be split unequally.

The last player who can make an allowed move wins

NIM GAME THEORY

A normal play game starting with a single heap of 5 object : Player 1 has two choices, splitting 5 int, 4-1 or 3-2 Player 1 : 5 4-1 Player 2 only has one choices, splitting 4-1 into 3-1-1 Player 1 : 3-1-1 2-1-1-1 Player 2 has no move left and and loses.

NIM GAME THEORY

NIM Game can be implemented in program using tree theory

If we implemented all possible move in NIM Game with a single of 5 the we will have tree like these :

ARTIFICIAL INTELLIGENCE (AI)

Intelligence was created and inserted into a machine (computer) in order to do a job like that can be human.

An example of AI : Gary Kasparov vs Deep Blue in a match of Chess game

ARTIFICIAL INTELLIGENCE (AI)

Job’s that can be done by AI : Natural LanguageGame Robot Control And many other

ALPHA-BETA PRUNING

Alpha-beta pruning is a procedure to reduce the amount of computation and searching during minimax.

Rules for Alpha-beta Pruning- Alpha Cut-off : Search can be stopped below any MIN node having

a beta value less than or equal to the alpha value of any of its MAX ancestors.

- Beta Cut-off : Search can be stopped below any MAX node having a alpha value greater than or equal to the beta value of any of its MIN ancestors.

Evalution Function :- 0 MAX / alpha (Computer Win)- 1 MIN / beta (Player Win)

ALPHA-BETA PRUNING

For example number of objects is 6 and will generate all possible path in tree of NIM Game

Computer first turn.

6

5-1 4-2

4-1-1 3-2-1

3-1-1-1

2-1-1-1-1

2-2-1-1

3-2-1

2-2-1-1

6

7

5

4

3

2 8

9

10

1

ALPHA-BETA PRUNING

Searching start from the last state

6

5-1 4-2

4-1-1 3-2-1

3-1-1-1

2-1-1-1-1

2-2-1-1

3-2-1

2-2-1-1

MAXDepth = 0

6

7

5

4

3

2 8

9

10

MINDepth = 1

MAXDepth = 2

MINDepth = 3

MAXDepth = 4

1= Komputer (AI) Menang

= Player Menang

Alpha = 0

ALPHA-BETA PRUNING

6

5-1 4-2

4-1-1 3-2-1

3-1-1-1

2-1-1-1-1

2-2-1-1

3-2-1

2-2-1-1

MAXDepth = 0

6

7

5

4

3

2 8

9

10

MINDepth = 1

MAXDepth = 2

MINDepth = 3

MAXDepth = 4

1= Komputer (AI) Menang

= Player Menang

alpha = 0

beta = 0

alpha = 0

beta = 0

ALPHA-BETA PRUNING

Process of Beta Cut-off

6

5-1 4-2

4-1-1 3-2-1

3-1-1-1

2-1-1-1-1

2-2-1-1

3-2-1

2-2-1-1

MAXDepth = 0

6

7

5

4

3

2 8

9

10

MINDepth = 1

MAXDepth = 2

MINDepth = 3

MAXDepth = 4

1= Komputer (AI) Menang

= Player Menang

alpha = 0

beta = 0

alpha = 0

beta = 0

Pemangkasan Beta

ALPHA-BETA PRUNING

Last Process of Alpha-beta Pruning

6

5-1 4-2

4-1-1 3-2-1

3-1-1-1

2-1-1-1-1

2-2-1-1

3-2-1

2-2-1-1

MAXDepth = 0

6

7

5

4

3

2 8

9

10

MINDepth = 1

MAXDepth = 2

MINDepth = 3

MAXDepth = 4

1= Komputer (AI) Menang

= Player Menang

alpha = 0

beta = 0

alpha = 0

beta = 0

Pemangkasan Beta

beta = 1

beta = 1

alpha = 1

ALPHA-BETA PRUNING

To make decision Komputer (AI) will search for maksimum of evaluation function.

