More on ryanmen tenpai with yasume and takame

Source: http://blog.jpmahjong.net/read.php/612.htm

A reader raised a question about the previous article, regarding yasume and takame.

For example, if the hand is:

The yasume of 6 wan is worth 2000 points, while the takame of 9 wan is 7700 points. I mentioned that you should immediately declare riichi with this type of hand, but he feels that damaten is more advantageous. The reasoning is shown in the hand below.

Similarly, it's hand with takame of 7700 points and yasume of 2000 points. 凸本 mentioned before that you can ignore 6 wan with this sort of hand. Then could you follow suit with the previous menchin hand? If you follow suit, would a damaten be more advantageous?

If you only win on the takame with this sort of pinfu hand, it becomes a tenpai with a bad shape. According to 凸本's statistics, the difference between the winning rate for damaten with a bad shape and riichi with a good shape is minimal. The problem is when you declare riichi, would the chances of winning on the yasume of 6 wan be higher than in damaten?

If you only calculate the rate of winning, the rate of winning for 6/9 wan is close no matter if it's damaten or riichi. However, riichi will increase the chances of tsumo and if tsumo depends on chance, the chances of 6/9 wan appearing is higher. Hence, riichi will increase the winning rate of 6 wan.

The value of the yasume after riichi is 3900 points without ura-dora. The chances of getting ura-dora is 30%, and the value is 7700 points with one ura-dora. Hence, the expected value is 5000 points. If it's the takame, it's a haneman with one ura-dora and 8000 points without ura-dora. The expected value is over 9000.

If you add the two together, the expected value of over 7000 points is similar to that of the damaten of 7700 points. But don't forget that this result has not factor in the following:
1. Riichi increases the chances of tsumo, increasing the expected value. During damaten, the difference in points after tsumo is only 300 points, but after riichi, but the increase will be larger.
2. The risk of drawing the yasume of 6 wan while in damaten.
3. The advantages that riichi bring: ippatsu and the ability to stop other players from reaching tenpai.

In summary, it's more advantageous to declare riichi. With exposed melds, you can choose to ignore the yasume.

You should only be in damaten for this sort of hand if there are very little or no more 6 wan left, or when mangan is enough.