Go
A pure game of competing — surrounding territory with black and white stones. I wrote about its origin in the myth badge above, but there is another thing worth noting. The old boards that survive are not the 19-line board used today. The board found at the Yangling tomb of Emperor Jing of Han, and the one from a Han-dynasty tomb at Wangdu, both had 17 lines. Go did not start in its present form — the number of lines grew over time. What is called the beginning usually looks different from what stands today. This is a shape the map keeps running into. After it crossed to Japan, it grew into a culture of hereditary houses and ranked dan grades (see The Archipelago of Play).
The myth, corrected
Go was invented by Emperor Yao for his son, around 2300 BCE.
This stays in the realm of legend. The earliest written mention is in the Zuo Zhuan (a passage dated 548 BCE), and the oldest physical evidence is a board from the Han-era tomb of Emperor Jing — a board with seventeen lines, not nineteen. Attributing an origin to a sage-king is a later habit of lending authority, one more instance of the structure this map keeps meeting: before the first, there is usually someone earlier.