Talk:Infinite chess/Archive 1

Solvability, determinacy of Trappist-1

The article currently contains the following paragraph:

Trappist-1 – This variation uses the huygens, a chess piece which jumps prime numbers of squares, possibly preventing the game from ever being solved. Although it is a game of perfect information, it may be mathematically undetermined (that is, immune to solution by mathematical game theory).

The mathematical claims here are sourced to this chess site, which says

Mathematical note of Interest: It may be mathematically impossible to devise an algorithm to "solve" Trappist-1. The huygens jumps prime numbers of squares, and the complete set of prime numbers is unknown (and no method to compute it), thereby placing Trappist-1 into a category of unsolvable games.

This analysis seems deeply confused and wrong-headed, both in its understanding of the prime numbers and in its understanding of the questions of solvability and determinacy of games. I have tagged the sentences as dubious, but I am also inclined to just remove them entirely as lacking a high-quality source. I welcome other thoughts. --JBL (talk) 22:43, 3 April 2017 (UTC)

Could you take a look at Huygens (chess piece) also please. (I've questioned notability on its Talk.) Thx. --IHTS (talk) 09:40, 4 April 2017 (UTC)

For the first of the two sentences, "possibly preventing the game from ever being solved":

The 8x8 form of Chess may never be solved (various sources can be found at Solving chess). I think with the added complexity of the infinite board (increases game-tree complexity), and the huygens which moves to positions which is not trivial to calculate (various sources at Prime number), it is a safe assumption to say that the game may possibly never be solved. I believe the statement can stand as is.

For the second of the two sentences, "Although it is a game of perfect information, it may be mathematically undetermined":

The subject of categorizing games with draws into determined and non-determined games has not been highly explored as I understand. I think this statement may also be fair. But if there is a way to modify the statement, or elaborte upon it without making it too complicated then that might be Ok to do. But I also welcome other thoughts.—LithiumFlash (talk) 14:36, 4 April 2017 (UTC)

It is difficult to know what to make of this comment: it does not engage substantively with the issue (that the source seems extremely dubious and confused on this point), and the basis you propose for including material (to paraphrase, "I kind of think it's ok") is not consonant with basic Wikipedia principles of sourcing. Wikipedia is not a blog for musing about interesting things -- it's an encyclopedia, reporting and synthesizing what is written in reliable secondary sources. --JBL (talk) 20:33, 4 April 2017 (UTC)

I added another reference to substantiate the statement. (Currently listed as ref #6). Please note that the main conclusion is qualified by a comment "More generally this strategy works for any chess-like game in which the pieces can be classified into "ultra-mobile" and "para-mobile" types with constant and linear freedom respectively." Feel free to comment here again if the statement in the article is still not substantiated by the references.—LithiumFlash (talk) 21:33, 4 April 2017 (UTC)

Since the reference you've added says nothing about the variant in question, no, obviously it is not a satisfactory reference for the claim you've attached it to. --JBL (talk) 22:03, 4 April 2017 (UTC)

I removed the 2nd of the two statements, adding a note that Trappist-1 is excluded from the mathematical conclusions of references (10) and (11).—LithiumFlash (talk) 12:48, 5 April 2017 (UTC)

The first source does not mention this game. I can't check the second source since it's subscription, but thus far the nb appears to be original research. I can confirm that the source mentioned at the beginning is erroneousin at least one statement. –LaundryPizza03 (dc̄) 05:42, 11 June 2018 (UTC)

Comment about Taikyoku shōgi

A "citation needed" tag is on the sentence "The exact rules of the game are unknown and it is unclear if it was every widely played." How does one go about citing this as true? The article currently has a link to Taikyoku shōgi, which in my opinion is sufficient for the reader who would like to know more about the game, or the sources of information about it.—LithiumFlash (talk) 15:36, 4 April 2017 (UTC)

The tag applies to the entire paragraph. The sentence that you mention sounds like another case of WP:OR, so I am going to remove it. If it's something that you composed yourself, versus paraphrased from a source, it shouldn't be there.–CaroleHenson (talk) 16:50, 4 April 2017 (UTC)

The statement that you removed can remain out of the article. It's not essential. For the remainder of the paragraph, according to [1] routine calculations and basic arithmetic do not need citations and is not original research. So the comment "would probably require more than an hour to setup" can be established by 804 pieces x 10 seconds (sort, find, and place in correct postion) = 8040 seconds = 134 minutes = 2:14 (hours, minutes). As for the remainder of the paragraph, I added four more references.—LithiumFlash (talk) 22:30, 4 April 2017 (UTC)

LithiumFlash Thanks for the citations.

