HPC Checkers By Andy Block Ryan 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 5x10 20 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 33 rd 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) {2,9},

Sample Jump Look Right (18) {2,9},

Sample Jump Enqueue (18) {2,9},

Sample Jump Look Left {2,9},{9,16},

Sample Jump Look Right (25) {2,9},{9,16},

Sample Jump Enqueue (18) {2,9},{9,16},

Sample Jump Look left {2,9},{9,16},{9,18},

Sample Jump Look Right {2,9},{9,16},{9,18},

Sample Jump Look Left {2,9},{9,16},{9,18},{16,25}

Sample Jump Look Right {2,9},{9,16},{9,18},{16,25}

Sample Jump Back to Root {2,9},{9,16},{9,18},{16,25}

Sample Jump Back to Root {2,9},{9,16},{9,18},{16,25}

Sample Jump Back to Root {2,9},{9,16},{9,18},{16,25}

Sample Jump Back to Root {2,9},{9,16},{9,18},{16,25}

Sample Jump 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 Moves 812 For all Red {8,12}

Future Moves 812 For all Red {8,12},{9,12} 912

Future Moves 812 For all Red {8,12},{9,12},{9,13}

Future Moves 812 For all Red {8,12},{9,12},{9,13},{10,13},

Future Moves 812 For all Red {8,12},{9,12},{9,13},{10,13}, {10,14}

Future Moves 812 For all Red {8,12},{9,12},{9,13},{10,13}, {10,14},{11,14}

Future Moves 812 For all Red {8,12},{9,12},{9,13},{10,13}, {10,14},{11,14}

Future Moves 812 White’s counter move {8,12},{9,12},{9,13},{10,13}, {10,14},{11,14},{11,15} REDWHITE

Future Moves 812 White’s counter move {8,12},{9,12},{9,13},{10,13}, {10,14},{11,14},{11,15} REDWHITE

Future Moves 812 White’s counter move {8,12},{9,12},{9,13},{10,13}, {10,14},{11,14},{11,15} REDWHITE

Future Moves 812 White’s counter move {8,12},{9,12},{9,13},{10,13}, {10,14},{11,14},{11,15} REDWHITE

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 Processing Player 1 Player 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 Processing Player 1 Player 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 P1P2

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