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Assume you have a game tree and the features $(f_1, f_2, f_3,\ldots,f_n )$ that describe the state of the game at any node. Also assume that you are using depth-limited minimax and always expand up to a fixed depth d. Say you have the following four evaluation functions:

$F_1=w_1f_1+w_2f_2+\cdots+f_n$.

$F_2=w_1f_1^2+w_2f_2^2+\cdots+f_n^2$.

$F_3=\exp(w_1f_1^2+w_2f_2^2+\cdots+f_n^2)$.

$F_4=w_1f_1f_2+w_2f_2f_3+⋯+w_nf_{n-1}f_n$.

The weights $(w_1,w_2,\ldots,w_n)$ are same for all evaluation functions. Then select all the statements that are correct:

  1. The optimal sequence of moves for the MAX player would be the different for the function $F_1$ and $F_2$.

  2. The optimal sequence of moves for the MAX player would be the different for the function $F_2$ and $F_3$

  3. The optimal sequence of moves for the MAX player would be the different for the function $F_1$ and $F_3$

  4. The optimal sequence of moves for the MAX player would be necessarily the same for all the functions

  5. None of the above are correct

I need help with this problem that I came across. My understanding on this is that unless weights are changed the evaluation function should be the same. that is, in this case statement 2 and 3 are the only ones correct.

Any ideas?

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  • $\begingroup$ Why is the weight of the last term of $F_4$ $w_n$? $\endgroup$ – xskxzr Sep 29 '19 at 4:38
  • $\begingroup$ edited. for first three functions there is no wn in the end. for last one there is. $\endgroup$ – m00s3 Sep 29 '19 at 5:49
  • $\begingroup$ For example, if $n=4$, what is $F_1$ and $F_4$? $\endgroup$ – xskxzr Sep 29 '19 at 5:53

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