Tile Efficiency 101 (Part 2)

The last post on tile efficiency was kind of basic, so today’s article now introduces the concepts we are going to use in the future articles. Especially, Shan-Ten (how many away), Uke-Ire (the amount of tiles that move you one shanten closer to tenpai) and Good Shape Evolution (when your hand will evolve towards good shape). So, enjoy.

Source: http://beginners.biz/h_02.html

Useful Tiles and Tile Numbers

Mahjong is a game where you systematically discard once and again an unwanted tile from your hand.
Last time, I said that selecting your discard prioritizing the easy win is basic.

So, what should we select to discard concretely…

1.Number of tiles and probability

Ex1:

1m2m3m3m3m4m7p7p7p5s5s7s8s9s

In ex1, as long as  3m isn’t very dangerous, we should discard3m .

Let’s try to think it over. Why is it a mistake to discard 1m or 4m?

Of course, it’s because discarding 3m leaves us with a better wait.
Let’s try to compare them virtually.

1m2m3m3m4m7p7p7p5s5s7s8s9s Wait: 2m5m

2m3m3m3m4m7p7p7p5s5s7s8s9s Wait: 3m5s

If you consider the number of winning tiles, the former has 7 tiles, while the latter has 3.
Of course, since some of them might be in the hands of our opponents or in the dead wall, in reality,
you should naturally wait on 7 tiles, since it’s not like if you wait on 3 tiles they’ll be alive.

There are cases where there aren’t any 2m5m remaining as well.
However, there is practically no way for us to tell how many tiles are remaning on the live wall.
That is because we are not psychic.

In reality, when comparing whether to wait on 7 or 3 tiles, judging that the 2m5m wait is more effective is good.

“The more tiles you wait on, the better your wait is” is a basic concept in mahjong.
Ignoring this basic concept, it is not possible to win at mahjong.

The 2m5m wait has more tiles.

=  It’s more likely we’ll win on 2m5m.

=  It’s more advantageous to wait on 2m5m.

It is important to play mahjong with this mindset.
Mahjong is not a game where you compete to see who has a better sixth sense, it’s a game where you compete to better evaluate advantages and disadvantages.

2.Number of uke-ire

In example one, we evaluated a tenpai hand, but if we also evaluate a hand that is not tenpai and compare whether there are too many or too few tiles, what to discard should become an obvious choice.

(…) — 3 shanten — 2 shanten ——- 1 shanten ———— tenpai ——————— Win

Let’s look at this graphic once again.

Since there is a large gap of distance until the win, it is hard to find the fastest way.
First, let’s find the fastest route to the next step (2shanten, 1shanten, etc), and think about the fastest route possible towards tenpai.

Using the number of tiles, the easiest wait to measure how close to the win the hand is, is to count and compare how many tiles will decrease the number of shanten.

Ex2

1m1m2m6m8m4p4p6p1s2s3s3s4s

Ex2 is a hand 2shanten. Let’s count how many tiles transform it into 1shanten.

1m 3m 7m 4p 5p 2s 5s that’s 7 types and 23 tiles

<<(remember to substract the tiles already in your hand [1m, 4p, 2s] or visible on the board).>>

This is the number of uke-ire towards 1shanten. This is, the uke-ire.

Ex3

1m1m2m6m8m4p4p6p2s3s3s4s4s

Ex3 is very similar to Ex2, but since it is also 2shanten or 2-away from chiitoitsu/Seven Pairs, the uke-ire is:

1m2m3m6m7m8m4p5p6p2s3s4s5s that’s 13 types and 35 tiles.

Its ukeire is far wider than Ex2, so it is clear that its shape is better than Ex2.

In this way, counting the ukeire of the hand, it is possible to measure a hand’s merit with numbers.

We will be using the value of uke-ire in the following lessons.

3.Evolving into good shape

1m1m2m6m8m4p4p6p1s2s3s3s4s tsumo: 4s

If we think about the earlier concepts, by cutting 1s when we draw 4s, the hand is still 2shanten, but since the uke-ire increases, we must think of 4s as a useful tile as well.

Useful tiles either:

A : Decrease the number of shanten (uke-ire)

B : Increase the number of uke-ire (good shape evolution)

one or both things.

Ex4

2m2m3p3p5p6p7p9s9s9s (pon) 1z1z1z tsumo: 4m

Ex4 is a decission about which wait to take.

With the current shanpon wait and even if we discard 2m for a kanchan, the uke-ire is the same number: 4 tiles. In that case, let’s think about evolution towards good shape.

2m2m3p3p5p6p7p drawing 2p 4p number of tiles UP.

2m4m3p3p5p6p7p drawing 5m number of tiles UP.

Since it can also improve to a three-sided-wait, keeping the shanpon wait is correct.

In cases like these where the uke-ire is the same, we use the technique of comparing evolution towards good shape.

The important thing here is uke-ire number has more value than good shape evolution number.

