Toitsu theory (2)

Source: http://blog.jpmahjong.net/read.php/517.htm

As mentioned before, unless you're aiming for a chitoitsu, you shouldn't have too many toitsu in your hand. Normally, the limit would be 2 toitsu, any more will result in a bad shape. If you find that there are too many toitsu in your hand, there a few options.

a) Dismantle and discard
b) Combine the toitsu with the other tiles in your hand to form a good shape
c) Make a chitoitsu

Beginners are often reluctant to discard redundant toitsu, for example

(sha as guest wind)

Discarding the isolated pin of 7 pin, 3 sou or 7 sou are common beginner discards. If it were me, I would bravely discard 1 pin or 3 pin.

Actually when it comes to effective tile loss, the loss of discarding 3 pin will only be the other two 3 pin. However if you discard 3 sou, the loss will be 124 sou, a total of 12 tiles. In a situation with a lack of mentsu, relying on the toitsu in your hand to complete your hand will often result in failure.

When you have 2-3 toitsu in your hand, and if deciding on a jantou is too early, you can consider discarding a toitsu, leave a useful isolated tile, yakuhai etc, and increase the chances of getting a good shape or forming of mentsu as much as possible... This is not only a method of playing that beginners neglect, even for an intermediate mahjong player, this is a blind spot that is often missed.

For those hands with 4 toitsu and above, normally you can view chitoitsu as a possible choice.

This is the game record of MFC, at that time I was the north player. At the fourth draw, I drew 9 sou. What should I do?
If you consider a mentsu hand's(4 mentsu + 1 jantou) tile efficiency, discarding 9 sou here is normal.
On the surface you can easily make mentsu hand with so many toitsu, but it's the opposite. Currently there is only one confirmed mentsu of 789. The rest of the tiles: 4 wan, 9 wan, 3 pin and sha require drawing two more tiles to win. Every type of tile only has two more tiles, the efficiency is really low. The most important thing is, for the toitsu here to have a good evolution, it's not an easy feat.

Therefore this hand should aim for a chitoitsu. I discarded 2 sou in the actual game.

PS: Tile efficiency is a huge learning ground, there are many more things to explain. But in order for the readers to learn other more important theories, I will first set aside theories regarding tile efficiency. Once other parts have been discussed, I will write more articles on tile efficiency.

Toitsu theory (1)

Source: http://blog.jpmahjong.net/read.php/513.htm

Let's revise the requirements needed to win in Japanese mahjong:
4 mentsu + 1 jantou + 1 yaku

You need 4 mentsu, while you only need 1 toitsu, and the formation of toitsu is easy. Often we do not need a lot of toitsu, unless we're aiming for a chitoitsu.

The extra toitsu, may become a mentsu, a toitsu only need to draw a third tile to become koutsu. However the chance of successfully turning into a mentsu is not high, as there are only 2 effective tiles, this is lesser than the 4 effective tiles of penchan. (Reader note: you might think of calling pon on discards and gambling on a toitoi. However since we're discussing about tile efficiency, the reader should put aside this discussion. The theory related will be explained during the yaku theory in the future.)

Hence, once the number of toitsu exceed what you need, the extra toitsu will become very inefficient. A common mistake between beginners, is keeping too many toitsu, thus slowing down their hand and being unaware of it.

The text below explains the basic principle of handling toitsu.
You should not determine the jantou too early
The need for jantou is low and it is easy to form. When the shanten number is high, and there is only a single pair in the hand, determining the jantou too early will put you at a disadvantage.

There are many people who would determine the 4 pin as the jantou too early and discard the 6 pin. However I am unable to accept this kind of thinking. The correct way of thinking is treating 2446 as two kanchan. Discarding 1 pin here is the correct answer.

The 23 wan here along with 34567 has the highest chance of becoming 3 shuntsu, but where would the fourth mentsu come from? If you discard 6 pin, the wait for the fourth mentsu would be 79 wan and 12 pin, but they are bad shapes, and have a low chance of good evolution. Succeeding is not going to be easy.

Discarding 1 pin, and keeping the chance of forming a mentsu with 5 pin is very important.
Even if on the side of manzu, 79 wan turns into 78 wan

If it's still at the early stages, discarding 1 pin here remains a very strong discard. Even though 2378 wan is a good shape, this sort of tiles do not guarantee a 100% chance of being added into the hand. In truth, drawing a kanchan tile is a common sight, an extra mentsu as backup is never disadvantageous.

