Analysis - Danger of Tiles Near Dora

I wanted to do a quick analysis looking at the waits of riichis based on what the dora is, to see how much more dangerous tiles near the dora are. Instead, I ended up going a bit insane.

Methodology

• 1.5 million Houou hanchans
• If the dora is an honor, that round isn't looked at.
• Anytime someone discards a dora or calls and reveals one, the number of visible dora is increased
• When someone calls riichi, their waits are recorded. Each tile within the dora suit is counted once, but tiles in other suits are only collectively counted once (so a 28 shanpon would log 2 and 8 to the dora suit, but if it was in another suit, it would log "other suit" once). The round is then skipped, so only first riichis are counted.

Now, let's look at the chart for completely live dora.

As expected, the dora tiles are more dangerous. Depending on the tile, somewhere around 50~100% more dangerous than they usually are.

You can also see the influence the dora indicator has. In the 5 row, 45 and 56 are both shapes using the dora, but 45 is less likely because one 4 is the indicator. So, the 3 has a lower rate than the 7. This doesn't bear out as well for the 12/89 waits since those have less shapes (a 2 wait can be 13, 2, 22, or 34, while a 6 wait can be 57, 6, 66, 45, or 78).

The rate of a wait being in the other suits is very high with a 1 dora. I think this can be attributed to opening decisions. When you're cutting terminals, you'd cut the one that's the indicator first, since it has one less chance to pair up. Then, the terminals from the other suits have an extra turn to become blocks, and from there, waits.

The 8 and 9 having a much lower other suit rate... We'll get to it. Let's look at the data for one of the dora tiles being visible first.

Okay, why would one being visible cut the danger in half?

Let's think. 1) The player calling riichi did not call the dora. If they had a valid yaku, they might do that, so them not calling makes it less likely they're waiting on it. 2) The player calling riichi might have cut it themselves. ... Yeah I should account for that.

Time to redo the analysis but ignore riichis from players who discarded the dora. Please hold for 100 minutes...

Alright that makes a bit more sense. Let's get the other charts in here too. Here's with two visible:

At this point, the number of visible middle dora are really affecting the ease of making shapes in that suit.

And with 3 visible. This could be a dora pon, or just three of them being discarded:

Alright. So, what's going on with the 8 and 9 doras?

First of all, let's consider that the dora indicator affects all of their shapes. If you want to wait on an 8, you need a 67 or 79 shape. The dora indicator is 7, so it's removing a tile from both. And if you're keeping the 6 around hoping it connects to the 8, it's a bit more likely that you connect with the 4 or 5. Then, you're also less likely to complete runs like 678. Incomplete shapes like 68 or 88 (with 1 or 2 visible) become more likely.

That's my best guess as to why the waits are more often in the same suit with those doras.

With the 2 on the other hand, the indicator is 1. 13 is affected, but 34 is not. The dora indicator points upwards, so the lower tiles are less affected than the higher tiles. It's still quite surprising it's to this degree, though. I checked the code and reran the analysis like three times because I didn't quite trust it.

I also recorded the ukeire as part of my debugging. With 0 visible, the average ukeire is 6.2~6.32. It increases slightly with each visible, up to 6.44~6.53 at 3 visible. The lower bound is always for the dora being 9, and the upper bound is among 2~8 doras.

I suppose the big takeaway from this is that the dora for the round significantly affects how hands develop, much more than I expected. You can see all the data in this spreadsheet.

Bonus: I can flip the check to make it only look at riichis where the player discarded the dora pre-riichi. Here's how that ends up looking: