2.  Summary  How to Play Go  Project Details  Demo  Results  Conclusions

3. Our project is to create an agent that will be able to play the game of Go on a competitive level against the members in our group. The decision making process of the agent will involve using a MAXIMIN tree to evaluate the strengths of each possible move.

4.  Summary  How to Play Go  Project Details  Demo  Results  Conclusions

5. There are 3 simple rules to remember: Two players (black and white) take turns, placing one stone on the board at a time. A stone must be placed on the intersection of the vertical and horizontal lines. Once a stone is placed, you can't move it, although under some conditions it may be removed. Objective: The objective of Go is to make your "territory" larger than that of your opponent. One way to make territory is to "capture" opponent's stones. Stones that are surrounded are removed from the board and are handed to the opponent as prisoners. Each prisoner will be worth one point.

6. With one more move, the white stone will be completely surrounded and will be removed. Stones that can be removed with one more move are said to be in "Atari".

7. The white stone is now surrounded. Therefore...

8. ... it is removed from the board.

9. If it were white's turn, it could "escape" by connecting another stone.

10. You can play almost anywhere on the board. However, there are some places where the rules say can't play. Black can't make a move at A. (White can.) Because, if black played there, that stone would be already surrounded. Such suicide behavior is forbidden.

11. However, black can play on B. With a black stone on B, the two white stones nearby will be surrounded and be removed.

12. The moves which produce the same board position are prohibited. This concept is called Ko (eternity). However, you can take the Ko stone back once you play somewhere else. To win the Ko fight: Find a place where you can gain a lot by making 2 successive moves. If the opponent doesn't allow it, the Ko fight continues. If he ignores your threat, you can make 2 successive moves while your opponent wins the Ko.

13.  Summary  How to Play Go  Project Details  Demo  Results  Conclusions

14.  The agent uses a MAXIMIN tree evaluation algorithm to find the best moves  It uses a heuristic to evaluate the strength of each board

15. Each new board will generate a tree of new boards

16. PASSPASS Score: -32 Score: 8 Score: -32 Will first evaluate the board as if a pass was taken Set MaxScore to score of the passing branch MaxScore : -32 Best Move (so far)

17. Old nodes are removed and the next branch is investigated MaxScore : -16 Score: 24 Score: -16 Score: -32 Best Move (so far)

18. MaxScore : 66 Score: 66 Best Move Score: -16 If many branches have the same max or min score a move will be chosen randomly.

19. Our AI uses the following heuristic to evaluate the strength of a move. H(move) = 32 myC + 16 myAT + 4 myLT – 8 oAT – 32 oC myC = Total stones I captured from opponent myAT = My actual territory myLT = My loose territory oAT = Opponent’s actual territory oC = Total stones Opponent captured from me

20. Any group of empty vertices surrounded by a single color is considered actual territory of that color.

25. Problem  Not all moves capture Opponent Stones  Not all moves gain Territory How we calculate:  We say we loosely own a territory if we have another stone within 3 territories from us that can possible be used to surround.  Meaning if we have a Wall or Similar Stone within 3 Territories in any direction of our stone then we loosely own the area in between them.

26. Loosely Owned TerritoryNo Loosely Owned Territory

27.  Summary  How to Play Go  Project Details  Demo  Results  Conclusions

28.  Summary  How to Play Go  Project Details  Demo  Results  Conclusions

29.  Ending being able to only search a depth of 2 Going deeper significantly slowed down Gobot  Was able to calculate loosely and actually owned territory as well as captures  Played better than random, with a tree depth of only 1 and some people when the Gobot used a depth of 2

30.  Able to defend by seeing when the opponent will attempt a capture  Able to see when stones cannot be saved  Able to make moves that increase territory even if not immediately  Knows when to pass  Intelligent sacrifices and captures

31.  Supposes that the opponent will make the optimal move according to our heuristic Some times our heuristic is wrong Humans will make suboptimal moves  Evaluating the tree at a depth of 3 causes the Gobot to be almost unplayable because of time

32. We played the Gobot against itself using different tree depths to see how it would perform.

34. Each depth increases the time by a factor of about 80. At depth 2 each move took about 3 seconds. At depth 3 each move would take about 4 minutes! So to go even 1 more depth would take the game almost 2 hours!

35. On average, Tree Depth 1 scored 7.1 higher than Random We played our Gobot against a Gobot making random legal moves to see how it would perform. Tree Depth 2 fared much better against Random

36. Clearly our Gobot was good enough to beat some people…

37. But not Allen

38.  Summary  How to Play Go  Project Details  Demo  Results  Conclusions

39.  Successes: It beat Art, Chris and Professor Clark  Problems: Could not go deep enough Speed Intelligence  Improvements: Strengthen our heuristic Optimize to improve depth of trees Making Strong connections