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 wino A "straight" is a full row or column of your

markero 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 loseo No looping

• There are no ties/draws

Searching

• Alpha-Beta minimax Searchingo We can prune of parts of the tree and save

search time if we know there is already a better move

• Iterative deepeningo 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 childo Either return, or spawn off all other children to

be searched in parallel

Evaluation Function

• Piece counto Each piece is valued at 4

• Centralityo - Each piece gets a bonus equal to the Manhattan

distance from the piece to the nearest corner

• Frank-squaredo Derived from file/ranko Valued at k^2 for each frank having k of your pieces

• Connectivityo Originally was defined as 2 points per piece for

adjacency and 1 point for each diagonalo 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 choiceo 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 algorithmo Good use of pruningo Iterative Deptho Keeping track of best stateso Tweaking evaluation functiono Parallelismo …

• No single piece is the key to a perfect Agent

References

Definition of the game Poussehttp://docs.racket-lang.org/games/pousse.html

MIT Cilk Poussehttp://people.csail.mit.edu/pousse/