Timeline for Motivation and Intuition for Sprague-Grundy Theorem
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 27, 2013 at 1:31 | answer | added | ericf | timeline score: 2 | |
| Apr 1, 2013 at 2:32 | answer | added | Mark Wildon | timeline score: 1 | |
| Mar 31, 2013 at 23:25 | answer | added | Douglas Zare | timeline score: 5 | |
| Mar 31, 2013 at 20:17 | comment | added | simpleton | Yes, that is part of what I am asking. The full question is: 1. Why is the Grundy Number (lowest non-negative number not in any direct-child game state) defined as such? How did the inventors come up with this idea? 2. Why does XOR works when we compose games? Is there a way for us to deduce this operation? I'm basically wondering how Sprague and Grundy came up with their ideas. I want to know some intuitive or deductive approach that allows us to derive the theorem. Otherwise it seems as if the theorem just dropped from the sky and all they did was to prove its correctness. | |
| Mar 31, 2013 at 9:13 | comment | added | Douglas Zare | If you understand Nim, then the Sprague-Grundy theorem mainly says every impartial game is equivalent to a Nim game. So, are you asking why the $\text{XOR}$ operation works in Nim? | |
| Mar 31, 2013 at 8:32 | history | asked | simpleton | CC BY-SA 3.0 |