Acro-Nim: A Two-Player Game

Acro-Nim (from the Latin "High Nim") is 1-3-5-7 Nim with some variant rules designed to make it more interesting. The rules and a formal specification are available [PS][PDF].

Your challenge is to:

1. Prove that Acro-Nim is always terminating. Make the proof as formal as you know how to.
2. Estimate the state space size of Acro-Nim as best you can. Is your estimate an over-estimate or under-estimate?
3. Implement a complete minimax search with alpha-beta pruning and a transposition table, and try to solve Acro-Nim.
4. If you are unsuccessful in solving the game due to time and/or memory constraints, build a heuristic function and iterative-deepen toward a solution.

Homework should be submitted by e-mail to <cs510games@cs.pdx.edu>. The words "cs510games hw4" should appear somewhere in the subject line. The homework submission should be a MIME message containing your source code, a writeup in ASCII answering all questions posed by the assignment, and the results of program runs. Please follow all accepted coding and software engineering practices for your programming language. Remember, if I can't understand your submission, I can't give you credit for it.

I'd like you to do this assignment by yourself. If you do work with anyone else, you must credit them in your submission.