Analysis - The Last Two Discards Of A Suit

In this post, we'll look at how a player's riichi tile, combined with the previous tile of that suit they discarded, affects the frequency of their ending waits. What does it mean when they cut a pair? Does it matter if they cut their kanchan starting from the inside or the outside? Let's find out.

For this, we'll only look at riichis that were on a non-honor tile. For the riichi tile, we have nine options, one through nine. For the previous tile in the suit, we have ten options, one through nine and also the case where they hadn't discarded any. Note that there may be other tiles in between. This is a total of 90 pieces of data. So, rather than look at it all at once, we'll go through it based on the kind of discard pattern it is.

We'll start with the case where they riichi without having discarded anything else in the suit. This case has the least information.

There's a lot of data here. It's even bleeding over the sidebar, and blogger's update makes that annoying to fix. Oh well. Let's just go through it column-by-column. In the first column, the pattern is shown. In this case, it's all the situations where they had no other tile in that suit. The next six are the modifiers for that ryanmen's usual rate. So, with a None->5 pattern, the 1-4 and 6-9 sujis are present almost twice as often. The next column is for when they have a ryanmen in a different suit.

The next four columns show other types of wait. In order, when they have a bad wait in the same suit, when they have a bad wait in a different suit, when they have a wait involving two tiles in any suit(s), and when they have a wide wait in any suit(s). The 2 Types column will be shanpon (2277), kantan (2224), and pentan (1112) shapes. The final column simply sums the first four.

All of these percents are multipliers for the original rate of that thing occurring. So, a 200% means it's twice as likely, while a 50% means it's half as likely.

Let's check out some other patterns so we can start comparing. We'll go through various shape cuts, starting with when they cut a pair (toitsu otoshi).

When they cut a pair, the matagi suji gets really safe. For example, with the 4->4 drop, a 34 or 45 ryanmen becomes really unlikely. So, the 1-4 and 4-7 suji become furiten, and the 2-5 and 3-6 suji become unlikely. The remaining two suji, 5-8 and 6-9, go up in danger to compensate. Another interesting thing here is that, with a 5->5 pattern, the chance of a bad wait in that suit doubles.

How about when they cut a kanchan? There are two options for each kanchan, as they could cut starting from the outside or the inside.

Here, the matagi suji of the first tile cut becomes safer, but the remaining suji become crazy dangerous. Just look at the numbers for 5->3 and 5->7. These patterns usually discount half of the suji in the suit, so it makes sense that the ones that remain are more dangerous. Also, for say the 5->3 discard, it could be a 2335 shape, where the 5 comes out easily and then the 3 is cut to riichi with a ryanmen. Matagi suji, at it again.

Another thing to note with these is that multiple squares can affect a certain tile. For example, in the 2->4 case, the 3-6 suji has a modifier of 173%, and the 6-9 has a modifier of 150%. A 6 deals into both of these, so it's affected by both increases. Anyway, let's check out another shape cut that kills a lot of suji, a ryanmen cut.

Most of these are strongly red, but there's some green smattered about. Most amusing of which is the 5->4 that waits on a 1-4 furiten. The squares are colored gray if they're less than 10%, but this furiten happens so often it escapes that. 

Let's look at the 4->5 vs 5->4 when it comes to a 3-6 wait. This would be a shape like 4455. If you don't have the red five already, you'd want to cut the 4, because then drawing the red would complete a triplet of fives. If you already have the red, then you'd want to cut the 4, because if you cut a 5 then drew another 4, the red five might have to go now that you have a triplet of fours.

As for the outer ones, such as 2->3 and 3->2, I'd think that's due to a 223 shape being easier to pon from than a 233 shape. Plus, the more outside tile will be safer to cut later.

We've covered all the shapes now. Next, let's see what it means when they cut both ends of a suji, such as 1 and 4.

Like with the kanchans, the matagi suji of the first tile discarded is made safer, while the matagi of the riichi tile is made dangerous, exempting the 1->4 and 9->6 patterns since the terminals don't have matagi. Something notable is that the 3-6 and 4-7 discards drastically lower the chance of a bad wait in that suit, the lowest we've seen.

Finally, a post like this wouldn't be complete without looking at aida yon ken.

2-7 and 3-8 patterns also result in a very low bad wait chance. Overall this mostly matches the data I've gathered before about aida yon ken. You can also see the usual "first tile matagi safe, riichi tile matagi dangerous" pattern with the 2-7 and 3-8 ones.

If you're curious about any other patterns or just want to see the full data, you can find it in this spreadsheet.