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<title>Tic-Tac-Toe Endgame Data Base</title>
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<h1>Info on Tic-Tac-Toe Endgame Data Base</h1>
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1. Title: Tic-Tac-Toe Endgame database

2. Source Information
   -- Creator: David W. Aha (aha@cs.jhu.edu)
   -- Donor: David W. Aha (aha@cs.jhu.edu)
   -- Date: 19 August 1991
 
3. Known Past Usage: 
   1. Matheus,~C.~J., \& Rendell,~L.~A. (1989).  Constructive
      induction on decision trees.  In {\it Proceedings of the
      Eleventh International Joint Conference on Artificial Intelligence} 
      (pp. 645--650).  Detroit, MI: Morgan Kaufmann.
      -- CITRE was applied to 100-instance training and 200-instance test
         sets.  In a study using various amounts of domain-specific
         knowledge, its highest average accuracy was 76.7% (using the
         final decision tree created for testing).

   2. Matheus,~C.~J. (1990). Adding domain knowledge to SBL through
      feature construction.  In {\it Proceedings of the Eighth National
      Conference on Artificial Intelligence} (pp. 803--808). 
      Boston, MA: AAAI Press.
      -- Similar experiments with CITRE, includes learning curves up
         to 500-instance training sets but used _all_ instances in the
         database for testing.  Accuracies reached above 90%, but specific
         values are not given (see Chris's dissertation for more details).

   3. Aha,~D.~W. (1991). Incremental constructive induction: An instance-based
      approach.  In {\it Proceedings of the Eighth International Workshop
      on Machine Learning} (pp. 117--121).  Evanston, ILL: Morgan Kaufmann.
      -- Used 70% for training, 30% of the instances for testing, evaluated
         over 10 trials.  Results reported for six algorithms:
         -- NewID:   84.0%
         -- CN2:     98.1%  
         -- MBRtalk: 88.4%
         -- IB1:     98.1% 
         -- IB3:     82.0%
         -- IB3-CI:  99.1%
      -- Results also reported when adding an additional 10 irrelevant 
         ternary-valued attributes; similar _relative_ results except that
         IB1's performance degraded more quickly than the others.

4. Relevant Information:

   This database encodes the complete set of possible board configurations
   at the end of tic-tac-toe games, where "x" is assumed to have played
   first.  The target concept is "win for x" (i.e., true when "x" has one
   of 8 possible ways to create a "three-in-a-row").  

   Interestingly, this raw database gives a stripped-down decision tree
   algorithm (e.g., ID3) fits.  However, the rule-based CN2 algorithm, the
   simple IB1 instance-based learning algorithm, and the CITRE 
   feature-constructing decision tree algorithm perform well on it.

5. Number of Instances: 958 (legal tic-tac-toe endgame boards)

6. Number of Attributes: 9, each corresponding to one tic-tac-toe square

7. Attribute Information: (x=player x has taken, o=player o has taken, b=blank)

    1. top-left-square: {x,o,b}
    2. top-middle-square: {x,o,b}
    3. top-right-square: {x,o,b}
    4. middle-left-square: {x,o,b}
    5. middle-middle-square: {x,o,b}
    6. middle-right-square: {x,o,b}
    7. bottom-left-square: {x,o,b}
    8. bottom-middle-square: {x,o,b}
    9. bottom-right-square: {x,o,b}
   10. Class: {positive,negative}

8. Missing Attribute Values: None

9. Class Distribution: About 65.3% are positive (i.e., wins for "x")