Cilk Pousse James Process CS534

Overview Introduction to Pousse Searching Evaluation Function Move Ordering Conclusion

Introduction 1998 ICFP Functional Programming Contest Write and AI system to play "Pousse" May be written in any language Teams had 72 hours to complete the programming Almost 50 programs were entered into the content Cilk Pousse written by Supercomputing Technologies Research Group of the MIT LCS won first place

Introduction - Pousse What is Pousse? 2 player game tic-tac-toe variant played on n-by-n board, typically 4- by-4 players place either X or O, X places first A marker is placed on the board by sliding it in from the side(left, right, top, or bottom) o Results in 4*n possible moves on a given turn If a marker is inserted where a maker is already placed, all markers on that row/column are pushed down one space. If the row/column is full, the last marker is pushed off the game board and removed

Introduction - Winning Similar to tic-tac-toe you are trying to create "straights" to win o A "straight" is a full row or column of your marker o Making a move that causes the configuration to contain more straights of your type than your opponents results in a win If you make a move that creates a configuration that is a repeat of a previous configuration you lose o No looping There are no ties/draws

Searching Alpha-Beta minimax Searching o We can prune of parts of the tree and save search time if we know there is already a better move Iterative deepening o For each iteration we start from the best possible move of the previous iteration. i.e. the depth-9 search places the best move into a hash table which provides a starting point for the depth-10 search

Cilk and Parallel Searching Cilk is a C-based language for multithreaded programming, did a lot of the work of multithreading/scheduling Took the approach that either a single child would be searched or all children would be (optimal game tree) Search first child o Either return, or spawn off all other children to be searched in parallel

Evaluation Function Piece count o Each piece is valued at 4 Centrality o - Each piece gets a bonus equal to the Manhattan distance from the piece to the nearest corner Frank-squared o Derived from file/rank o Valued at k^2 for each frank having k of your pieces Connectivity o Originally was defined as 2 points per piece for adjacency and 1 point for each diagonal o Was not used in final version

Evaluation Function Cont. Sum this for our pieces and subtract opponents sum at each state Optimized by incrementally updating score for each position rather than computing from scratch

Move Ordering Two heuristics used to improve move ordering First keep a hash table with the best move information from the previous search Second keep a table of countermoves. o previously when the opponent made move x, we decided move y was a good choice o In the case of Cilk Pousse they saved the last 2 good countermoves for each move If the best move hash table has a move start there, else go to the countermoves table

Conclusion Even relatively simple problems require a large amount of thought and optimization to solve. All of the following were considered o Effective search algorithm o Good use of pruning o Iterative Depth o Keeping track of best states o Tweaking evaluation function o Parallelism o … No single piece is the key to a perfect Agent

References Definition of the game Pousse MIT Cilk Pousse