6

5-1 4-2

4-1-1 3-2-1

3-1-1-1

2-1-1-1-1

2-2-1-1

3-2-1

2-2-1-1

MAXDepth = 0

6

7

5

4

3

2 8

9

10

MINDepth = 1

MAXDepth = 2

MINDepth = 3

MAXDepth = 4

1= Komputer (AI) Menang

= Player Menang

alpha = 0

beta = 0

alpha = 0

beta = 0

beta = 1

beta = 1

alpha = 1 The best move

SYSTEM DESIGN

SYSTEM DESIGN

Menu permainan

User memilih jumlah batang NIM untuk dimainkan

User memilih siapa yang bergerak pertama

Permainan dimulai

Komputer melakukan proses Alpha-beta Pruning

Permainan berakhir sampai jumlah batang tidak dapat dipisahkan

Keluar

User mengaktifkan aplikasi

Back tomain menu

Permainan dilakukan hingga 3 Ronde

TESTING PROGRAM

PLAYING TEST

Playing test will use the data from Game Configuration interface

Game Configuration:- Number of Object: 7- Game Mode: VS Computer- First Turn: Player- With Alpha-beta Pruning

PLAYING TEST

7 objects shown in the board as the game configuration ask for 7 objects.

The first turn is Player

PLAYING TEST

User chose to split 7 into 6-1 The Game board change into two heap, 6-1

PLAYING TEST

Computer Turn From a single heap of 6-1, Computer (AI) splitting from 6-1

to 4-2-1.

PLAYING TEST

Why Computer (AI) chose to split 6-1 into 4-2-1 ? A single heap of 6-1 have 2 childs.

7

5-26-1 4-3

5-1-1 4-2-1

4-1-1-1 3-2-1-1

3-1-1-1-1

2-1-1-1-1-1

2-2-1-1-1

3-2-1-1

2-2-1-1-1

4-2-1 3-2-2

3-2-1-1

2-2-1-1-1

2-2-2-1

3-3-1

3-2-1-1 3-2-1-1

2-2-1-1-1 2-2-1-1-1

4-2-1

3-2-1-1

2-2-1-1-1

ComputerMAX

PlayerMIN

Alpha = 0

Beta = 0

Alpha = 1

ComputerMAX

PlayerMIN

ComputerMAX

PlayerMIN

= Komputer Menang

= Player Menang

Alpha = 0

Beta = 0

Beta = 1

Alpha = 1

Beta = 1

Beta Cut-off

Computer Position

PLAYER TURN

Computer movement :- Computer will always move according to the

maximum value of the Childs- If the Childs consist two of more same maximum

value the Computer will use random move of the same value.

PLAYING TEST

Player turn Player chose to split 4-2-1 into 3-2-1-1. The game board change into four heap, 3-2-1-1

PLAYING TEST

Computer turn Computer only has one move it’s to split 3-2-1-1 into 2-2-1-

1-1

PLAYING TEST

And Computer won the game because Computer is the last player who can make an allowed move

The games will be played as many as three rounds.

Most winners will win the game.

PLAYING TEST

This is the interface high score after playing the game.

ANALYSIS AND CONCLUSION

ANALYSIS

We will compare with Minimax method starting 7 to 15 objects. Whether the Alpha-beta pruning can to reduce the amount of computation and searching during minimax ?

And the result is :Jumlah

BatangJumlah Node

Jumlah Node yang Di lewati

Minimax Alpha-beta Pruning

7 26 22 15

8 58 54 36

9 176 171 76

10 470 465 112

11 1.687 1.681 353

12 5.595 5.589 635

13 22.178 22.171 1.389

14 82.370 82.363 3.427

15 372.074 372.066 10.671

CONCLUSION

Human can play the NIM Game with Computer using Alpha-beta Pruning method.

The Alpha-beta pruning method is an improvisation of Minimax method in the search nodes.

THANK YOU