Analysis - Yaku Combinations

It's the holidays. All the couples are out having fun. But those aren't the couples I care about right now. What are the biggest power couples in Mahjong? The yaku that always show up together? Let's find out.

This analysis was run on 1,246,147 Hanchan games played in Tenhou's Houou room. Whenever a hand was won with two or more different yaku, all possible combinations were counted once. Let's see which combinations turned up the most.

Hmm. This isn't too interesting. It's just a bunch of dora and tsumos. Let's try to filter the list a bit, removing any combination that involves some type of dora, a riichi, a tsumo, or an ippatsu. That should make it be more "real" yaku.

That's more along the lines of what I was looking for. Pinfu + Tanyao is likely expected to be at the top. However, if you add together the Yakuhai Wind + Honitsu and Yakuhai Dragon + Honitsu rows, you get 486,066. This is actually more frequent than Pinfu + Tanyao! Interesting.

The Yakuhai also stack together frequently. Adding up all the Yakuhai combos, it's 654,270. Of course, these numbers might have come from the same hands (eg, a Hontisu + Wind + Dragon hand would count once to each combination), so who knows, really.

How about the opposite? What combinations are the rarest?

A Double Riichi + Toitoi is just sad. Well, we should probably actually do something useful with this data. In the spreadsheet, I've set up a sheet called "Pretty" which allows you to select a yaku and see all the combinations that happen with them. Here's a couple examples:

Note that these percentages are totally separate. We can't say that 99% of the time, Honitsu is paired with a Dragon or Wind, because there are hands where Honitsu is paired with both. If a Honitsu hand had two Dragon triplets, it would also count twice (since they have different names).

Chanta has 9.28% with Riichi, and only 0.89% with Pinfu. That's pretty interesting. Doujun being so high is also neat, but makes sense given the low number of possible sets a Chanta hand can have.

Make a copy of the spreadsheet and you can go through whatever yaku you desire, and see how rare every combination of yaku is. If you'd like to see the code, you can find it here. I hope everyone is enjoying their holidays. See you in the new year!