A Fast Thinking Connect Four Machine! 6.846 Final Project Presented by Tina Wen.

A Fast Thinking Connect Four Machine!

6.846 Final ProjectPresented by Tina Wen

Goal

Write a fast connect k game on m by n grid from scratch

m

nk

Small m and n: exhaustive search

Big m and n: search to a good depth

Basic Idea

Negamax search (recursively call expand and combine)

ME: MAX

OPPO: MIN

2 4 1 5 4 2 1 7 9 2 0 3 4 5 2 1 3 5 7 8 4 6 5 4 3 2 1

ROOT

OPPO: MIN

4

4 5 9 3 5 5 8 6 3

4 33

ME: MAX

Approaches1. Sequential exhaustive search

2. One dynamic queue in shared memory (TSP)

3. Master-Slave Message Passing

Tile 0

tile1

tile2

tile3

tile4

3

5 2

6

0

COMBINE

Approaches4. Master-Slave Individually allocated shared memory

(no mutex)tile0 Where to write to to distribute work?

Where to get the results?

tile1

From which tile Ready? Result

1 0

2 0

Where to get work

Ready? work

0

Where to return work?

To which tile Pointer

1

2

tile2Where to get work

Ready? work

0

Where to return work?

Heuristic• Search for 4 in a row in 4 different orientations

• Count only rows that consist of one color and space (either red or black == 0)

Out of 4: # for black

# for red

• If one color has 4 in a row, then score = (infinity + spaces)

Else score +=

If we are red

2 2

score

9 + 4 + 1 = 14

9 + 4 + 4 = 17

9 + 4 +1 = 14

1234

score += 2 2

9 + 9 + 4 = 22

Heuristic

Performance Comparison (connect 3)Performance of connect 3 on 4x4 grid

Num

ber o

f cy

cles

Number of processors (P)Purple: sequential no pruning


Num

ber o

f cy

cles

Number of processors (P)

0.83

Purple: sequential no pruningRed: dynamic queue


Num

ber o

f cy

cles

Number of processors (P)Purple: sequential no pruningUpper Red: dynamic queueLower Red: message passing

Performance of connect 3 on 4x4 gridN

umbe

r of

cycl

es


Performance Comparison (connect 3)

5.05

0.83

Purple: sequential no pruningUpper Red: dynamic queueLower Red: message passingBlue: individually allocated shared memory


umbe

r of

cycl

es



Purple: sequential no pruning


umbe

r of

cycl

es



1.15

Purple: sequential no pruningRed: dynamic queue


umbe

r of

cycl

es



9.59

1.15

Purple: sequential no pruningUpper Red: dynamic queueLower Red: message passing


umbe

r of

cycl

es


Number of processors (P)Purple: sequential no pruningUpper Red: dynamic queueLower Red: message passingBlue: individually allocated shared memory


umbe

r of

cycl

es



9.87

9.59

Blue: individually allocated shared memoryRed: message passing

Load Balancing


Load

bal

anci

ng s

prea

d

Better balanced

Worse balanced

90 billion cycles

177 billion cycles

114 billion cycles

4 children7 children

Sequential Pruning

2

5

ME: MAX

OPPO: MIN

ME: MAX

<=2

>=5

Number of cycles Sequential pruning Individually allocated shared memory (min)

3x3 connect 3 0.157 billion 3 billion

3x3 connect 4 0.162 billion 23 billion

Final Version

Tile 0 Other tiles: sequential pruning

Pros: Take advantage of both dynamic queue for load balancing and pruningCons: Can’t do pruning between processors

Number of cycles Sequential pruning Individually allocated shared memory (min)

Final Version (min)

3x3 connect 3 0.157 billion 3 billion (P=50) 0.069 billion (P=20)

3x3 connect 4 0.162 billion 23 billion (P=50) 0.14 billion(P=20)

Interactive Mode

Conclusion

My connect four• searches fast • has a good heuristic

By using • Pruning • Master slave structure• Individually allocated shared memory

COME TRY IT!

A Fast Thinking Connect Four Machine! 6.846 Final Project Presented by Tina Wen.

Documents