First of all comparing the number of uke-ire before anything else is basic tile efficiency.

A : Decrease the number of shanten (uke-ire )

B : Increase the number of uke-ire (good shape evolution)

Rarely, there are also people who give A and B the same value, and people who sum and compare A+B.

Since it’s very simple to get confused, let’s be careful.

有効牌と枚数

麻雀は手牌のうち1枚不要な牌を捨てる作業の繰り返しです。
前回アガリやすさを最優先して打牌を選択することが基本だと言いました。

では、具体的に何を指標にして選択すれば良いのでしょうか。

1.枚数と確率

例1

例1は が余程危険でない限り を切ります。

改めて考えてみましょう。なぜ  を切るのが間違いなのか。

もちろん を切ったほうが待ちが良いからですね。
実際に比較してみましょう。

待ち

待ち

待ちの枚数としては上が7枚、下が3枚です。
もちろん他家の手牌や王牌に何枚かまぎれているでしょうから、
純粋に7枚、3枚が残っているわけではありません。

が山に1枚も残っていないこともありえます。
しかし実際に山に残っている枚数を確実に知る方法はありません。
私達は超能力者ではないのですから。

現実的には、7枚と3枚という理想値での比較をし、

待ちにした方が有利、と判断して良いでしょう。

「枚数が多ければ多いほど有利」なのは麻雀の基本原理です。
この基本を無視して麻雀で勝つことなどできません。


の方が待ちの枚数が多い

=  の方があがれる確率が高い

=  に受けたほうが得をすることが多い

このような思考で麻雀を打つことが大切です。
麻雀は勘の良さを競うゲームではなく、損得感覚の鋭さを競うゲームなのです。

2.受け入れ枚数

例1は テンパイしていた場合の待ちを比較しましたが、
テンパイしていない手牌においても枚数の多い・少ないで手牌を比較できれば
捨てるべき牌が明確なります。

有効牌と枚数

麻雀は手牌のうち1枚不要な牌を捨てる作業の繰り返しです。
前回アガリやすさを最優先して打牌を選択することが基本だと言いました。

では、具体的に何を指標にして選択すれば良いのでしょうか。

1.枚数と確率

例1

例1は が余程危険でない限り を切ります。

改めて考えてみましょう。なぜ  を切るのが間違いなのか。

もちろん を切ったほうが待ちが良いからですね。
実際に比較してみましょう。

待ち

待ち

待ちの枚数としては上が7枚、下が3枚です。
もちろん他家の手牌や王牌に何枚かまぎれているでしょうから、
純粋に7枚、3枚が残っているわけではありません。

が山に1枚も残っていないこともありえます。
しかし実際に山に残っている枚数を確実に知る方法はありません。
私達は超能力者ではないのですから。

現実的には、7枚と3枚という理想値での比較をし、

待ちにした方が有利、と判断して良いでしょう。

「枚数が多ければ多いほど有利」なのは麻雀の基本原理です。
この基本を無視して麻雀で勝つことなどできません。


の方が待ちの枚数が多い

=  の方があがれる確率が高い

=  に受けたほうが得をすることが多い

このような思考で麻雀を打つことが大切です。
麻雀は勘の良さを競うゲームではなく、損得感覚の鋭さを競うゲームなのです。

2.受け入れ枚数

例1は テンパイしていた場合の待ちを比較しましたが、
テンパイしていない手牌においても枚数の多い・少ないで手牌を比較できれば
捨てるべき牌が明確なります。

もう一度この図を持ち出しましょう。

アガリまで遠い段階で、直接アガリまでの最短を考えるのは難しい。
まずは次のステップ(リャンシャンテンならイーシャンテン)までの最短距離を目指し、
できるだけ早くアガリに近づけることを考えます。

アガリやすさを枚数で考えるもっとも簡単な方法は、
シャンテン数を下げることのできる牌の枚数で比較することです。

例2

例2はリャンシャンテンの手牌です。
この手でイーシャンテンになるツモ牌を羅列すると

の 7種23枚です。

これが「イーシャンテンへの受け入れ枚数」です。

例3

例3は例2とほとんど同じ形ですが、
チートイツでもリャンシャンテンなので

牌は13種35枚。

例2よりもずっと受け入れ枚数が多く、
例2より例3の方が良い形であることは明白です。

このように、受け入れ枚数を数えることで手牌を定量的に評価することができます。

受け入れ枚数による評価は、以後の講座で何回もやります。

3.好形変化

18 thoughts on “Tile Efficiency 101 (Part 2)

  1. “Mahjong is not a game where you compete to see who has a better sixth sense, it’s a game where you compete to better evaluate advantages and disadvantages.”

    Thus, Saki is not a mahjong manga/anime.

    1. In mahjong there are 2 kind of playstyle :
      Digital style : based on probability and statistic.
      Occult style : based on momentum, flow, miracle, or sixth sense.
      Most of mahjong manga/anime adopt occult style.
      Some of them adopt digital style.
      No matter what style they use, mahjong is just a mahjong.
      However, digital style is known as the best way to win the mahjong.

