Talk:Nim

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Nim is now used as a simple illustration of the Sprague-Grundy theorem.

A version of this game is played in Alain Resnais' movie L'année dernière à Marienbad.

A typical normal game starts with heaps of 3, 4 and 5:

A B C           (Heaps A, B, and C)
3 4 5           I take 2 from A
1 4 5           You take 3 from C
1 4 2           I take 1 from B
1 3 2           You take 1 from B
1 2 2           I take entire C heap
2 2 0           You take 1 from A
1 2 0           I take 1 from B (In the misere game I would take the entire 2 heap)
1 1 0           You take 1 from B
1 0 0           I take the last 1 and win.

Error in heap A. why is there a 2? Should be 1.

quote: " Now here, C was the one we artificially subtracted from, so we have to pick another one. You can think of it as that we pretend you took one from another stack, say A.

1 2 0   011   I take one from B
1 1 0   000   You take one from B
1 0 0   001   I take one from A, and I win.

But you see, since A was our artificial stack, it still looks like 1,0,0, and they have to make the last move "

But, if in the 1 1 0 situation, which is actually a 2 1 0 situation, You can take the two from A, and leaving a -1 1 0 situation, which is a 0 1 0, and I loose.

[edit] Cleanup

I have rewritten the mathematical part of the article, and deleted most of the material on strategy, because it was (IMO, anyway) disorganized, confusing, didn't contain any information (all the painfully constructed "winning patterns" there are simply special cases of the general Bouton's characterization), and sometimes incorrect (why the hell was Ling Kah Jai credited for a well-known 100 years old result?). Nevertheless, in case somebody decides to reintroduced bits of the text, here it is. -- EJ 9 July 2005 17:12 (UTC)

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I've put the text from the old version of the article that was once here on the subpage /Deleted text. 4pq1injbok 19:33, 30 July 2005 (UTC)

I've rewritten much of the explanatory material to be more explanatory and correct, especially the relation to combinatorial game theory. The mathematical part got minor edits, mostly to make the stuff consistent.--Dan Hoey 19:33, 26 October 2005 (UTC)

Dan, while most of your edits here are certainly valuable, please don't attempt to link every word in the article. It clutters the text, distracts the readers, and serves no useful purpose. As a general rule, it usually suffices to link to a particular page only once. Thanks. -- EJ 03:49, 18 December 2005 (UTC)

[edit] Last move game

Does the name last move game for normal Nim actually have any currency? 4pq1injbok 06:30, 24 July 2005 (UTC)

I don't know if last move game or last stone game is really used, so I deleted it. Anyone who wants it back should say something more specific than asserting that it is used in some regions.--Dan Hoey 19:28, 26 October 2005 (UTC)

[edit] Linking blindly to a binary

It is extremely unsafe to link toa binary from an untrusted source the way you are doing it. The program isn't that great, so I don't see why we are linking to it in the first place.