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Shanten: Difference between revisions
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→Counting shanten
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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 | 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 | 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 | **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. | ||
* | *"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 | 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 | ** 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). | ||