GAME PLAYING COMPUTERS & ARTIFICIAL INTELLIGENCE

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Presentation transcript:

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

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

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)

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.

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”.

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.

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).

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

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).

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.

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.

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”.

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.

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

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.