Someone might ask, is it disadvantageous to draw 3 pin after discarding 1 pin?

It's a little disadvantageous, but it's not severe. The loss here is only a jantou. Drawing 2378 wan, 14 pin, 3467 wan will replace the lost jantou. The situation is better than discarding 6 pin and drawing 5 pin.

Choosing between multiple shanten shapes: problem discussion

Source: http://blog.jpmahjong.net/read.php/510.htm

Revision
There are already quite a number of articles related to taatsu theory. If you're purely going for the fastest way to reach tenpai, you should start discarding in order, beginning with the taatsu with the lowest possibility of effective tiles.
If you find yourself with similar taatsu, you can consider with the following:
a) future evolution of the taatsu (penchan good evolution etc)
b) is it a bad shape, for example having effective tiles overlapping
c) how easy it is to win when in tenpai
d) yaku etc

Among them, a and b are the most important.

Example 1:

This is choosing between discarding 89 pin or 12 sou. The readers who have read the article about overlapping effective tiles , should be able to easily find the answer.
As 89's effective tiles overlap with 68, discarding 9 pin is the correct answer.
This problem can be attempted with the "loss of effective tiles" method, the correct answer would be the discard with the lowest loss of effective tiles.
Discarding 12 sou: the loss of effective tiles include 3 sou along with 1/2 sou
While discarding 9 pin, the loss will only be 9 pin, therefore discarding 9 pin is better than 12 sou.

Example 2:

This is a rather famous beginner tile efficiency problem(smile): Choosing between 23 wan, 78 wan, 34 pin.
The correct answer is discarding 8 wan. After you discard 8 wan, you're left with the shape 233457, 6 wan is still an effective tile! If you discard the remaining two taatsu, you'll lose two types of effective tiles.
Like the 233457 shape, it's very common in Japanese mahjong, beginners should pay more attention.

Example 3:

This question is harder.
68 wan and 24 pin are both kanchan in the same position, both seem to be similar.
But if you consider the evolution: when 68 wan draw 5 wan, 2356 wan becomes the aforementioned overlap of effective tiles shape. Therefore the value of 68 wan is lower, you should discard it first.

Important complex taatsu (2)

Source: http://blog.jpmahjong.net/read.php/508.htm

Two chapters before introduced quite a number of good shapes in Japanese mahjong that are important but often overlooked, this time I'll introduce some other commonly seen taatsu.

6. Double/Triple middle taatsu
Double/Triple middle taatsu refers to 468, or 2468 etc continuous kanchan type of shape.
Quite a few beginners think of kanchan as a bad shape, and do not like this type of shape. But we have to be aware: a 246 double middle taatsu has the same number of effective tiles as a ryanmen. The difference is that the former require 3 tiles, while the latter only require 2 tiles, the former has a lower efficiency. It may not be a good shape, but when the number of taatsu in your beginning hand is not enough, the double middle taatsu is still useful.

7. 3556 shape
On the surface, the two taatsu of 35 + 56 seems to be similar to the aforementioned 35 + 67, in fact there's a huge difference between them. The reason is that 35, 56 violates the problem of effective tiles overlapping. In this situation, 35 taatsu has a low value, if there's enough taatsu, 35 should be the first to be discarded. Having 56, or 556 remaining should be enough.

8. 5566 shape
Everyone might think of 5566 as two ryanmen, and there's a chance of becoming ippeiko. But to me, it's a bad shape. 5566 definitely has effective tiles overlapping. It might seem easy to draw 47 twice, but when there are other good taatsu, this should be quickly disposed of.

Discussion regarding taatsu stops here. If there are any questions, feel free to ask them. The next chapter will be discussing some examples of problems.

Effective tiles overlap(Received twice)

Source: http://blog.jpmahjong.net/read.php/507.htm

Look at the example below.

Which tile should you discard?

45 pin is ryanmen, therefore you should choose between 12 wan and 12 pin. On the surface both are penchan, discarding either group shouldn't matter. Let's first count the number of effective tiles.
a) discard 12 man: drawing 36 pin to tenpai
b) discard 12 pin: drawing 3 wan, 3, 6 pin to tenpai

Therefore, discarding 12 pin is the correct answer here. This has 50% more effective tiles. Both are penchan, but discarding 12 pin is better, the reason is because 1245 pin is a bad shape with effective tiles overlapping.

