GAME PLAYING COMPUTERS & ARTIFICIAL INTELLIGENCE

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

GOBANG(Go-moku) • Introduction ( History ) • Go Bang(Go-moku) • 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 RULES OF GAME · 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. · 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 • 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 LEFT DIAGONALLY RIGHT 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. The correctness of DB-Search implementation applied and inferred this game as “solved one”.

FUTURE RESEARCH 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.

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 • 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.

GAME PLAYING COMPUTERS & ARTIFICIAL INTELLIGENCE