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• Use of rules of probability
Your statement seems incomplete since it does not state why one should use the rules of probability.I assume that it is a question with slightly awkward grammar.
There are numerous instances in which the rules of probability theory have been ignored in the construction of an evaluation function.Unfortunately, a lot of it is a case of re-inventing the wheel or uses specialized knowledge for one particular problem that can't be generalized to a larger class of problems. You might find Peter Cheeseman's 1985 paper, IN DEFENSE OF PROBABILITY to be of interest.
http://citeseer.ifi.unizh.ch/cache/papers/cs/27258/http:zSzzSzwww.cis.ksu.eduzSz~robbyjozSzcszSzcheeseman85defense.pdf/cheeseman85defense.pdf
There is also interesting material in Professor Edwin Jayne's posthumously published book, PROBABILITY THEORY:THE LOGIC OF SCIENCE.
What is imperfect is the available information to be used in making a winning decision or series of decisions.If you had a game with perfect information such as in CHESS (all moves are known by both sides) you know there is a strategy such that the first player to move can always win. Knowing that strategy may not always be easy to find but it exists. You can do a lot with brute force straight trial and error just as a computer can multiply by fast addition rather than using human algorithms.
In games of imperfect information, (moves of an opponent are unknown or accurate figures are not available)the imperfect information becomes a part of the evaluation function. You can get away with shortcuts but eventually one needs to be guided by an overarching set of principles for reasoning with imperfect information that can allow movement into areas where humans are not capable of assessing thousands of possibilities.The computer is on its own.
The field of probability, however,has its own problems with lack of an overarching theory and the proliferation of ad hoc methods which Professor Jaynes discusses and attempts to remedy with what others have called INFERENTIAL CALCULUS.
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