As 12, 45 taatsu both require 3 pin, once you discard 12 pin, the number of effective tiles will not decrease. In fact, overlapping of effective tiles is an important efficiency theory in Japanese mahjong, you should pay attention to this during actual play.

Example:

Beginners often hope to draw 5 wan for a 3 sided wait and discard 23 sou, this is incorrect. In fact, because 3467 wan has effective tiles overlapping, you should discard manzu instead.

Important complex taatsu(1)

Source: http://blog.jpmahjong.net/read.php/506.htm

The taatsu mentioned in the previous article, are isolated and easy to spot taatsu. This time, we'll go through some common complex taatsu.

1. 4556 shape
The most common mistake made by beginners, is to see this as [456 shuntsu + isolated 5], and discard 5 too early. In truth, this shape should be seen as two ryanmen 45 + 56, allowing 3467 to be added into the hand. It also allows a good chance of getting ippeiko. In Japanese mahjong, it's a shape that is highly valuable. If there's a shape this like this in my hand, I won't easily dismantle it.

2. 4567 shape
The logic is the same here, this shape should be viewed as two ryanmen 45 + 67. This shape can evolve into many shapes. You can draw 56 to form a mentsu + ryanmen, draw 38 for a three sided wait, draw 47 to form a jantou + mentsu. It's value is not lower than the previous 4556.

3. 4456 shape
This is a toitsu + 56 ryanmen shape, there are quite a number of effective tiles. However, since there's a large probability of not forming a good ryanmen, it's not as valuable as the previous two shapes, but it's still a good shape.

4. 3567 shape
This is a shape that even intermediate players would sometimes forget. We can view it as 35 + 67. There are 6 useful tiles of this shape: 1, 2, 3, 4, 5, 8. Among them, 1, 5, 8 will create a kanchan. It's value is lower than 4456.

5. 4445 shape
This shape is no stranger to those who play mahjong, this is a common 3 sided wait shape. But if the hand is not in tenpai, the value of this shape is normal.
This shape is incapable of giving you two mentsu, at the most it'll give a jantou + mentsu. The important thing to remember, is that you need 4 mentsu in order to win, while you only need 1 jantou. Therefore, your need of mentsu is much higher than that of jantou. In fact, when you have many toitsu in your hand, this 5 here will often become a useless tile.

Beginner tile efficiency: Taatsu

Source: http://blog.jpmahjong.net/read.php/505.htm

After a few rounds of discards, you'd normally be able to get rid of any useless honour tiles. If the remaining tiles do not form mentsu, you can roughly separate them into three types.
1. Taatsu
2. Isolated tiles (Number tiles that are alone)
3. Toitsu

The next few paragraphs will first explain the taatsu problem.

The types of taatsu
Taatsu can be separated into ryanmen, kanchan and penchan. The value of penchan is the lowest, followed by kanchan, while ryanmen holds the highest value. Therefore when you have too many taatsu and need to break up one, start with the one with the lowest value.

You should discard 12 wan here.
If you need to choose between discarding taatsu of the same type, you can consider which one of the two will be able to evolve into a better shape.

In this kind of situation, there are two ways of breaking down the taatsu: 24 wan and 35 pin. On the surface, 24 and 35 are the same, but there are differences. You can form ryanmen with 35 pin by drawing 2 or 6 pin. However with 24 wan, drawing 1 wan will turn it into a penchan. Therefore the probability with 24 wan is lower than 35 pin. To preserve the possibility of drawing 5 wan, discard 2 wan first.

Therefore beginners should memorize this order of values
Penchan < 13 Kanchan < 24 kanchan < 35 kanchan << Other middle kanchan <<< Ryanmen

Beginner tile efficiency: Beginning with the tile distribution

Source: http://blog.jpmahjong.net/read.php/504.htm

Tile efficiency is a skill that allows you to win in the fastest time. In Japanese mahjong, winning as fast as possible means quickly making [4 mentsu + 1 jantou + 1 yaku]. Therefore tile efficiency is about thinking in this direction, discarding the tile that gives you the smallest probability in making a mentsu, and increasing the probability of making a mentsu as much as possible.

In fact, tile efficiency is already useful at the start of the game.

Facing this typical hand, how should you deal with it?

