Analysis - Fu Rates in Non-Limit Hands

I haven't had much time this week to put together a substantial analysis, so we'll look at something quick: the rate of each han fu combination in Houou hands.

Part of the reason why I haven't had much time is that I wrote a Mahjong Discord bot! You can add it to your server at this link if you own a Mahjong-related server. There are definitions, ukeire calculations, memes, and more!

Anyway, onto the analysis. When talking about the score table, I'll often tell people, "You don't have to memorize the whole thing. Just remember the 20, 25, and 30 fu columns and you'll know most of the hands that come up." But, just how much is "most of the hands"?

Well, let's find out. Here's a score table, but with all the scores replaced with the percentage each score appeared in my dataset of 8,535,286 winning hands. You can click on it to expand it.

The first thing that jumps out is that the 30 fu column is more than two thirds of all winning hands just by itself. If you add in the 40 and 20 fu columns (which are the same values), you have around 95% of all non-limit hands covered.

Since the dealer 20 fu column is the same as the non-dealer 30 fu column, that means you only have to remember the dealer 30 fu, non-dealer 30 fu, and non-dealer 20 fu to know how to score almost all hands.

The 25 fu columns are pretty easy to remember since it's a linear doubling. If you add that, you also get the 50 fu columns, since those are the same series, and your coverage jumps to around 99.6% of non-limit hands. Considering 60 fu is the same sequence as 30 fu, that brings it up to 99.9%.

In the data set, there were zero 110 fu non-limit hands, and zero 100 fu dealer hands. There were only four 2 han 100 fu non-dealer hands. The total number of 90 fu hands was nineteen, across both. So, you can pretty much ignore everything past 80.

The 70 fu column is a bit annoying, since it's unique, but remembering it only gets you an extra 0.08% or 0.09% of coverage. At least there's only four cells.

Well, this post was short and not particularly enlightening, but it did answer some questions I had. You can find the data in this spreadsheet. You can see the code used to generate the data on GitHub. Back to the Mahjong grind! See you next time.