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 Member since Oct 2014 1 post 2019-11-18, 15:55   #1   Subject: Assignment 4.2, Problem 3 - Evaluation function There seems to be no definition to which value X_2, X_1, O_2 and O_1 evaluate. Does that mean that we are supposed to write answers unresolved, e.g. for s=[[X, _, _], [_, O, _], [_, _, _]], Eval(s)=2X_1(s)-3O_1(s)? Or are we supposed to assume theses cases evaluate to the same values as X_3 (+1) respectively O_3 (-1)? In this case the evaluation function would not always valuate a terminal winning state higher than another state: For s=[[X,_,O], [_,X, X], [_,O,O]] and (obviously) X's turn, there are three possible successor states: - s_1=[[X,X,O], [_,X, X], [_,O,O]] - s_2=[[X,_,O], [X,X, X], [_,O,O]] - s_3=[[X,_,O], [X,X, X], [_,O,O]] Where s_2 is the best state, because it is a terminal state that wins the game for X. Eval(s_i) is therefor: - i=1: 3X_2(s)+X_1(s)-3O_2(s)=3+1-3=+1 - i=2: X_3(s)=+1 - i=3: 6X_2(s)=+6 => This state would be chosen, when maximizing (=X is trying to win). The followup state of s_3 would be a draw (if O is minimizing), resulting in an worse result, than when choosing the winning terminal state s_2.
 Member for 2 months 54 posts 2019-11-19, 10:13   #2   With the evaluation function, the idea is just to evaluate the nodes at depth 2. The definition of X_2, X_1, etc is in the first paragraph of the problem: we define X_n as the number of rows, columns, or diagonals with exactly n X’s and no O’s. Similarly, O_n is the number of rows, columns, or diagonals with exactly n O’s and no X’s. For example, the state [[X, _, _], [_, O, _], [_, _, _]] has - X_2 = 0 (because there are no rows, columns or diagonals with only two Xs) - X_1 = 2 (there is one row and one column with exactly one X, and no diagonals, since the diagonal also includes O) - O_2 = 0 (because there are no rows, columns or diagonals with two Os) - O_1 = 3 (there is one row and one column with exactly one O, as well as one diagonal) Does this help?
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