Priorities in tile discarding
The tile efficiency here is simple, just discard the most useless tile. What do you mean by most useless tile?? Isolated guest wind tiles are the most useless, because you can't make shuntsu with them, you can only wait to make a pair with them, which has a low probability. What you need to note is, a single tile of your seat wind or round wind is a different story. As long as you can pon with it, you can clear the 1 yaku requirement. You can also chi others' tiles afterwards. Therefore it's value far surpasses the value of guest wind tiles.

After guest wind tiles, it's isolated 1 or 9 tiles. If you're using them, they will most likely turn into kanchan or penchan. However with the hand above, the value of 1 pin is lower than 9 pin, the reason is because of the 4 pin. Even if you discard 1 pin and draw 2 or 3 pin, they can form a mentsu with 4 pin without wastage. On the other hand, if you discard 9 pin and draw 7 and 8 pin, you'll have wasted a tile. In this example, the value of 1 pin is on the same level as isolated guest wind tiles due to 4 pin. 

In simple terms, the order of tile discarding is as below:
1. Isolated guest wind tiles, isolated 1 or 9 when there is 4 or 6
2. Isolated 1 or 9 tiles
3. Isolated yakuhai
4. Isolated 2 or 8 tiles
5. Isolated 3-7 tiles, penchan tiles
Note: The order of 3-5 may differ for different hands.

Here's some more examples

1 pin is the most useless here, discard it first. With this kind of bad shape, discarding chun is a bad move.

Discarding sha is the correct move. Despite the presence of 4 wan, 1 wan here will be viewed as an isolated 1 or 9 tiles as 456 is already a mentsu.

Translation:
4 mentsu + 1 jantou: mentsu refers to shuntsu or koutsu groups (Example 234, 555 etc)
Jantou is a Japanese mahjong term, equivalent to Cantonese mahjong's eyes.

Writing it beforehand - Why do you want to discard efficiently?

Source: http://blog.jpmahjong.net/read.php/503.htm

This is the first article to address intermediate players of Japanese Mahjong. After reviewing feedback from readers, the author will first start with tile efficiency.

I believe that the readers here have all played Cantonese or Taiwanese mahjong. Compared to them, Japanese mahjong requires a higher requirement of tile efficiency. So once everyone has learned the rules, they'll have to spend some time learning tile efficiency, in order to improve their results. As I explain why tile efficiency is so important in Japanese mahjong, I'll also explain the special characteristics of Japanese mahjong's system.

Japanese mahjong compares position, not points
Beginners in Japanese mahjong has to remember this, Japanese mahjong compares position, not points. Japanese mahjong uses a tonpuusen or a hanchan as a calculation unit. Your results will be equivalent to every unit's average position. In a tonpuusen, just because you win a hand doesn't mean you'll be first, but if you can't even win a single hand, you definitely won't win. Cantonese mahjong allows you to make a big hand every time, because a single big win is equivalent to 10 small wins. However, this playing style won't work in Japanese mahjong. If you can't win a single hand, you'll lose badly.

The importance of closed hands
If you look closely at the yakus of Japanese mahjong, you'll realize the importance of closed hands in Japanese mahjong. You can declare riichi as long as your hand is closed, not only does it fulfill the requirement of having at least one yaku but also allows you to flip open the ura-dora. Japanese mahjong also has a lot of yakus that require closed hands, or having reduced value if your hand is open.

If you want a closed hand, then you'll need to rely on the tiles that you draw. Because the tiles that you can rely on is lesser, good tile efficiency is about increasing the probability of improving your hand. The importance of tile efficiency is much higher than in Taiwanese mahjong.

Japanese mahjong's scoring system
Japanese mahjong's scoring system is also unique. For a 1-4 han hand, every extra han is equivalent to double the score, but 5 han and above is another story. For example, a 5 han hand is mangan. Add an extra han and it'll be haneman, but the score will only increase by 50%. Adding an extra han to a 6 han hand is useless, as 7 han is also a haneman.

A 8 han hand's scoring in Cantonese mahjong is 8 times of a 5 han hand, while it's only 2 times in Japanese mahjong. Hence in Japanese mahjong, few will go for a big hand, since the efficiency is too low. In a game with 3 aka dora, everyone has an average of close to 2 doras. This becomes clearer when you are getting 3-4 han just by winning.

Because there's a lot of dora, winning with a 3-4 han hand is not hard, thus winning with a closed hand is more advantageous than waiting for a big hand. If you want to increase your winning rate, a good efficiency is required.

Now that the useless stuff is over, the next article will get to the main point.