Tic-Tac-Toe - Data Mining
The Goal
My goal is to find the probability of wining in tic-tac-toe game given that you make the first move. To obtain hypothesis bases on my goal I have to state some conditions and facts on the game. They are: 1) There are 362, 880 ways of placing O’s and X’s. 2) When X make first move, possibility of X winning is 131,184, O winning is 77, 904, and 46, 080 tied games (Source: http://en.wikipedia.org/wiki/Tic-tac-toe). After eliminating rotations and/or reflections of other outcomes, there are only 138 unique outcomes. X won 91 times, O won 44 times and 3 ties (Source: http://en.wikipedia.org/wiki/Tic-tac-toe). Basically, the win of X is the concept. There are 8 possible ways of creating three X in row. Based on this my hypothesis states:
Hypothesis
“If X makes the first move then the probability of the player with X will win is 60% and above.”
Null Hypothesis
“If X makes the first move then the probability of the player with X will win is less than 60%.”
Data Collection and Preparation
To prove or refute the hypothesis, data has to be collected. As we all know this step requires a great amount of time and effort. Also in order to build an effective model a data mining algorithm must be presented with a few hundred or few thousands relevant/applicable records. As mentioned above there are thousands of winning combinations, I have collected datasets with 958 instances which encodes set of possible board configurations at the end of tic-tac-toe game given X makes the first move.
The data set for tic-tac- toe board end game was taken from UCI machine learning repository website (Source: http://archive.ics.uci.edu/ml/datasets/Tic-Tac-Toe+Endgame). The data was in a command delimited text file without attributes name on the top. After downloading the data in CSV format, I converted into excel spreadsheet using the options available from MS Excel. Since the attributes name was missing I have to read the data description file which was provided at the same website to
My goal is to find the probability of wining in tic-tac-toe game given that you make the first move. To obtain hypothesis bases on my goal I have to state some conditions and facts on the game. They are: 1) There are 362, 880 ways of placing O’s and X’s. 2) When X make first move, possibility of X winning is 131,184, O winning is 77, 904, and 46, 080 tied games (Source: http://en.wikipedia.org/wiki/Tic-tac-toe). After eliminating rotations and/or reflections of other outcomes, there are only 138 unique outcomes. X won 91 times, O won 44 times and 3 ties (Source: http://en.wikipedia.org/wiki/Tic-tac-toe). Basically, the win of X is the concept. There are 8 possible ways of creating three X in row. Based on this my hypothesis states:
Hypothesis
“If X makes the first move then the probability of the player with X will win is 60% and above.”
Null Hypothesis
“If X makes the first move then the probability of the player with X will win is less than 60%.”
Data Collection and Preparation
To prove or refute the hypothesis, data has to be collected. As we all know this step requires a great amount of time and effort. Also in order to build an effective model a data mining algorithm must be presented with a few hundred or few thousands relevant/applicable records. As mentioned above there are thousands of winning combinations, I have collected datasets with 958 instances which encodes set of possible board configurations at the end of tic-tac-toe game given X makes the first move.
The data set for tic-tac- toe board end game was taken from UCI machine learning repository website (Source: http://archive.ics.uci.edu/ml/datasets/Tic-Tac-Toe+Endgame). The data was in a command delimited text file without attributes name on the top. After downloading the data in CSV format, I converted into excel spreadsheet using the options available from MS Excel. Since the attributes name was missing I have to read the data description file which was provided at the same website to
Bibliography: Asuncion, A. & Newman, D.J. (2007). UCI Machine Learning Repository [http://archive.ics.uci.edu/ml/datasets/Tic-Tac-Toe+Endgame]. Irvine, CA: University of California, School of Information and Computer Science. http://en.wikipedia.org/wiki/Tic-tac-toe http://www.infoacumen.com/ http://www.kdnuggets.com/software/classification-decision-tree.html#tree-free o http://www.geocities.com/adotsaha/CTree/CtreeinExcel.html o http://www.tetris1d.org/zigah/mangrove/ Data Mining – A tutorial based primer, Richard J. Riger and Michael W. Geatz, Second impression 2008, Pearson Education Inc.