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I have a memory that must be from before the year 2000, so I'm very unsure of the details, of reading what I think was a mythology book from a country with less famous mythology, maybe from the Middle East or South Asia. There was a story in the book that ended with two deities playing a game for the rest of time. I think it was a board game in which one controlled white pieces, and wherever the white pieces go on the board mapping, a star appears in the sky.

I think it might make sense if they were playing othello, if not for historical inaccuracy (this also slightly makes me doubt it wasn't just modern fiction). I got the impression they were playing checkers, but I may have just seen it that way because I was a child and didn't know what they were really playing and never played othello. I thought the opponent in the game had black pieces, but it's possible they had white pieces too or just had to remove the white pieces from the board.

There were illustrations in the book, which I don't vividly remember, and I think the one for that story depicted the dieties in a style that looked like ancient egyptian, as two thin men in the starry sky sitting at the board. I think there was another illustration for another story, depicting a flower like a lotus in the ocean (this is not rare imagery so I have doubts about remembering this right) for the first story in the book which was a creation myth in which the world was covered in ocean, and a flower appeared, and a woman came out of it, or there was no flower.

What is this story? Where is it from?

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I think it might be Game of the Gods, from Norse mythology. It is described in The Poetic Edda, in stanza 8:

  1. In their dwellings at peace | they played at tables,
    Of gold no lack | did the gods then know,--
    Till thither came | up giant-maids three,
    Huge of might, | out of Jotunheim.

From a note below (emphasis mine):

Tables: the exact nature of this game, and whether it more closely resembled chess or checkers, has been made the subject of a 400-page treatise, Willard Fiske's "Chess in Iceland." Giant-maids: perhaps the three great Norns, corresponding to the three fates; cf. stanza 20, and note. Possibly, however, something has been lost after this stanza, and the missing passage, replaced by the catalogue of the dwarfs (stanzas 9-16), may have explained the "giant-maids" otherwise than as Norns. In Vafthruthnismol, 49, the Norms (this time "three throngs" in stead of simply "three") are spoken of as giant-maidens; [fp. 6] Fafnismol, 13, indicates the existence of many lesser Norns, belonging to various races. Jotunheim: the world of the giants.]

Wikipedias claims that it is a variant of Tafl, which has black and white pieces, like you said.

Stanza 57 describes the Earth going into the sea - similar to what you mentioned:

  1. The sun turns black, | earth sinks in the sea,
    The hot stars down | from heaven are whirled;
    Fierce grows the steam | and the life-feeding flame,
    Till fire leaps high | about heaven itself.

I can find no mention of a flower, in either the Poetic Edda or The Prose Edda. Stars are also not mentioned, unfortunately.

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Little disclaimer: I haven't been able to find the myth/legend in question but hopefully my answer will help narrowing it down.

The game you're describing in your question looks a lot like the game of go (also known as weiqi in China, baduk in Korea and igo in Japan; because it arrived only in Europe/USA during the 20th century, early translations in english would call it chess or checkers). It is a very old game: although the first occurrence of this game in chinese literature date from the 4th century BC, legends date its origins in the 2nd millenium BC. Consequently, due to its age, it is a game that one encounter frequently in eastern Asia legends.

Links between the game and astrology/astronomy are legions, due to the inherent look of a game in progress. In fact, in modern japanese, the central point of the board is referred to as the tengen (litt. origin of Heaven) and the other marked intersections as hoshi (litt. stars).

Chinese historian Ban Gu (32-92 AD) in Yi Zhi (Essence of Go) wrote about the game:

The board must be square, for it represents the Earth laws. The lines must be straight for they embody the spirit of pure virtue. The pieces are white and black, and so are divided into the Yin and the Yang. Paired and set out in order, they represent the patterns of the Heavens.

Additionally, gods are often pictured playing the game, in Chinese and Japanese tradition: see piece of arts like this sculpture of Hotei, god of Wealth, playing against Jurojin, god of longevity or the Yuan Dynasty painting representing the Three Stars Playing Weiqi, just to give a couple of examples.

And to finish, on the idea of an ever lasting game, there is this famous (among go player) legend that approaches this idea: the Ranka story. Here is an account of it from Asian popular culture: new, hybrid, and alternate media:

... such as the famous Axe Story which told of a lumberjack who, wandering the woods of Shi Bao mountain in Zhejiang Province, saw two immortals playing Weiqi. He stopped to watch them play, and they shared their nectar of the gods with him. After some time had passed, one of the immortals looked up and exclaimed, "What? You are still here? Shouldn't you be going home now?" and pointed to the lumberjack'axe, the wooden handle of which had rotten away with age. When the lumberjack returned home, he discovered that so much time had gone by in his absence, that everyone he knew had long since perished.

It is therefore possible that the story you read was a mishmash of legends about the game of go.

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