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Tile efficiency: Difference between revisions
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→Five-block theory
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"Five-block theory" states that a standard winning hand has five "blocks" - four groups + one pair. Each joint and sequence in the hand is considered a block. Since pairs can turned into triplets, each pair is also a block. When a hand has 6 blocks, one of them will eventually need to be discarded. Thus, it is good to build hands with 5 blocks in mind (i.e., having 6+ blocks is redundant). | "Five-block theory" states that a standard winning hand has five "blocks" - four groups + one pair. Each joint and sequence in the hand is considered a block. Since pairs can turned into triplets, each pair is also a block. When a hand has 6 blocks, one of them will eventually need to be discarded. Thus, it is good to build hands with 5 blocks in mind (i.e., having 6+ blocks is redundant). | ||
Example | Example hand split into blocks: | ||
* {{#mjt:12367m23p334s334z}} can be split into: | * {{#mjt:12367m23p334s334z}} can be split into: | ||
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* {{#mjt:4z}} is an isolated tile which does not add anything to the hand. | * {{#mjt:4z}} is an isolated tile which does not add anything to the hand. | ||
To see why 5 blocks is important, look at example 2-shanten hands: | To see why 5 blocks is important, look at these example 2-shanten hands: | ||
{| class="wikitable" | {| class="wikitable" | ||
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!align=center|Hand with 5 blocks | !align=center|Hand with 5 blocks | ||
| align=center| {{#mjt:12367m23p334s334z}} | | align=center| {{#mjt:12367m23p334s334z}} | ||
| {{#mjt:58m14p235s3z}} ( | | {{#mjt:58m14p235s3z}} (24 tiles total, not counting the tiles in the hand) | ||
|- | |- | ||
!align=center|Hand with 6 blocks | !align=center|Hand with 6 blocks | ||
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|} | |} | ||
The hand with 6 blocks has a better tile acceptance right now, since it can accept 28 tiles total. (Note: the 5 block hand can accept the same # of ''types'' of tile, but since some of the tiles are used in the hand, the acceptance is lower. In this case, 2/4 of the 3-sou tiles are used in the hand, so they can't be drawn | The hand with 6 blocks has a better tile acceptance right now, since it can accept 28 tiles total. (Note: the 5 block hand can accept the same # of ''types'' of tile, but since some of the tiles are used in the hand, the acceptance is lower. In this case, 2/4 of the 3-sou tiles are used in the hand, so they can't be drawn, so accepting 3-sou equates to only +2 tiles of acceptance.) | ||
However, once a useful tile is drawn, the hand with 6 blocks has to discard one of the blocks, lowering the efficiency in the future. | However, once a useful tile is drawn, the hand with 6 blocks has to discard one of the blocks, lowering the efficiency in the future. | ||
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|} | |} | ||
As the hand reduces in shanten, its tile acceptance is also reduced. So going from 1-shanten to tenpai is the slowest part of hand development. Therefore, it's better to improve tile efficiency at 1-shanten than 2-shanten - the returns are bigger. In this example, the 5-block hand is 15% worse (24/28 tiles) at 2-shanten, but 25% better (20/16 tiles) at 1-shanten. | |||
For this reason, aiming for 5 blocks is generally better for tile efficiency. | For this reason, aiming for 5 blocks is generally better for tile efficiency. | ||
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*When discarding the 6th block, discard the weakest block you have (the one that improves tile acceptance the least). For example, if deciding between a penchan and ryanmen, discard the penchan. If you have two blocks of 23-man + 56-man, they have "duplicate acceptance" on the 4-man, so discarding one of those only leads to a loss of 4 tiles of acceptance. | *When discarding the 6th block, discard the weakest block you have (the one that improves tile acceptance the least). For example, if deciding between a penchan and ryanmen, discard the penchan. If you have two blocks of 23-man + 56-man, they have "duplicate acceptance" on the 4-man, so discarding one of those only leads to a loss of 4 tiles of acceptance. | ||
*You may want to keep 6 blocks when aiming for a yaku, such as [[pinfu]] or [[sanshoku]]. | *You may want to keep 6 blocks when aiming for a yaku, such as [[pinfu]] or [[sanshoku]]. | ||
*Sometimes, there may be multiple different ways to interpret a | *Sometimes, there may be multiple different ways to interpret a hand's blocks (e.g. 5568 can be seen as 556 + isolated 8, or 55 + 68). | ||
==Yaku== | ==Yaku== | ||