Analysis - Wait Reading against Open Hands

There are some popular theories about what waits are dangerous against certain calls. Let's take a look.

Let's get the disclaimers out of the way:

• This data is from 1.5 million Houou hanchan games. At lower levels reading is less reliable.
• This is looking at when someone makes their second call on the second row, and they're only counted if they're tenpai. Two calls on row two is tenpai more often than not (in Houou) but the actual deal-in rates of the tiles will be lower than is shown here.
• Replays stop being analyzed if someone calls riichi.

Okay, let's go over the theories one by one.

Theory 1) You can't read much from pons

The standard theory is that there are so many possibilities after a pon that for the most part you can't make any reads based off them. For example, pon and cut 3 could be making a head out of a 344 shape, or it could be making a ryanmen out of a 334 shape.

There are a lot of rows with pons, so I'll just show from 1~5. The rest are mirrors of that anyway. To start, let's look at someone calling pon and discarding a tile from the same suit.

Click to enlarge.

These cells are coloured based on the usual danger of those tiles. White means it's about as dangerous as non-suji, red means it's more dangerous, and the deepest green is when it's about as dangerous as a suji version of that tile. The grays are when the rate is very low, often furiten or hell waits.

Now, why is 555->8/9 dangerous, but 555->1/2 not dangerous? Probably a quirk of these cases only having 1000~3000 entries.

Let's look at pons with a follow up discard from a different suit.

Not really any surprises here. They're all pretty close to their normal values, no dark reds or dark greens.

Verdict: Yeah, you can't read much from pons.

Theory 2) Chii -> Related Tile is Safe

In standard theory, something like calling a 34 ryanmen then discarding a 3 or 4 makes that area safe. This is clearing up a 344 or 334 shape, and thus, the discard is likely unrelated to their wait. Let's look at the data. I'll also include the ryankans here, since calling 3 on a 24 and cutting 6 is also cleaning up a shape, but I'll leave out the outside hands for now.

The first digit in the "Call" column is what tile they called. So, 567 is calling a 67 ryanmen with a 5, and 867 is calling a 67 ryanmen with the 8. 657 is calling a 57 kanchan with a 6, etc.

That checks out. The area around the discard is made safer, while the opposite side retains some danger.

Verdict: True!

Theory 3) Chii -> Unrelated Tile is Dangerous

The opposite of the previous case. The tile after a chii is supposed to be dangerous, if it doesn't hit the above case. Let's first look at when they chii, then cut tiles in the same suit, beginning with kanchan chiis.

Looks good so far. The further away from the call, the more dangerous. Ryanmen next.

Some of these are kuinobashi style calls. For example, the first in the row, 423->5 waiting on 3-6. That means the shape was 23455, then they called the 23 and cut the 5 to change from a shanpon to a 45 ryanmen.

The theory seems to largely hold up here, with the exception that cuts "outside" of the call (eg 345->2) don't really get dangerous.

Now, let's go over to when they cut a tile of a different suit, starting with kanchans.

Most of these aren't really significantly more dangerous than usual, especially when the tile cut is in the middle. There are a lot of ryanmen cases here and they can't be filtered out like when it was the same suit, so let's just look at a chunk of them here.

Things get a bit more dangerous than with the kanchan chiis, but overall about the same.

Verdict: True in the same suit, different suit is more complicated. But, definitely not safe, so treating them as dangerous is fine.

Theory 4) Kuinobashi

I had a post about kuinobashi before, so I won't go into deep detail. But, these are calls people do specifically to improve their wait. In that post, I didn't have the calculation capabilities I have now, so I had to resort to looking at their winning tile. Here's the first image from that post, but using this dataset:

As you can see, the kuinobashi waits are quite dangerous. This pretty much completely matches the image from the other post, so I won't bother gathering all of them, it takes quite a while to organize this.

Verdict: Extremely yes.

Bonus) Outside Hands

I separated out chiis involving terminal tiles from the previous sections. These could be yakuhai hands, or they could be chanta or flush hands. Here's what those are, first for discarding into the same suit:

Very dangerous when they cut opposite of the chii.

Now, for discarding into a different suit. There's a lot of rows here so I have to cut out the 789 penchan call, but it's close to a mirror of the 312 anyway.

Less dangerous. Looks pretty close to the other chiis.

You can find all the data in this spreadsheet.