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GAME PLAYING COMPUTERS & ARTIFICIAL INTELLIGENCE

Go Bang – The Game

Presented to:

Pascal Hitzler

&

Sebastian Bader

Presented by: Zulqernain Akhter

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GOBANG(Go-moku)

Introduction ( History )o Go Bang(Go-moku)o Renju

Description of the Gameso Classification of Game Typeo Rules of Gameo How to Play o Variant (Other Row-Games) o Computer as an opponent

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GOBANG(Go-moku)

Background Requirementso Searching Strategies

Alpha-Beta Search Proof Number Search

Solving the Gameso AI Games Solved Now and in Future

Conclusiono Summary of Results o Future Researcho New Predictionso Two New Games (LOA, Amazons)

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INTRODUCTIONHistory:

o It is very old five-in-a-row game kakugo ( year 100 A.D. )

o In Japan they played on a 19x19 Go-board since about 700 A.D. when Go was introduced in Japan from China.

o The ancient Chinese game of wutzu as prototype of the Five-In-A-

Row games.

o Winner is known as Japanese “Meijin” named in game “Renju”, means “five pearls in a row“.

o In 1931 Nobel prize winner Yasunari Kawabata "The Master of Go“, proposed the change from Go-board from 19x19 to 15x15intersections.

o COMPUTER OLYMPAID GAMES in the year 2000 predicted Go-Moku as a Solved Game.

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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”.

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.

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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 onespace to the next empty cell either horizontally,

vertically, or diagonally.

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VARIANT (OTHER ROW GAMES)Row or Mill Games - Morris - Linea - Tabula – Mühle-TTT

o Free-style Go-moku: An overline (six consecutive moves) win.

o Standard Go-moku: Only five stones as win.

o Tic-Tac-Toe(333-game): Three consecutive markers on a restricted 3x3 board.

o Othello 8x8 as variant of Gobang(Go-moku).

Game Name Region

Games of Alignment, or

Row games

Egypt, India, and Greece

Mühle. Germany

Mill Games, or Morris Games England

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COMPUTER AS AN OPPONENT

HORIZONTALLY VERTICALLY

RIGHT DIAGONALLY LEFT DIAGONALLY

There are 20 situations that computer will win next step

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SEARCHING STRATEGYALPHA-BETA SEARCH

o This algorithm is based on Depth-First Search.

o The idea is that two scores are passed around in the search.

o val = AlphaBeta(5, -INFINITY, INFINITY);

This does a five-ply search as (int depth, int alpha, int beta).

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PROOF NUMBER SEARCHDECISION

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 computermoves the step to the point.

Else Calculate all the values of empty points:o Plus100 to value of the empty point which can make opponent 4 in a line.o Plus 90 to value of the empty point which can make computer 4 in a line.o Plus 80 to value of the empty point which can make opponent 3 in a line.o Plus 70 to value of the empty point which can make computer 3 in a line.o Plus 60 to value of the empty point which can make opponent 2 in a line.o Plus 50 to value of the empty point which can make computer 2 in a line.

SEARCHING STRATEGY

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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.

 

AI GAMES SOLVED NOW AND IN FUTURE

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o 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.

o For both free-style and standard Go-moku, Allis [Ref. VU, NL] established that the game theoretic value is a first-player win.

o Go-moku & Renju have same State-space and Game-tree complexities.

SUMMARY OF RESULTS

Game Days Systems Internal Memory Processor Speed

Free-Style

Go-moku 11.9 SUN SPARC

Stations

64 / 128 MB 16 to 28 MIPS

Standard

Go-moku

15.1 SUN SPARC

Stations

64 / 128 MB 16 to 28 MIPS

Calculation performed in parallel on Systems at Vrije University in Amsterdam.

The correctness of DB-Search implementation applied and inferred this game as “solved one”.

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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:o free-style and standard Go-moku on smaller boards.o Go-moku with new Opening Rules, including swapping.o 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.

FUTURE RESEARCH

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Computer Olympaid Games in the year 2010 predicted:

o Awari, Othello, and Checker(8x8) as Solved Games.o In Scrabble, computers are believed to be closed to perfect play.

Lines of Action (LOA) Amazons

The Prospects of both are rather different.o LOA has complexity similar to Othello.o LOA is a game, for which interest only arose recently. o At the fifth Computer Olympaid three strong LOA programs participated.o Expectation for LOA game not to be solved before 2010.o Assumption of weak solution is possible, but o Best Solution is expected in the year 2010.

NEW PREDICTIONS

TWO NEW GAMES

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o Amazons is a game with a Complexity comparable to that of Go.

o For Competitive programs, simple evaluation functions work quite reasonable.

o Due to variety of possible moves and branching factor, Amazons will only be solved on relatively small boards,

o 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.

o 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.

TWO NEW GAMES