Do we know that? I'm not a huge history researcher, but while I do know that the history of Go is very long... Do we actually know that we play it now like it was in its original incarnation? Or that we know the historic rules? Maybe simply "the oldest known board game" because I doubt that even with a 4000 year history it is older than hide and seek!

Another very old board game is Go. This has been played in China for over 2,500 years and bears mentioning because there has been little change in the game since the Tang Dynasty in the sixth to ninth centuries. As far as unchanged games go, it may be the oldest in the world.

The earliest written reference to the game is generally recognized as the historical annal Zuo Zhuan[50] (c. 4th century BC),[51] referring to a historical event of 548 BC.

Legends trace the origin of the game to Chinese emperor Yao (2337–2258 BC), said to have had his counselor Shun design it for his unruly son, Danzhu...

Go originated in ancient China. Archaeological evidence shows that the early game was played on a board with a 17×17 grid, but by the time the game had spread to Korea and Japan, in about the 5th and 7th centuries CE respectively, boards with a 19×19 grid had become standard.[7]

The Western world's version of chess has only really been in existence for a few hundred years, but its predecessors appeared as early as the sixth century in India.
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Similarly, backgammon is documented in the sixth or seventh century. However, its predecessors run much farther back than chess, with the earliest similar board being one found in Burnt City, Iran and dated around 3000 BC. That puts it right up there as Senet's little brother, assuming the historians are correct.

The Royal Game of Ur, also known as the Game of Twenty Squares, refers to two game boards found in the Royal Tombs of Ur in Iraq by Sir Leonard Woolley in the 1920s. The two boards date from the First Dynasty of Ur, before 2600 BC, thus making the Royal Game of Ur one of the older examples of board gaming equipment found, although Senet boards found in Egyptian graves predate it as much as 900 years.

The earliest Weiqi game record came from Wu and was known as the Wu Diagram, as mentioned in Du Mu's poem (Tang Dynasty). This game played between Sun Ce and Lu Fan, was recorded in Wang You Qing Yue Ji of the Song Dynasty. Because the board size is 19x19, a lot of people doubt its authenticity. Regardless whether it was played between Sun Ce and Lu Fan, it is the oldest Weiqi record in the world.

the earliest surviving game record appears to be the game, in "Wang You Qing Le Ji", between the Wu prince Sun Ce (175-200) and his general Lü Fan. It is on a 19x19 board (see Figure 2 [available from ftp://ftp-igs.joyjoy.net/Go/games/ancient.sgf.Z in Smart-Go format]). Until the discovery of the Wangdu board and Tibetan go, it was long assumed by modern players that the Sun-Lü game was a forgery (or Handan Chun was wrong). However, the whole question of its authenticity has been reconsidered recently in Li 1980b. He establishes that the conditions for it to have been true did probably exist, that is 19x19 boards were being used. He suggests too that this board, whether new or evolved, contributed to the upsurge in popularity of go.