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Tile Theory at Two-Shanten (2)

Next comes the pattern with one completed set and four taatsu blocks.

When there are no obvious floating tiles, the choice is basically between two plans:

(1) Drop the weakest taatsu.
(2) Break a three-tile taatsu block back into a single taatsu and keep all four taatsu blocks.

Recent research tends to favor line (1), so this site also treats (1) as the default approach.

Now let us look at actual hands.

Example 1
五万牌图六万牌图七万牌图七万牌图一索牌图二索牌图四索牌图五索牌图二筒牌图三筒牌图三筒牌图八筒牌图八筒牌图 Tsumo 八万牌图

=> Cut 二索牌图

The souzu taatsu is a nido-uke shape against 三索牌图, so this block should obviously be the one you remove.

Cutting 三筒牌图 is a bad move because it reduces the acceptance toward one-shanten.

Example 2
三万牌图四万牌图五万牌图八万牌图八万牌图四索牌图四索牌图七索牌图八索牌图二筒牌图三筒牌图七筒牌图九筒牌图 Tsumo 三索牌图

=> Cut 七筒牌图

The kanchan wait on 八筒牌图 is 4 tiles, and the shanpon on 八万牌图四索牌图 is also 4 tiles.

If the numbers are equal, would cutting 四索牌图 and making Pinfu more easily be better?

Some older strategy books do indeed give 四索牌图 cut as the answer.

But the real difference appears after the hand reaches one-shanten.

Change A

三万牌图四万牌图五万牌图八万牌图八万牌图三索牌图四索牌图七索牌图八索牌图二筒牌图三筒牌图七筒牌图九筒牌图 Tsumo 四筒牌图

Change B

三万牌图四万牌图五万牌图八万牌图八万牌图三索牌图四索牌图四索牌图七索牌图八索牌图二筒牌图三筒牌图九筒牌图 Tsumo 四筒牌图

It is obvious that the lower one is the better one-shanten shape.

四索牌图 still works as an effective tile even after the hand reaches one-shanten.

By contrast, 七筒牌图九筒牌图 are basically only waiting to be discarded.

Also, once you drop the kanchan, the hand becomes more flexible.
You can keep one safe tile in reserve, and if you later draw 六万牌图 七万牌图 九万牌图 七索牌图 八索牌图 二筒牌图 三筒牌图, the acceptance toward one-shanten widens even more.

Change C

三万牌图四万牌图五万牌图八万牌图八万牌图三索牌图四索牌图四索牌图七索牌图八索牌图二筒牌图三筒牌图九筒牌图 Tsumo 七万牌图

Example 3
二万牌图四万牌图七万牌图八万牌图三筒牌图三筒牌图五筒牌图八筒牌图八筒牌图三索牌图四索牌图五索牌图七索牌图 Tsumo 二索牌图

=> Cut 二万牌图

If you think in terms of “drop the weakest taatsu,” the pinzu block is clearly worth keeping, because together with the shanpon it has 8 tiles of acceptance.

So the comparison is between the manzu and souzu kanchan blocks.
The souzu side changes into a ryanmen more easily.

On the manzu side, even drawing 五万牌图 only creates another nido-uke shape, so the correct play is to drop the manzu block by cutting 二万牌图.

Example 4
三万牌图四万牌图二筒牌图二筒牌图四筒牌图五筒牌图六筒牌图一索牌图一索牌图五索牌图八索牌图九索牌图九索牌图 Tsumo 六索牌图

=> Cut 一索牌图

If you understand the rule “drop the weakest taatsu,” you should not hesitate here either.

You compare pair blocks in the same way: by the kinds of good-shape improvements they allow.

For example, the pair of 二筒牌图 can become a three-sided wait on a draw of 三筒牌图, and 一筒牌图四筒牌图七筒牌图 are all still effective tiles.

By contrast, the isolated pair 一索牌图一索牌图 has only two direct acceptance tiles, making it the weakest taatsu block.

So the correct answer is to cut 一索牌图.

And even if you later draw 七索牌图, cutting 一索牌图 is still the best line.

Still, there are cases in real play where comparing taatsu is not easy.

Example 5
二万牌图三万牌图七万牌图九万牌图二索牌图二索牌图三索牌图九索牌图九索牌图三筒牌图四筒牌图七筒牌图九筒牌图 Tsumo 二筒牌图

The comparison between the manzu and pinzu kanchan blocks is difficult here.
Either cut can be justified.

So in this case, cutting 二索牌图 and postponing the decision is also a strong option.

In fact, simulation shows that directly dropping a kanchan is slightly better for raw tenpai speed.

However, if later on either 八万牌图 or 八筒牌图 becomes thin, you can still adjust according to the live situation.

Also, if the hand later ends up waiting on 一索牌图四索牌图, the early discard of 二索牌图 also makes 一索牌图 slightly easier to ron.

So cutting 二索牌图 here is not bad at all.

Theory

For a two-shanten hand with one completed set, one completed head, and four taatsu blocks, the basic rule when there are no floating tiles is to drop the weakest taatsu. However, if the taatsu comparison itself is difficult, in other words if there is no clearly weak taatsu, you can also fix a ryanmen and postpone the decision.

Original Japanese page: http://beginners.biz/pairi/pairi11.html

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