HPC Checkers ByAndy BlockRyan Egan
Table of Contents• Overview of Checkers
▫Overview of Checkers▫Rules of the Game
• AI Theory• The Program
▫Board▫Sample Jump▫Future Moves▫Parallel Processing▫Using the Future Table
• Work in progress
Overview of Checkers•8x8 checkered board using only the black
squares•32 positions•Search space of 5x1020
•Each Player starts with 12 men
Rules of Checkers• Pieces
▫ Men can only move forwarded diagonally 1 space▫ Kings can move forwarded and backward diagonally 1
space▫ Upon reaching the opposite back row men become kings▫ Each player starts with 12 men
• Jumping▫ Men and kings are required to jump when possible▫ Multiple jumps are allowed and required when possible▫ When a man or king is jumped it is removed from the
board▫ If a man jumps into the back row and becomes a king the
turn is ended.
Rules of Checkers cont.•Start Game
▫Red always moves first•End Game
▫The game ends when one player can no longer move
▫Game can end it a draw
AI Theory•Heuristics
▫Not perusing paths that appear to not be as beneficial as other paths
▫Alpha-beta pruning •Planning
▫Future moves are calculated to generate a plan of attack that maximizes benefit and minimizes loss.
The Program •The Board
▫Stored as 33 value integer array▫Starting board
{1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0 ,3,3,
3,3,3,3,5}▫Adjacency matrix used to navigate board.▫The 33rd value in the board array is used
for locations that are off the board in the Adjacency matrix.
The Program cont.•Jumps
▫For men jumps form a directed and acyclic graph (DAG)
▫A breadth first search is used to build a list of adjacent jumpable locations
▫Starting from the last found location the adjacency list is traversed in reverse to find the longest path.
▫This will return the greatest number of possible jumps. Issue: This may miss jumps that would have better
outcomes later on.
Sample Jump
Enqueue Root (2)
2
{2
Sample Jump
Look Left (9)
2
{2
Sample Jump
Enqueue (9)
2
9
{2
Sample Jump
Look Right
2
9
{2
Sample Jump
Look Left (16)
2
9
{2,9},
Sample Jump
Enqueue (16)
2
16
9
{2,9},
Sample Jump
Look Right (18)
2
16
9
{2,9},
Sample Jump
2
16 18
9
Enqueue (18)
{2,9},
Sample Jump
2
16 18
9
Look Left
{2,9},{9,16},
Sample Jump
2
16 18
9
Look Right (25)
{2,9},{9,16},
Sample Jump
2
16 18
9
25
Enqueue (18)
{2,9},{9,16},
Sample Jump
2
16 18
9
25
Look left
{2,9},{9,16},{9,18},
Sample Jump
2
16 18
9
25
Look Right
{2,9},{9,16},{9,18},
Sample Jump
2
16 18
9
25
Look Left
{2,9},{9,16},{9,18},{16,25}
Sample Jump
2
16 18
9
25
Look Right
{2,9},{9,16},{9,18},{16,25}
Sample Jump
2
16 18
9
25
Back to Root
{2,9},{9,16},{9,18},{16,25}
Sample Jump
2
16 18
9
25
Back to Root
{2,9},{9,16},{9,18},{16,25}
Sample Jump
2
16 18
9
25
Back to Root
{2,9},{9,16},{9,18},{16,25}
Sample Jump
2
16 18
9
25
Back to Root
{2,9},{9,16},{9,18},{16,25}
Sample Jump
2
16 18
9
25
Back to Root
{2,9},{9,16},{9,18},{16,25}
Future Moves•For each move of player 1 each possible
move of player 2 is calculated•For each move of player 2 each possible
move of player 1 is calculated•This is repeated until a given search
depth is reached.•Very quickly this can result in very large
search area.
Future Moves• To improve the play of the AI the benefit of possible
moves is calculated.• For each move of player 1 each possible move of
player 2 is calculated• For each move of player 2 each possible move of
player 1 is calculated• This is repeated until a given search depth is
reached.• When a given depth is reached the value of that path
is calculated.• Very quickly this can result in very large search area.
Future Moves
For all Red
Future Moves8 12
For all Red
{8,12}
Future Moves8 12
For all Red
{8,12},{9,12}
9 12
Future Moves8 12
For all Red
{8,12},{9,12},{9,13}
9 129 13
Future Moves8 12
For all Red
{8,12},{9,12},{9,13},{10,13},
9 129 1310 13
Future Moves8 12
For all Red
{8,12},{9,12},{9,13},{10,13},{10,14}
9 129 1310 1310 14
Future Moves8 12
For all Red
{8,12},{9,12},{9,13},{10,13},{10,14} ,{11,14}
9 129 1310 1310 1411 14
Future Moves8 12
For all Red
{8,12},{9,12},{9,13},{10,13},{10,14} ,{11,14}
9 129 1310 1310 1411 1411 15
Future Moves8 12
White’s counter move
{8,12},{9,12},{9,13},{10,13},{10,14} ,{11,14},{11,15}
20 1620 1721 1721 1822 1822 1923 19
RED WHITE
Future Moves8 12
White’s counter move
{8,12},{9,12},{9,13},{10,13},{10,14} ,{11,14},{11,15}
20 1620 1721 1721 1822 1822 1923 19
RED WHITE
Future Moves8 12
White’s counter move
{8,12},{9,12},{9,13},{10,13},{10,14} ,{11,14},{11,15}
20 1620 1721 1721 1822 1822 1923 19
RED WHITE
Future Moves8 12
White’s counter move
{8,12},{9,12},{9,13},{10,13},{10,14} ,{11,14},{11,15}
20 1620 1721 1721 1822 1822 1923 19
RED WHITE
Parallel Processing
•Can‘t have player 2 waiting for player 1’s move to be completed.
•Search must be conducted in a timely manner.
•To improve performance multiple branches of the future move table are computed at the same time.
Parallel ProcessingPlayer
1Player
2Player
2Player
2Player
2Player
2Player
2Player
2
•Each set of responses are run as a separate threads
•Each set can be computed independently of other sets of the same or greater depth as well as steps that did not directly precede it.
P7P6P5P4P3
Parallel ProcessingPlayer
1Player
2Player
2Player
2Player
2Player
2Player
2Player
2
•This allows the task of searching for the best move to be split among multiple processors as well as multiple threads.
•This makes it well suited to being run on the cluster
P1 P2
Using the Future Table• When a move made by player 1 or player 2 make a
path in the table no longer possible they are removed.
• The path that yields the highest possible point value is taken.
• The point value of a path is determined by multiple factors.• Jumping a man gets points• Taking a king gets more points than taking a man• Points are deducted for being jumped and losing pieces
• Point values for each move are determined by the total value of the possible paths that result.
Work in Progress•Finish Threading•Migrate to Cluster•King jump logic
▫Requires a modification to the man jump logic
•End game detection▫Draw
If nothing changes in the future lookup within 40 moves call it a draw.
•Finalize point strategy
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