Tile efficiency: Difference between revisions

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==Important concepts==
==Important concepts==
===Five-block theory===
===Five-block theory===
"Five-block theory" states that a standard winning hand has five "blocks" - four groups + one pair. Each joint in the hand can be turned into 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 (e.g. 6+ blocks is redundant).
"Five-block theory" states that a standard winning hand has five "blocks" - four groups + one pair. Each joint in the hand can be turned into 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 2-shanten hands:
Example 2-shanten hands:
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Going from 1-shanten to tenpai is the slowest part of the hand. 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.
Going from 1-shanten to tenpai is the slowest part of the hand. 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 overall better for tile efficiency.  
For this reason, aiming for 5 blocks is generally better for tile efficiency.  
*That being said, ''having 6 blocks is better than 5 blocks with 2 useless isolated tiles''. A 6th block is redundant, but better than useless. Don't be afraid to have 6 blocks for a bit. When you have excess blocks, you can discard one when:
*That being said, ''having 6 blocks is better than 5 blocks with 2 useless isolated tiles''. In other words, discard floating tiles before joints; a 6th block is redundant, but better than useless. When you have excess blocks, you can discard one when:
**You can upgrade one of your joints (e.g. turning a 45 ryanmen joint into a 445 complex joint).
**You can upgrade one of your joints (e.g. turning a 45 ryanmen joint into a 445 complex joint).
**You enter 1-shanten.
**You enter 1-shanten.
*When discarding the 6th block, discard the weakest (least tile acceptance) block you have. For example, if deciding between a penchan and ryanmen, discard the penchan, unless the ryanmen has less available tiles.
*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, unless the ryanmen has less available tiles. If you have two blocks of 23 + 56, they have "duplicate acceptance" on 4-pin, so discard one of them.
*You may want to keep 6 blocks when aiming for a yaku, such as [[pinfu]] or [[sanshoku]]. E.g. keeping a kanchan so that you have a chance to draw into sanshoku.
*You may want to keep 6 blocks when aiming for a yaku, such as [[pinfu]] or [[sanshoku]].


==Yaku==
==Yaku==
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