Pai Sho

"I will decide when Aang trains and when he gets his butt kicked at Pai Sho"- Monk Gyatso

Pai Sho (Possibly Spelled Pie-shou, Pi Sho, or Pi Shou) a game probably simular to Xiangqi (Chinese Chess) or Mah jong. So far there is only one major mention of this game and that is in the episode The Waterbending Scroll where Iroh turned Zuko's ship around just to retrieve his lotus tile. It is a large two-player strategy game that uses tiles as pieces. Each player is given a certain amount of tiles. The large board is split into 8 sections, with white and orange squares in the center. Round tiles are used as pieces, and each of them has a different picture on them representing different values and each tile has a different meaning and strategic use. Monk Gyatso and Aang have also played this game, so it isn't exclusive to the Fire Nation.

content credit: distant horizon

in the "movie" (double-length episode) [Aang's fury], Uncle Iroh plays a game as a way of identifying himself as part of a exclusive society or club.

The key to recognition between members seems to be a scripted dialogue revolving around the opening move of a game, followed by the rapid placement of pieces in an exact patern that mirrors the central piece, always a White Lotus. It is possible that this dialogue has several outcomes to allow not only identification as a member of the group but as a certain rank within the group.

Content credit: Wikipedia.com

Pai Sho seems to be possibly be inspired by japaneese flower aranging, Speficily the Sogetsu school which deals with angle and lines, which could be a play mechanic.