Analysis - Sotogawa Effectiveness by Turn and Tile

We've talked about sotogawa before, but the exact effectiveness and extent wasn't really clear. Does a 4 discard create sotogawa tiles? How late can a tile come out before not counting for sotogawa? I dug into the Houou replays hoping to answer these questions.

First, a quick recap on what sotogawa is, for those who may not be familiar. Sotogawa is a theory that says tiles outside of those discarded by a player are safer. So, if they had an early 3 discarded, the 1 and 2 in that suit would be safer. It makes sense, because shapes like 113, 233, 334 are all strong and would be kept for a while.

For this analysis, I used pretty much the same method as in the Tile Deal-in Rates By Live Suji analysis, except instead of counting live suji, I counted what discard the sotogawa tile first came out on. When there wasn't a sotogawa tile, I counted the turn they called riichi. So, the columns for non-sotogawa and sotogawa tiles are actually different data, so don't compare those.

The columns for the sotogawa rows mean, "When the sotogawa tile came out on turn X, this is the deal-in rate for the tile." The columns for the non-sotogawa rows mean, "When the riichi was declared after X discards, this is the deal-in rate for the tile." Confusing, I know.

I looked at every tile that could be even vaguely argued as sotogawa. If they had a 5 in their discards, I counted it as creating sotogawa for every tile above and below it. A 4 or 6 would count for 123 and 789 respectively, and so on.

Anyway, let's take a look at the full, granular chart, then condense the data into something more readable.

As always, clicking the image will make it bigger. Sotogawa actually occurs quite often. There are 1,700,433 instances of a non-sotogawa non-suji 1 discarded. The total for the three sotogawa tiles is 1,319,101, so almost half of the discards had some sort of sotogawa going on. If you compare the deal-in rates for the non-suji non-sotogawa tiles, they are higher than the non-suji rates seen in my previous Tile Deal-in Rates By Live Suji post, for this reason.

Simply by looking at the colors, we can see a couple interesting things. First of all, all of the possible sotogawas make the tiles safer, except for an early 5 making the 19 more dangerous (because of chantaoutside hand and ura-suji). Additionally, no matter when the tile came out, it makes the outer tiles safer, though the later, the less reliable.

Still, this chart is very hard to read. Let's condense it!

This makes everything much easier to compare. There are some interesting things. Please look at the 4 / 6 column in the non-suji first 6 discards quadrant, and compare it with the suji rates. A 4 in the first six discards makes 2 and 3 almost as safe as suji, which is incredible. I didn't expect such a high effectiveness.

Another interesting thing is the early 4/6 with a suji 1/9. When the suji comes out early, it makes it less reliable (though still very safe). This can again be attributed to chantaoutside hand, I think. The not-sotogawa suji 1 would be suji created post-riichi.

Suji 4/6 becomes very safe when there's also a 5 in the discards before riichi. This is because having a 5 in the discards pre-riichi mostly removes the possibility of a kanchanclosed wait, and a tankisingle wait or shanpondual-pon wait 4 with a 5 in the discards is also strange. These reasons are also why a 5 makes the non-suji 46 slightly less dangerous (but still very dangerous).

For the full chart, check out this spreadsheet, which has all the different types of suji and sotogawa, including riichi suji, half-suji, and riichi nakasuji. Turns out sotogawa is pretty powerful.