Reversi Meng Tran Faculty Advisor Dr Barry Silverman

Reversi Meng Tran Faculty Advisor: Dr. Barry Silverman Abstract: l Approach: Strategies: The purpose of this project was to explore the field of artificial intelligence using Reversi. l Corners t Brief History: Reversi was invented around 1880 by Englishmen, Lewis Waterman and John W. Mollett. l Mattel produced the game Reversi under the name Othello. l Mattel was probably referencing the conflict in Shakespeare's play. l Since 1978 there has been a World Othello Championship. l t t l l l l The game starts with 2 pieces of each color in the center: Black on E 4, D 5 and White on E 5, D 4. Each player takes alternate turns with Black going first. Each move must flank one of your opponent’s color. There must be at least one of your opponent’s chip between your current move and one of your existing chip on the board. The flanked chips changes to your color. Each player must move if a valid move exists on the board. If a valid move does not exist then the player must forfeit the turn. The game ends when neither player can make a valid move on the board either because there is no more room or no valid moves exist. The player with the most chips on the board wins. New Game Black moves E 6 flanking Whites E 5, thus flipping it to Black t l Edges are the squares on the top and bottom rows and leftmost and rightmost columns (marked with an X). Edges like corners gives the most potential in flipping the most pieces across the board. Edges are harder to flank as the only places that can flank an edge is another edge. Mobility t t l Corners are marked with an X and dangerous squares are marked with an O. Corners can not be flanked which can give you an edge since it can flip pieces across the diagonal of the board or to another corner. Squares around the corner are dangerous as it might give your opponent access to the corner. Edges Rules: Simple strategy Instead of randomly choosing a square for the default computer opponent, I used a priority matrix developed by Peter Frey. l The top priority is 1 and lowest is 60. l t One of the hardest strategies to pull off. Limits your opponent’s moves by planning ahead. Gains an extra move and also limits the squares your opponent can play. Extremely advantageous, but easier to pull off in the later stages of the game. End Game t t t At the end of the game, when 8 to 12 squares are left anybody can perform a look-ahead to see which squares are most advantageous. Can predict where your opponent might move after you. Would be able to estimate if you can with certain moves. Since there are only a few steps left, simulating each move would not be too difficult. Less time simulating what would happen. l 1 49 5 17 18 6 50 2 51 57 41 33 34 42 58 52 7 43 13 25 26 14 44 8 19 35 27 28 36 20 21 37 29 30 38 22 9 45 15 31 32 16 46 10 53 59 47 39 40 48 60 54 3 55 11 23 20 12 56 4 Smart AI: l l l The Smart AI option plays using the End Game strategy. It uses a 12 step look-ahead. Simulates the game and returns a heuristic of 1 for win, -1 for loses, and 0 for draws. Each node sums up the heuristic of all its children. The move with the highest heuristic value is the best possible move with the most chances of ending in a win. Conclusions: This extensive depth-first search can only be done near the end of the game as it takes a lot of time and space. l Smart AI does not take into account Frey’s weights, thus giving the opponent the upper hand when it comes to corners. l End Game is not perfect unless it takes into account the position’s weight. l Future research should go into the beginning of the game where the search branches are extremely long. l Senior Project Poster Day 2007, CIS Dept. University of Pennsylvania