  Mahjong is a very popular tile-based game commonly played by four players.
Each player begins with a hand of 13 tiles and, in turn, players draw and
discard (i.e., change) tiles until they complete a legal hand using a 14th
tile. In this paper, we initiate a mathematical and AI study of the Mahjong
game and try to answer two fundamental questions: how bad is a hand of 14
tiles? and which tile should I discard? We define and characterise the notion
of deficiency and present an optimal policy to discard a tile in order to
increase the chance of completing a legal hand within $k$ tile changes for each
$k\geq 1$.
