Calculating Shanten in Mahjong April 1, 2014
Move aside, poker! While the probabilities of various poker hands are well understood and tabulated, the Chinese game of chance Mahjong [1] enjoys a far more intricate structure of expected values and probabilities. [2] This is largely due in part to the much larger variety of tiles available (136 tiles, as opposed to the standard playing card deck size of 52), as well as the turn-by-turn game play, which means there is quite a lot of strategy involved with what is ostensibly a game of chance. In fact, the subject is so intricate, I’ve decided to write my PhD thesis on it. This blog post is a condensed version of one chapter of my thesis, considering the calculation of shanten, which we will define below. I’ll be using Japanese terms, since my favorite variant of mahjong is Riichi Mahjong; you can consult the Wikipedia article on the subject if you need to translate.