A few basic questions about combinatorial game theory

AI Thread Summary
The discussion focuses on understanding combinatorial game theory, specifically regarding impartial games, Nim, and the Sprague-Grundy theorem. Key questions include the rationale behind using binary exclusive OR (XOR) for calculating Nim-sums and the distinction between Nim-sums and the Minimum Excludant (Mex) rule. The user seeks clarification on how Nim-sums indicate winning or losing positions and the role of the Mex rule in this context. Additionally, a new website has been launched for further inquiries and learning about combinatorial game theory. The conversation emphasizes the need for clearer explanations of these concepts.
andrassy
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I am trying to teach myself the basic theory behind combinatorial game theory regarding impartial games, the solution to Nim, and the Sprague-Grundy theorem. I understand most of it, but I have a few questions about parts that are still unclear to me.
1. Why are Nim-sums computed using binary exclusiveor addition? I am having difficulty conceptualizing the theory behind using binary addition to represent nim heaps mathematically.
2. What is the difference/purpose of Nim-sums versus the Mex rule? I know that Nim-sums can be used to determine if any position in a game of Nim is winning or losing, and they they can also be used to determine the correct move. I don't really understand the mex rule and what it's point is. I have seen both of them but if someone could better explain mex and how it is related to Nim-sums and how it is used to solve Nim or impartial games in general, I would really appreciate it!
 
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If no one knows could someone maybe point me somewhere else I can ask?
 
Sorry for bumping this old thread, but I've got a new website that I just launched where you can go and ask me questions and learn about combinatorial game theory.

www.combinatorialgametheory.com

Doesn't have much there now because it's only a day old, but you can drop by and leave comments.
 
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