# Talk:Go and mathematics

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## Number of legal positions on 1x1

The Tromp number is right, number of legal positions on 1x1 is 1 (empty board). Legal positions are those with no stones without liberties, and therefore both other 1x1 cases (single black/white stone) are illegal. For the 2x2 case, see page 3 of Tromp/Farneback, the position with 4 white stones is crossed, meaning it is illegal.

Also on the reference [1] for the 1x1 case, I could not find anything on legal 1x1 positions, only on the longest possible game (4 moves, allowing suicide and no positional superko). This includes a 1x1 diagram featuring a white stone, but that is used to illustrate the suicide move, not a legal position.

I take it that you are referring to the fact that the only legal board position for a 1x1 board is the blank board, because the position illustrated has no liberties? If so I will remove the 1x1 board as not playable. Myself I prefer the play of one stone as shown in the reference. 199.125.109.106 22:13, 29 May 2007 (UTC)

## Longest Game?

With a triple Ko or Eternal Life configuration the game is infinitely long... Isn't that a critical oversight?Doomed Rasher 15:09, 2 July 2007 (UTC)

Calculations such as these are generally based on the use of a Superko rule. HermanHiddema 08:00, 3 July 2007 (UTC)
10^48 is as close to infinity as I care to see anyway, and much more interesting than the trivial observation of triple Ko, however if you want to add the observation, feel free to do so. Putting 20 stones on the board and making a triple Ko out of it and playing the triple Ko for the rest of your life is not very interesting. 199.125.109.106 02:04, 2 September 2007 (UTC)

## Percentage of legal moves

In the tabel a percentage of 1.1196% is given for a 19x19 board, whereas just above in the text the figure of 1.196% is given. Which of these is the correct one? —Preceding unsigned comment added by 78.51.216.132 (talk) 18:28, 16 March 2008 (UTC)

I have looked it up in the original paper by Tromp and Farnebäck, and 1.196% is the correct number. I have edited the page to correct the error, thanks for pointing it out! HermanHiddema (talk) 20:13, 16 March 2008 (UTC)

## Rename to "Go and mathematics"?

I'm proposing to rename this article to "Go and mathematics" or "Mathematics and go". That would allow inclusion of more mathematics related material, such as the invention of surreal numbers by Conway due to his research into the game of go. Inclusion of such material would enable us to flesh out the article and maybe push for GA or FA in the future. The current scope is rather limited, and all of the tables make that the article is lacking in prose and as such would probably not pass GA or FA. HermanHiddema (talk) 14:43, 14 April 2008 (UTC)

## 2x2, limit of games

386,356,909,593

or just 40? that is: 8(for basic symmetry and rotation) * 5(the total of games I see)

PS with 1x1 one black is the starting position. Therefore I think that "1 empty" is not allowed at all. Shouldn't we count no-liberties as legal at the end of game? Ninjatheclown (talk) 21:13, 19 June 2010 (UTC)

## Computer limitations

Could we either get a source for that part about no computer projected to pass a yottaflop, or take it down? I think that is at best uncontemplatable, and I in my humble and grossly unimformed opinoin would have to disagree without seeing their source. — Preceding unsigned comment added by 76.26.104.63 (talk) 02:49, 24 August 2011 (UTC)

## Program strength updated

There are currently programs that play at 4-5 dan strength, notably Zen. There are a couple others which are about this level. AIUI, these use Monte Carlo methods to play out vast trees unto some point where they can evaluate a position. Can we update the article? -Stevertigo (t | c) 07:36, 6 May 2012 (UTC)

## Deleted Pointless Go vs Chess Section

Which was based on two sources, a newspaper article by a journalist and the American Go Association website. That is not knowledge. — Preceding unsigned comment added by 68.99.162.190 (talk) 15:57, 16 April 2013 (UTC)

## Date of Invention

This article claims that “Chinese scholars of the 11th century already published work...” However, Go (game) only claims that “Go … originated in China more than 2,500 years ago.” So, when was Go invented? --76.24.2.149 (talk) 22:30, 15 December 2013 (UTC)

Tradition gives the date ~ 2500 BCE during the reign of Emperor Yao. The Chinese version of Pascal Triangle is using a Wei Qi Board, recorded at the latest ~1000 ACE. [Karolus]

## Number of atoms in the universe

The phrase: "Keep in mind that the universe just has 1082 atoms in it at most." is lacking any reference. Where did you get this number? --psi36 (talk) 09:40, 1 October 2014 (UTC)

## Rubbish

This article appears to be rubbish. I have several problems with it. First, it should be obvious that discussing a 1x1 square "game" is meaningless. I understand that beginners use small (9x9?) boards. This article should limit its discussion to REAL situations and not interpolate between them. Second, estimates of the "number of possible moves" is different from estimating the "number of possible positions". It makes zero sense to include estimates that ignore (ie include in its count) illegal moves. Third, the number of possible moves on a 19x19 board has NEVER been calculated, despite the claims here that it has. The calculations are estimates based on various unproven assumptions (at best) or on monte-carlo methods (which have hidden assumptions about (lack of) structure of the game/position space). Fourth, a Go board has both rotational and mirror symmetries; any "calculation" of the number of moves should take this fact into account. (ie. On a 19x19 board there are 361 square, but placing a stone on one corner is equivalent to placing it on any of the other 3, this reduces the number of unique positions for the first stone to 55). Fifth, the paper cited as computing the number of moves for a 19x19 game does not. Sixth, it is wild conjecture to say how many seconds we have remaining till "the end of time" (to paraphrase), just as it is to imply that quantum computers or advances in mathematical knowledge won't allow us to "compute" all of the moves of a 19x19 game. Seventh, there is one goal during a Go game: determine the optimal next move. This does not (as far as we know) REQUIRE that all 361! positions be included. That is, running through all possible games is not the same thing as determining the optimal next move, nor can we show that the former is necessary for the latter.Abitslow (talk) 19:13, 8 March 2016 (UTC)

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