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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

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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
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 moku3
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
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.
rules of 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
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 m hle ttt
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
COMPUTER AS AN OPPONENT

There are 20 situations that computer will win next step

HORIZONTALLY

VERTICALLY

LEFT DIAGONALLY

RIGHT DIAGONALLY

searching strategy
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).
proof number search

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.
slide11

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.

slide12

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”.

slide13

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.
slide14

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

slide15

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.