Summary How to Play Go Project Details Demo Results Conclusions.

CHALLENGE OF THE GOBOTS

SPRING 2009 FINAL

MIKE TRANCHRIS CUNEO

ARTURO SALAZARALLEN DUNLEA

Gobots

Summary How to Play Go Project Details Demo Results Conclusions

Summary

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.

Gobots


How to Play GoThere 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.

Capturing Stones

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".

Capturing Stones

The white stone is now surrounded. Therefore...

Capturing Stones

... it is removed from the board.

Escaping

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

Illegal Moves

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.

Illegal Moves

However, black can play on B.

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

Ko (eternity)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.

Gobots


Project Details The agent uses a MAXIMIN tree

evaluation algorithm to find the best moves

It uses a heuristic to evaluate the strength of each board

MAXIMIN Tree

Each new board will generate a tree of new boards

MAXIMIN Tree

PA

SS

Score: -32

Score: 8

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)

MAXIMIN Tree

Old nodes are removed and the next branch is investigated

MaxScore : -16

Score: 24Score: 24

Score: -16

Score: -16

Score: -32 Best Move (so far)

MAXIMIN Tree

MaxScore : 66

Score: 66

Score: 66 Score: 66

Score: 66

Best Move

Score: -16

If many branches have the same max or min score a move will be chosen randomly.

Scoring HeuristicOur 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 territorymyLT = My loose territory oAT = Opponent’s actual territoryoC = Total stones Opponent captured from me

Actual TerritoryAny group of empty vertices surrounded by a single color is considered actual territory of that color.

Actual Territory

Loosely Owned Territory

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.

Loosely Owned Territory

Loosely Owned Territory No Loosely Owned Territory

Gobots


Results

Ending being able to only search a depth of 2Going 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

Successes

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

Problems to Improve Upon

Supposes that the opponent will make the optimal move according to our heuristicSome times our heuristic is wrongHumans will make suboptimal moves

Evaluating the tree at a depth of 3 causes the Gobot to be almost unplayable because of time

Tree Depth 1 vs. Tree Depth 2

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

Average Scores

Avg Territory

Avg Prisoner

Avg Score

-10 -5 0 5 10 15 20

Depth 1Depth 2

Average Time

Depth 2

Depth 1

0:00:00 0:00:17 0:00:34 0:00:51 0:01:09 0:01:26 0:01:43

•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!

Random vs. Our Tree

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

Art vs. Our GoBot

Clearly our Gobot was good enough to beat some people…

Allen vs. Our GoBot

But not Allen

Gobots


Conclusion

Successes:It beat Art, Chris and Professor Clark

Problems:Could not go deep enoughSpeedIntelligence

Improvements:Strengthen our heuristicOptimize to improve depth of treesMaking Strong connections

Summary How to Play Go Project Details Demo Results Conclusions.

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