Talk:Hackenbush

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"Also known as Nim"?[edit]

From the current article:

In the original folklore version of Hackenbush, also known as Nim, any player is allowed to cut any edge...

I'm changing that sentence so as not to seem to claim that single-color Hackenbush is reduceable to (the modern game of) Nim. I see how any Nim position can be represented by a Hackenbush position (just turn each pile of pebbles into a "chain" of green segments one of whose ends is grounded), but I don't see how an arbitrary green-only Hackenbush position can be turned into a Nim position. To take a concrete example, I think the three-segment position consisting of a "torso" and two "legs" is not representable as a Nim position. So Nim is a special case of R-G-B Hackenbush, but G-only Hackenbush is not a special case of Nim.

I assume that the original sentence meant that G-only Hackenbush was also known as "Nim", before that name came to be applied specifically to the pebble game in its modern incarnation. --Quuxplusone (talk) 01:35, 21 December 2008 (UTC)[reply]

Looks like it was originally Lizzie Borden's Nim, which I suppose was a somewhat sick joke, but an IP-only user cut out what he thought were unsourced statements. If these names do have sources, maybe we should add them back. (I don't know math geek culture well enough myself.) BlueGuy213 (talk) 04:32, 24 December 2008 (UTC)[reply]

Impartial/partisan game distinction[edit]

Is there any real distinction (from the point of view of the combinatorial game theory) between the single-color ("green"), red-blue, and red-blue-green hackenbush? The article says that RB/RGB is not impartial, because given a game position, the available moves depend on whose turn it is. But I say that the game can be easily transformed into an impartial one by adding a binary flag indicating whose turn it is: if the flag is blue, then valid moves consist of removing a blue (or green) line and simultaneously flipping the flag to red, and vice versa. (It seems to me that the Sprague–Grundy theorem applies equally to all variants of the game - or am I missing something?)

Yes, I am aware that such analysis constitutes original research unless I can find a reference - but I can't be the first one to analyze the game in this way, can I? - Mike Rosoft (talk) 20:40, 18 January 2014 (UTC)[reply]

Probably, the answer is that the analysis is correct, but not very useful; in a partisan game we want to be able to distinguish between the four possibilities: the game is won by the player A, regardless of who moves first; the game is won by player B; the game is won by whoever plays first, regardless of if it's player A or B; the game is won by whoever plays second. This distinction is lost if I were to transform the game into an impartial one. - Mike Rosoft (talk) 21:00, 18 January 2014 (UTC)[reply]

Also, a game can often split into non-interacting components, and from that point we can evaluate the position as a function of the component positions, which are interpreted as separate games. This fails in your model, because it's no longer true that the two colors alternate within each component -- it's possible that Blue plays in some component, and then Red plays elsewhere, and then Blue plays again in that component. Joule36e5 (talk) 05:55, 8 March 2014 (UTC)[reply]

Please explain[edit]

Two mysterious terms appear in the article: a 'nim sum' and a 'colon principle'.

The nim sum seems related to a game of Nim, but it's not immediately obvious what exactly it is, and one needs to crawl through two articles (on Nimbers and on Nim itself) to find out, and even there it's just mentioned instead of being stated directly.
The colon principle is defined quite clearly (once you understand what a nim sum is!), but its name remains obscure. Could anyone explain its meaning, origin, connotations...?

Best regards, CiaPan (talk) 09:43, 14 January 2021 (UTC)[reply]

Figure 5.4?[edit]

There's mention of a figure 5.4 in this article; I cannot find it. Is the figure in this article at all? Besenj (talk) 09:21, 8 July 2022 (UTC)[reply]

Gameplay section does not make sense to me![edit]

It says: "On their turn, a player "cuts" (erases) any line segment of their choice. Every line segment no longer connected to the ground by any path "falls" (i.e., gets erased). According to the normal play convention of combinatorial game theory, the first player who is unable to move loses."

Now look at the picture of a starting setup. Apparently I could just choose to cut the lowest vertical line; this would remove the entire tree and leave nothing for the other player to do; so I have won in one move. Is that right? Equinox ◑ 18:49, 2 June 2023 (UTC)[reply]