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Shanten: Difference between revisions
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→Counting shanten: add a more intuitive way of calculating basic shanten
m (→Lower bound estimate: 13 disconnected is only 8-shanten, despite having 13 tiles, so "# useless tiles" doesn't *always* work) |
m (→Counting shanten: add a more intuitive way of calculating basic 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 | 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 === | === 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 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 "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. | ||
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 would be 8-shanten from the "4 groups + 1 pair" shape, and is the highest shanten from that shape. Drawing a [[taatsu]] or [[pair]] will get you 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 would be 8-shanten from the "4 groups + 1 pair" shape, and is the highest shanten from that shape. Drawing a tile, forming a [[taatsu]] or [[pair]], will get you 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. | *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, 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. | ||
*In addition to 4 groups, the hand requires at least one pair. So, when (taatsu + pairs + 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. | ||
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 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 3-shanten. | ||
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- max(''taatsu'' + ''pairs'', 4 - ''groups'') | - max(''taatsu'' + ''pairs'', 4 - ''groups'') | ||
- 1, if at least one pair and (''taatsu'' + ''pairs'' + ''groups'') >= 5 | - 1, if at least one pair and (''taatsu'' + ''pairs'' + ''groups'') >= 5 | ||
=== Basic shanten (simpler calc.) === | |||
There is a simpler way of explaining the above basic shanten calculation: | |||
*Every hand starts at 8-shanten. | |||
*Each complete group reduces shanten by 2. Each taatsu/pair in hand reduces shanten by 1. | |||
*If a hand has >= 6 blocks: +1 shanten | |||
*If a hand does not have a pair: +1 shanten | |||
** 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 all cases except when a hand waits on a pair, which is why the "4 groups + 0 pair = tenpai" exception is in place. | |||
=== Chiitoitsu === | === Chiitoitsu === | ||