Pong Hau K'i

Pong Hau K'i is a Chinese traditional board game for two players. In Korea, it is known as Ou-moul-ko-no or Umul Gonu or as Gang Gonu. "Umul" translates as "a spring", and the appearance of the board is like that of a spring in the center, with water running out in all directions. "Gang" translates as "river", and has a similar interpretation. Equivalent games are also played in Thailand and in northern India.
The board consists of 5 vertices and 7 edges. Each player has two pieces. Players take turns to move. At each turn, the player moves one of their two pieces into the adjacent vacant vertex. If a player can't move, they lose.
Only one type of position can make a player lose. If both players play perfectly, the game continues endlessly with no winner.
It is a children's game in both China and Korea, and is often used for childhood education.

Analysis

This game has been analyzed by P. Straffin, who showed that it is a draw so long as both players can see 2-ply ahead, i.e. see the results of their move and of what their opponent would do in response.
Thus with "2-ply lookahead", player Red can see the result of a potential bad move of the bottom piece, realize that Blue then has a winning move, and hence choose to not make that move.