An evolutionary approach for computing the winning strategy for Nim-like games is proposed in this paper. The winning strategy is computed by using the Multi Expression Programming (MEP) technique - a fast and efficient variant of the Genetic Programming (GP). Each play strategy is represented by a mathematical expression that contains mathematical operators (such as +, -, *, mod, div, and , or, xor, not) and operands (encoding the current game state). Several numerical experiments for computing the winning strategy for the Nim game are performed. The computational effort needed for evolving a winning strategy is reported. The results show that the proposed evolutionary approach is very suitable for computing the winning strategy for Nim-like games.

We demonstrate the use of a program that generates conjectures about positions of the combinatorial game Chomp--explanations of why certain moves are bad. These could be used in the design of a Chomp-playing program that gives reasons for its moves. We prove one of these Chomp conjectures--demonstrating that our conjecturing program can produce genuine Chomp knowledge. The conjectures are generated by a general purpose conjecturing program that was previously and successfully used to generate mathematical conjectures. Our program is initialized with Chomp invariants and example game boards--the conjectures take the form of invariant-relation statements interpreted to be true for all board positions of a certain kind. The conjectures describe a theory of Chomp positions. The program uses limited, natural input and suggests how theories generated on-the-fly might be used in a variety of situations where decisions--based on reasons--are required.