I'm a little confused by the calculation - I would agree with the point about routine calculations. What you're mentioning seems to require an assumption about taking 10 seconds to sort, find, and place each piece. Is that in a source? Is there anything in any of the four sources about the time it takes to set up the board or time to position pieces?–CaroleHenson (talk) 22:44, 4 April 2017 (UTC)

Are any of these reliable sources? These seem to be a combination of blog, personal page, forum or book promotion. I didn't see anything about timing.–CaroleHenson (talk) 22:48, 4 April 2017 (UTC)

I removed the content re time required to set up pieces [2]. FYI. --IHTS (talk) 23:25, 4 April 2017 (UTC)

forcing a win in a finite number of moves

The article currently states "mathematical investigations have shown that in a general endgame, one player can force a win in a finite number of moves.", and gives 2 references for that. The "Mate-in-n Problem" reference does nothing like supporting that statement: In fact, the paper expressly mentions at least the possibility "that a player may have a winning strategy from a position, without there being any finite bound on the number of moves required."

The other reference is to a site which, at least as of when I last checked, had split-second chameleon terms: According to them, other than arbitration and class-action waiver, accessing the site at a wrong time can result in one becoming bound by any terms the owners choose.

Accordingly, I am not willing to access the linked page to see if it now supports the statement "mathematical investigations have shown that in a general endgame, one player can force a win in a finite number of moves.". However, that page was quite developed well-before the split-second chameleon terms were adopted, and at least back then, its content gave positions that seemed to be examples of a player having "a winning strategy from a position, without there being any finite bound on the number of moves required.".

It is perhaps also relevant that the user who put in the statement was blocked indefinitely for sockpuppeting: https://en.wikipedia.org/wiki/User:LithiumFlash

If no one replies to this within a month, then I will remove that from the article. JumpDiscont (talk) 03:08, 28 September 2019 (UTC)

@JumpDiscont: The quote from the paper is consistent with the statement it's sourcing. It describes the following situation: you have a certain strategy X that guarantees a win. I, who am guaranteed to lose, have a choice of strategies Y_1, Y_2, Y_3, .... If I choose strategy Y_k, then you (playing strategy X) will win in k moves. In this situation, it is true simultaneously that you are guaranteed to win in a finite number of moves, and that there is no finite bound on the number of moves required. LithiumFlash was an extremely annoying user who frequently made pages worse, but in this case the content is fine. --JBL (talk) 03:23, 28 September 2019 (UTC)

@Joel B. Lewis: ​ ​ ​ ​ ​ ​ ​ Ah, I see that I misunderstood my quote. ​ ​ ​ However, it now seems to not support the article's next sentence. ​ ​ ​ Those sorts of positions ("checkmate in omega moves") are forced wins, but not ​ mate-in-n s . ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ JumpDiscont (talk) 10:57, 28 September 2019 (UTC)

I do not understand what you think is not supported. --JBL (talk) 16:30, 28 September 2019 (UTC)

I do not think "More specifically, it has been found that infinite chess is decidable; that is, ..." is supported.

For at least a substantial part of the cited web-page's existence, that web-page did not support that quote, and due to the split-second chameleon terms, I'm not willing to check whether-or-not that has changed.

The paper cited says "... as a result, it remains open whether the general winning-position problem of infinite chess is decidable.".

JumpDiscont (talk) 22:40, 28 September 2019 (UTC)

@Joel B. Lewis: ​ ​ ​ I'm pinging you again mainly because you haven't responded for 1.5 weeks, and somewhat to let you know about another quote from the Springer paper that addresses the issue more squarely: ​ "Although we have proved that the mate-in-n problem is decidable, we conjecture that the general winning-position problem is undecidable and indeed, not even arithmetic." ​ ​ ​ ​ ​ ​ JumpDiscont (talk) 14:50, 9 October 2019 (UTC)

@JumpDiscont: Thank you for the reminder to take a second look. Yes, I agree with you: the section adheres poorly to the sources. (Also its title is ridiculous, since this has nothing at all to do with game theory.) The citation to MathOverflow is completely redundant with the Brumleve--Hamkins--Schlicht paper, so you don't have to worry about there being information at that link not covered by the paper. I invite you to have a go at correcting the section; or I could (but it may require a couple more pings before I make time for it :) ). --JBL (talk) 21:35, 9 October 2019 (UTC)

@Joel B. Lewis: ​ ​ ​ I have now corrected that section. ​ If I figure out how the reference system works, then I might also add in that decidability of mate-in-n for Trappist-1 would follow (https://arxiv.org/abs/1601.07099) from "Dickson's conjecture", even though I had never heard of Dickson. ​ ​ ​ ​ ​ ​ ​ JumpDiscont (talk) 19:44, 10 October 2019 (UTC)

Thanks, it looks a lot better. I did some mild cleanup. I'd be happy to help you format a reference, but I'm a bit confused about what the source is for your statement. --JBL (talk) 21:32, 11 October 2019 (UTC)

@Joel B. Lewis: ​ ​ ​ Well, I had intended theorem 1.2 of https://arxiv.org/pdf/1601.07099.pdf as the reference, although I now realize that checking expressability of mate-in-n in that language is probably not simple-enough for the conclusion to go into this article. ​ JumpDiscont (talk) 05:14, 15 October 2019 (UTC)

Yeah, I'm afraid that's right -- a nice piece of original research, but original research nonetheless. --JBL (talk) 11:37, 15 October 2019 (UTC)