Isolation – Champion Program COMS W4701 Project 3 Spring 2011 Isolation – Champion Program Albert Jimenez (alj2110)

Board Representation Graph Representation Boolean 2D Array Each node is a free block Gets smaller as the game progresses Boolean 2D Array Simpler 3 – 5 times faster when generating new boards 1

Alpha Beta Generating and Ordering New Boards Evaluation Function Statistical analysis Correlation between distance of players of chosen board and whether the players are directly reachable. Exploited correlation to achieve more pruning Evaluation Function Early in the game it is not clear who is losing/winning Eval(board) = currentPlayer.numMoves – opponent.numMoves Ensures more freedom to apply other strategies Reduces the chances of the opponent trapping you O X

Main Strategy: Achieving Isolation Detecting Isolation Determine if players are separated after generating new boards If so, this is a terminal node and the second evaluation function can be applied Can immediately determine if board is likely to be a win/loss without going any deeper Evaluation Function 2 Compute number of blocks reachable from both players Compute difference in reachable blocks = ‘diffReachable’ Positive value means a likely win Negative value means a likely loss Eval2(board) = (diffReachable > 0) ? INFINITY + diffReachable : -INFINITY + diffReachable Distinguishes between ‘good’ or ’bad’ win/loss O X

Main Strategy: During Isolation Alpha Beta becomes Obsolete It is unnecessary to care about what move the other player might take By focusing on only one’s own moves, can reach twice the depth Computing Optimal Isolation Path Recursive approach to choose the longest path Heuristics were used to prune bad moves (moves that decrease number of reachable blocks) O X