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Tile Theory at One-Shanten (2)

First, let us look at hands with too many blocks.

If you have fully absorbed everything up to this point, you should be able to derive the correct discard in every case on this page.

Example 1
一万牌图三万牌图五万牌图六万牌图七万牌图二筒牌图三筒牌图三筒牌图四筒牌图四索牌图五索牌图九索牌图九索牌图 Tsumo 五筒牌图

=> Discard 一万牌图

It is basic knowledge that a ryanmen wait is better than a kanchan wait.

Since drawing 四万牌图 also creates a sanmenchan improvement, the basic discard order is 一万牌图 first, then 三万牌图.

Example 2
五万牌图五万牌图五万牌图二筒牌图二筒牌图六筒牌图八筒牌图二索牌图四索牌图四索牌图五索牌图八索牌图八索牌图 Tsumo 二筒牌图

=> Discard 二索牌图

This is a comparison between two kanchan shapes.

The double acceptance on 三索牌图 is awkward, so cutting 二索牌图 is correct.

Example 3
一万牌图一万牌图二筒牌图二筒牌图三筒牌图三筒牌图六筒牌图七筒牌图八筒牌图三索牌图四索牌图七索牌图八索牌图 Tsumo 九索牌图

=> Discard 三筒牌图

Chasing Iipeikou reduces the number of accepting tiles, and it is still inferior even after factoring in the extra value.

The correct answer is still to dislike the double acceptance on 一筒牌图四筒牌图.

Example 4
一万牌图三万牌图五万牌图六万牌图五筒牌图七筒牌图二索牌图二索牌图二索牌图三索牌图七索牌图八索牌图九索牌图 Tsumo 一索牌图

=> Discard 一万牌图

Both choices have the same acceptance count, 12 tiles, and both leave a kanchan wait. So the difference is not there.

Then what about the number of improvements into a better shape?

The manzu side only has one good-shape improvement: drawing 五万牌图 to make a ryan-kan shape.

The pinzu side, by contrast, can improve with 三筒牌图四筒牌图八筒牌图九筒牌图, which is much richer.
(Shanpon improvements are equivalent here, so they are excluded.)

There is a slight difference in how easy it is to win on kan 二万牌图 versus kan 六筒牌图, but the orthodox choice is still to value the number of improvements and drop the manzu side.

Example 5
二筒牌图三筒牌图五筒牌图七筒牌图八筒牌图九筒牌图二索牌图三索牌图五索牌图六索牌图七索牌图七索牌图八索牌图 Tsumo 五筒牌图

=> Discard 二索牌图

This is a choice between two ryanmen taatsu.

It is a shape-reading mistake to think the 七索牌图八索牌图 side is worse just because you already use one 六索牌图 yourself.

By discarding 二索牌图, the souzu side can become a ryanmen plus kanchan composite shape.

☆ 二筒牌图三筒牌图五筒牌图五筒牌图七筒牌图八筒牌图九筒牌图三索牌图五索牌图六索牌图七索牌图七索牌图八索牌图 Tsumo 四索牌图 and you are in tenpai.

Example 6
四万牌图五万牌图七万牌图八万牌图九万牌图九万牌图四筒牌图五筒牌图一索牌图一索牌图一索牌图四索牌图五索牌图 Tsumo 九万牌图

=> Discard 四万牌图 (or 五万牌图)

At first glance, it may look as though you could discard manzu, pinzu, or souzu.

However, if you drop the manzu side, then the reverse draw 六万牌图 still remains an effective tile.

☆ 五万牌图七万牌图八万牌图九万牌图九万牌图九万牌图四筒牌图五筒牌图一索牌图一索牌图一索牌图四索牌图五索牌图 Tsumo 六万牌图

If the table situation does not create a special difference, the correct move is to drop 四万牌图五万牌图 first.

This is a fairly fine point, so missing it is not a major disaster. Even so, keep the idea of covering a reverse draw somewhere in the back of your mind.

Original Japanese page: http://beginners.biz/pairi/pairi14.html

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