The application of an evaluation function to a terminal node results in a static score for that terminal node.
/home/dream4/paul/teaching/ai1problemsolving/slides/games/slideminmax1a.eps
The above example features a lookahead tree of depth 2. The evaluation function is applied to the terminal states resulting in the static scores for those nodes. For example, node f has a static score of +10. Note that the evaluation function returns a value for MAX - even when it is MIN's turn. The higher the score the better for MAX. /home/dream4/paul/teaching/ai1problemsolving/slides/games/slideminmax1a.eps
Now we propagate the static scores up the tree in an attempt to figure out just which of the several options is likely to lead to a better chance of a win.
First looking at MIN's options, MIN would select options that minimise the scores. So node b is given a dynamic score of -2. (The term dynamic score indicates it is derived from static scores.) When it is MAX's go, MAX maximises the chance of winning by choosing the option with the largest score - in this case, the +3 indicating that the move to node d is most favourable.