      1. My thoughts on the identity of “Occult Mahjong”:

        Occult Style could only be called something of “intuition” which is gained after probably countless games to the point where you can instinctively “feel” what hands the other players are going for, what tiles they could be waiting on, along with which remaining tiles that could be in the wall. Even without the exact depth of “knowing” their hands, you have certainly tapped into a depth of “understanding,” greatly limiting those possibilities, and from that, you have a strong sense of what moves to make based on that information.

        It’s not about always making magical rinshans or dubious hell waits that turn miraculous, but certain “reads” can certainly lead to making some of these odd events to happen. Perhaps you could tell what tiles can easily overflow from your opponents’ hands, making a hell-wait pursuit riichi, sensing that another player likely holds most of the other player’s winning tiles. Taking a more extreme example, perhaps you could tell you have a high chance at drawing a certain tile after combining the discard pile with seeing two players going for opposite suit chinitsu/honitsu while the third is trying for a lower sanshoku, so you find yourself declaring riichi right before you could draw the last tile.

        They call certain events miracles when they seem to defy the feat of ordinary probability, however, if you have more information that gives you a firmer grasp of the situation, perhaps that one “miracle” that others see outside of their reach is more possible than you think. For better or worse, it’s not Saki where you could unconditionally pull the same rare yaku out of a hat anytime, anywhere.

  2. Saki is fiction. Fun fiction. But hence, I like Nodoka’s digital style the best. In the manga, you can briefly see she is Rate 2300. Can’t beat that.

    1. Is a double pair wait considered good as the trap play? Because double pair wait can not be easily read and discarding suji can be dangerous. The odds to win is smaller, but it can make your enemy get mad and lose their mind in the next game.

    2. Is a double pair wait considered good as the trap play? Because double pair wait can not be read easily and discarding suji can be dangerous. The odds to win is small, but it can make your enemy get mad and lose their mind in the next game (especially when one of the pair is dora).

  3. There’s an error in ex3. It’s missing one c4, I guess (there are 12 tiles total, should be 13, right?).

  4. so, is there a fast way to calculate uke-ire/shanten? coz I know I’m too slow to calculate something like that in the 5s or whatever I get per draw.

  5. A trick you can use, is count your pairs. 4 pairs is chii-toi 2shanten, as 5 pairs is 1shanten. Remember that if you’ll go menzen, two pairs is the strongest possition (this is because you get 4 extra tiles to help you). So, the best thing you can do, is calculate the uke-ire “raw.” This is, if you have a closed wait “4,” a shanpon “4” a penchan “4” a ryanmen “8” and a tanki “3.” And you just substract the number of those tiles that you see in your hand (and the board). Likewise, a three sided wait would be 12 tiles, substract the one you already have in your hand, and it’s 11 (I automatically count it as 11, but just in case you don’t want to fck up).

    If you always count them as you play, you can begin to easily notice even without counting, just by the structure, in most hands. When I look at the hand, I can easily distinguish hands with an uke-ire of between 8 and 20 as those are the most common. Any more than that, and I have to count a little more, but I normally just take all hands above 20 as “good enough” and in those cases just choose according to yaku/dora/final wait/etc.

    The author says any hand with an uke-ire towards tenpai of 16 tiles is good enough. And fair enough, if my uke-ire is 16, I draw my tenpai 90% of the time. An example of not understanding this concept and failing is as follows:

    一ニ三五六七 ②③ 6799 北
    The uke ire is 16, pinfu is confirmed. Here, you would keep pei as a safe tile, since having a ⑥ floating around in your hand or anything like that doesn’t help your hand. Assume you draw ②

    一ニ三五六七 ②②③ 6799

    If you have dora (one or more), discarding pei to keep the 223 shape is correct, as it increases your uke-ire to 20 tiles, by adding the 4 extra tiles of the ②②99 shanpon. Given that the risk of discarding ② later on is not that big either, I believe this is the best.

    Another common mistake would be

    一ニ三五六 ⑦⑧⑨ 899 北北

    Here, discarding 8, 9 or north is generally a rather bad mistake. The shape -looks- bad, maybe, but it has a decent uke-ire, same as two ryanmen, 16 tiles. (四七79北)
    More so, if you get to tenpai with 7, 9 or North, you have a ryanmen. With 7, you have pinfu.
    If you get to tenpai with 四or七, the 9-North shanpon is very easy to win with. If you have dora, consider to keep pushing ahead with this shape, as you’re not likely to improve it and 16 tiles is a good enough uke-ire.

    I think I just used up most of the material for one of the next posts. orz

  6. Also, never forget to substact tiles that are visible in discards/dora indicator/calls/your own hand and tiles that are repeated (34 67m, you aren’t expecting 16 tiles, but 12).

Leave a Reply

Your email address will not be published.