Tic-Tac-Toe - Data Mining

1794 Words Nov 19th, 2009 8 Pages
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
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After that I performed ESX supervised learning with all data as training data as shown below: Then I performed another mining session with only first 658 instances as training data and other 300 as testing data in order to evaluate the model. The parameter window is shown below. Apart from supervised learning, several other mining techniques are used to evaluate the data. They are: Mangrove, a freeware which generates decision tree and classification tree using excel file. All of them will be described more in detail under the evaluating the results division.
Interpretation of the results (from Data Mining)
When talking about interpreting the results, first we have to check whether the formed classes are solid one. To do this we have to check whether the class resemblance score which should be higher than the domain resemblance score. In this case both Positive and Negative class has score higher than the domain resemblance score. They are only slightly higher because of the nature of the values of the attribute. The scores are shown below. When we look at the domain statistics for the categorical attributes we can see the predictability score for all the attribute value X is more than the predictability score of other two possible values of O (other player move) and b (blank). The scores are shown below. When we examine the class individually I found that the attribute value highly sufficient for being class membership is M-M = X, and the attribute

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