1. GAME PLAYING COMPUTERS & ARTIFICIAL INTELLIGENCE
Go Bang – The Game
Presented to:
Pascal Hitzler
&
Sebastian Bader
Presented by: Zulqernain Akhter

2. GOBANG(Go-moku) Introduction ( History ) Description of the Games
Renju
Description of the Games
Classification of Game Type
Rules of Game
How to Play
Variant (Other Row-Games)
Computer as an opponent

3. GOBANG(Go-moku) Background Requirements Searching Strategies
Alpha-Beta Search
Proof Number Search
Solving the Games
AI Games Solved Now and in Future
Conclusion
Summary of Results
Future Research
New Predictions
Two New Games (LOA, Amazons)

4. INTRODUCTION History:
It is very old five-in-a-row game kakugo ( year 100 A.D. )
In Japan they played on a 19x19 Go-board since about 700 A.D.
when Go was introduced in Japan from China.
The ancient Chinese game of wutzu as prototype of the Five-In-A-Row games.
Winner is known as Japanese “Meijin” named in game “Renju”, means “five pearls in a row“.
In 1931 Nobel prize winner Yasunari Kawabata "The Master of Go“, proposed the change from Go-board from 19x19 to 15x15
intersections.
COMPUTER OLYMPAID GAMES in the year 2000 predicted Go-Moku as a Solved Game.

5. CLASSIFICATION OF GAME TYPE
· Category-3 Game:-
"If solvable at all, then by Knowledge-based methods".
Go-Moku and Renju are considered as divergent games. i.e. If the size of the state-space increases, the game is said to be divergent.
·  
RULES OF GAME
Rule 1. Play Alternates.
Rule 2. Winning Criteria:
Unbroken line of five stones (marks) whether
vertically, horizontally, or diagonally.
Rule 3. If neither player succeeds, the game is “Draw”.

6. HOW TO PLAY Players may decide how many cells of the
lattice may be used for the game.
For example:-
A 10x10 lattice (100 cells) or
The entire 15x15 lattice (225 cells).
Each player in turn moves one stone one
space to the next empty cell either horizontally,
vertically, or
diagonally.

7. VARIANT (OTHER ROW GAMES) Row or Mill Games - Morris - Linea - Tabula – Mühle-TTT
Game Name
Region
Games of Alignment, or
Row games
Egypt, India, and Greece
Mühle.
Germany
Mill Games, or Morris Games
England
Free-style Go-moku:
An overline (six consecutive moves) win.
Standard Go-moku:
Only five stones as win.
Tic-Tac-Toe(333-game):
Three consecutive markers on a restricted 3x3 board.
Othello 8x8 as variant of Gobang(Go-moku).

8. COMPUTER AS AN OPPONENT
There are 20 situations that computer will win next step
HORIZONTALLY
VERTICALLY
RIGHT DIAGONALLY
LEFT DIAGONALLY

9. SEARCHING STRATEGY ALPHA-BETA SEARCH
This algorithm is based on Depth-First Search.
The idea is that two scores are passed around in the search.
val = AlphaBeta(5, -INFINITY, INFINITY);
This does a five-ply search as (int depth, int alpha, int beta).

10. SEARCHING STRATEGY PROOF NUMBER SEARCH DECISION
Best-First search method
Cost function used for decision (which node to expand next) to prove the goal.
If empty point can make x 5 in a line, computer moves and wins. Game over.
Else if there was a empty point which can make o 5 in a line, then computer
moves the step to the point.
Else Calculate all the values of empty points:
Plus100 to value of the empty point which can make opponent 4 in a line.
Plus 90 to value of the empty point which can make computer 4 in a line.
Plus 80 to value of the empty point which can make opponent 3 in a line.
Plus 70 to value of the empty point which can make computer 3 in a line.
Plus 60 to value of the empty point which can make opponent 2 in a line.
Plus 50 to value of the empty point which can make computer 2 in a line.

11. AI GAMES SOLVED NOW AND IN FUTURE
Three different definitions of a solution
     Ultra-weakly solved: the game theoretic value of the initial position has been determined.
   Weakly solved: for the initial position, a strategy has been determined to achieve the game-theoretic values against any opposition.
      Strongly solved: such a strategy has been determined for all legal moves.

12. SUMMARY OF RESULTS
The Category-3 games are solved by a combination of expert knowledge, threat-space search, threat-sequence search, proof-number search,as well as alpha-beta search.
For both free-style and standard Go-moku, Allis [Ref. VU, NL] established that the game theoretic value is a first-player win.
Go-moku & Renju have same State-space and Game-tree complexities.
Calculation performed in parallel on Systems at Vrije University in Amsterdam.
Game
Days
Systems
Internal Memory
Processor Speed
Free-Style
Go-moku
11.9
SUN SPARC
Stations
64 / 128 MB
16 to 28 MIPS
Standard
15.1
The correctness of DB-Search implementation applied and inferred this game as “solved one”.

13. Future Research can be splitted into three areas
Leftovers of current investigations.
Selection of fragment, player wants to play in.
Question remains: Is a long-term strategy computable by a machine?
Weakly solve the remaining variants of Connect Five – different board-sizes, different rules – including:
free-style and standard Go-moku on smaller boards.
Go-moku with new Opening Rules, including swapping.
Renju with opening rules.
4th Computer Renju Tournament (2004) and Solving Problems Competitions.
Discover minimax-win solutions from opening positions.
Strongly-solve weakly-solved games.

14. The Prospects of both are rather different.
NEW PREDICTIONS
Computer Olympaid Games in the year 2010 predicted:
Awari, Othello, and Checker(8x8) as Solved Games.
In Scrabble, computers are believed to be closed to perfect play.
Lines of Action (LOA)
Amazons
The Prospects of both are rather different.
LOA has complexity similar to Othello.
LOA is a game, for which interest only arose recently.
At the fifth Computer Olympaid three strong LOA programs participated.
Expectation for LOA game not to be solved before 2010.
Assumption of weak solution is possible, but
Best Solution is expected in the year 2010.
TWO NEW GAMES

15. TWO NEW GAMES Conclusion:
Amazons is a game with a Complexity comparable to that of Go.
For Competitive programs, simple evaluation functions work quite reasonable.
Due to variety of possible moves and branching factor, Amazons will only be solved on relatively small boards,
Since a game starts with 8 Amazons and every move exactly fills one empty square, the initial position on m x m boards with odd m favours the First Player.
The Second Player has an advantage IF m is even.
Conclusion:
Many additional games with Mathematical properties recently have come to the attention of Computer Scientists.