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=== Lower bound estimate ===
=== Lower bound 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 will be the lower bound for the "4 group + 1 pair" shape. The shanten could be higher, but cannot be 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 will be the minimum #-shanten for the "4 group + 1 pair" shape. The shanten could be higher, but cannot be lower for the standard winning shape.


It is important to note that counting useless tiles does not account for [[chiitoitsu]] or [[kokushi musou]].
It is important to note that this method of counting useless tiles does not account for [[chiitoitsu]] or [[kokushi musou]].


  ''minimumShanten'' = ''Useless_tiles''
  ''minimumShanten'' = ''Useless_tiles''
1,759

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