Shanten: Difference between revisions

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== Counting shanten ==
== Counting shanten ==
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.
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.
Blocks are defined as taatsu, pairs, and tile groups.


=== "Useless" tile 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.  
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.
The actual shanten count tends to be lower if a hand contains 4 or fewer blocks. 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]].
It is important to note that this method of counting useless tiles does not account for [[chiitoitsu]] or [[kokushi musou]].
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=== Basic shanten ===
=== Basic shanten ===
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:
A hand with 13 disconnected tiles, the furthest a hand can be from the "4 groups + 1 pair" shape, would be 8-shanten from that 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.  
*Every hand starts at 8-shanten.
*Each complete group reduces shanten by 2. Each taatsu/pair in hand reduces shanten by 1.  
*"Group shanten" factor: Each complete group reduces shanten by 2. Each taatsu/pair in hand reduces shanten by 1.  
*However, a mahjong hand requires exactly 4 groups. This means the hand's (taatsu + pairs + groups) count is capped at 4. In other words, if a hand would have more than 4 taatsu/pairs/groups, any taatsu/pair past the 4th won't count.  
**However, once a hand has 4 blocks, any blocks past the 4th no longer count towards group shanten. This is because mahjong hands require exactly 4 tile groups.
*In addition to 4 groups, the hand requires at least one pair. So, when (taatsu + pairs + groups) >= 5, having at least one pair will reduce shanten by 1.
*"Pair shanten" factor: When the hand has at least 5 blocks, having at least one pair will reduce shanten by 1.


For example, a hand with 6 taatsu and a lone tile is not (8-6=) 2-shanten; it is instead (8-4=) 4-shanten. A hand with 5 taatsu + 1 pair would be (8-4-1=) 3-shanten.
For example, a hand with 6 taatsu and a lone tile is not (8-6=) 2-shanten; it is instead (8-4=) 4-shanten. A hand with 5 taatsu + 1 pair would be (8-4-1=) 3-shanten.
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=== Basic shanten (simpler calc.) ===
=== Basic shanten (simpler calc.) ===
There is a simpler way of explaining the above basic shanten calculation:
There is a simpler way of figuring out the above basic shanten calculation:


*Every hand starts at 8-shanten.  
*Every hand starts at 8-shanten.  
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*If a hand has >= 6 blocks: +1 shanten  
*If a hand has >= 6 blocks: +1 shanten  
*If a hand does not have a pair: +1 shanten  
*If a hand does not have a pair: +1 shanten  
** If a hand has 4 groups + 0 paira: Set to tenpai
** If a hand has 4 groups + 0 pairs: Set to tenpai


For "blocks" = (taatsu/pairs/groups). This is identical to the above calculation, but assumes all hands have a pair, then adds +1 shanten if it doesn't actually have a pair. This generalization works in most cases; notable exceptions include hands with 3 groups + 1 taatsu + 2 isolated tiles (which is 1-shanten), or 4 groups + 1 lone tile (which is tenpai).
For "blocks" = (taatsu/pairs/groups). This is identical to the above calculation, but assumes all hands have a pair, then adds +1 shanten if it doesn't actually have a pair. This generalization works in most cases; notable exceptions include hands with 3 groups + 1 taatsu + 2 isolated tiles (which is 1-shanten), or 4 groups + 1 lone tile (which is tenpai).
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