Shanten: Difference between revisions

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 Multiple methods can be used to count a hand's shanten. These can be used to get a quick estimate of shanten during a game.
-=== Lower bound estimate ===
+=== "Useless" tile estimate ===
-For the standard "4 groups + 1 pair" shape, every "useless" tile (any lone honor tile; number tiles with no neighbors in a +/- 2 interval) must be discarded or grouped in order to reach tenpai. Therefore, the # of useless tiles is a good minimum for the "4 groups + 1 pair" shape. The actual shanten may be higher, but usually isn't lower for the standard winning shape.
+For the standard "4 groups + 1 pair" shape, every "useless" tile (any lone honor tile; number tiles with no neighbors in a +/- 2 interval) must be discarded or grouped in order to reach tenpai. Therefore, the # of useless tiles is a good minimum for the "4 groups + 1 pair" shape.
+The actual shanten count tends to be lower if a hand contains 4 or fewer blocks (defining "blocks" as groups/taatsu/pairs). It tends to be higher if it has 6 blocks, or if it lacks a pair.
 It is important to note that this method of counting useless tiles does not account for [[chiitoitsu]] or [[kokushi musou]].
-  ''minimumShanten'' = ''Useless_tiles''
+  ''EstimatedShanten'' = ''Useless_tiles''
 This method is most effective at the start of a game, and less towards the end.
 === Basic shanten ===
-A hand with 13 disconnected tiles would be 8-shanten from the "4 groups + 1 pair" shape; such a hand would be the highest shanten from said shape. Drawing a tile, forming a [[taatsu]] or [[pair]], brings it a tile closer to tenpai, thus reducing shanten by 1. Completing a taatsu/pair, thus forming a tile group, will reduce shanten by 1 again (2 total). This results in the following calculation:
+A hand with 13 disconnected tiles, the furthest a hand can be from the "4 groups + 1 pair" shape, would be 8-shanten from said shape. Drawing any tile, forming a [[taatsu]] or [[pair]], brings it a tile closer to tenpai, thus reducing shanten by 1. Completing a taatsu/pair, thus forming a tile group, will reduce shanten by 1 again (2 total). This results in the following calculation:
 *Every hand starts at 8-shanten.