Analysis - Yaku Rates by Hand Type

People commonly wonder how rare certain yaku are. Something I've been curious about is how common certain yaku are in open hands. So, let's look at the yaku distribution for all hands, riichi hands, dama (closed tenpai without riichi) hands, and open hands.

When teaching new players, I tell them that the only yaku they need to learn are Riichi, Yakuhai (value tiles), Tanyao (all simples), and Honitsu (half flush). The other yaku are more nuanced, complicated, or prone to backfire and don't need to be learned right away, and the majority of calls involve one of those three yaku. Let's check out the Hanchan yaku rates and see what percentage of hands those three yaku cover.

If you look in the "Open" column, Yakuhai is present in about 64% of hands, and Tanyao is present in about 28%. So, together, Yakuhai and Tanyao cover 92% of open hands. Honitsu is present in about 8% of hands, but it has some overlap with Yakuhai. So, even if you only know those three yaku, you're not missing out on many calls, and Honitsu is basically optional.

This list doesn't include ura dora (because Tenhou adds it to every riichi hand, even if it hits 0), but if you're curious about it, I have a blog post about ura specifically.

Let's look at the chart for Tonpu games while we're at it.

In open hands, the percentage of Yakuhai goes down a bit, and the percentage of Tanyao goes up a bit, maintaining the 92% coverage. I'd theorize that this is because of people wanting to call more in Tonpu, and Tanyao being a yaku you can force. Honitsu also goes down, perhaps due to it being seen as a slow yaku and speed having a higher importance.

Let's also look at Sanma.

More than three-quarters of Sanma hands have at least one dora. This is of course due to the kita calls. Yakuhai makes up 89% of calls on its own, while Tanyao only represents 4%, covering 93% of calls. Honitsu's representation is now nearly one fifth of open hands, thanks to the removal of most of the character tiles.

Something interesting is that the Hanchan and Tonpu ippatsu rate is 18~19%, while in Sanma, it's a bit over 20%. That's not much of a difference, despite the removal of seven tiles from the pool. I guess having a fourth opponent to deal in to you helps mitigate it. The tsumo rate is also only a bit higher.

We can also look at the reverse. We've been looking at the yaku per hand type, but we can also check the hand type per yaku to see how often a yaku is opened, riichi'd, and dama'd. Let's start with hanchan. The dama/closed column shows what percentage of closed wins were dama.

About 14% of wins are from dama. A quarter of closed wins are dama. This is a bit over-represented because we're only looking at wins. People won't dama a quarter of their hands (I think? We'll look at that in the next post), but the increased winrate from dama makes it appear more in the data.

The most common yaku to dama are Chinitsu, Chankan, and Honitsu. Chinitsu and Honitsu have high value, 6 and 3 han respectively, so that makes sense. Chankan is kinda funny, but if someone is in riichi, you're probably not going to call kan and give them more dora, so that also makes sense.

There's only one instance of a dama sankantsu. It's quite an amusing hand. Here's the replay.

We can look at Tonpu too.

Compared to Hanchan, there's a greater proportion of dama. The proportion of dora and aka dora in open hands also goes up, perhaps indicating a lower calling requirement.

Finally, let's see Sanma.

The percentage of called hands has gone down compared to the four player games, but the ratio of dama and riichi is about the same as in Tonpu.