Analysis - Flush Overflow

Today we'll be talking not about toilets, but about honitsu or chinitsu hands. It's often said that a flush hand becomes particularly dangerous once they cut the first tile of their suit (known as overflow), so let's dive into the Houou replays and see what the data says.

My dataset has expanded to include games up to the end of 2020, increasing the sample size to 1,539,555 replays. In these, there's a bit over four million instances of an overflow occurring that the analysis captures.

We'll only be looking at open hands, since it's easier to know whether they are going for a flush. We'll also stop looking at a particular player if anyone in the game calls riichi. This will prevent a lot of folds from being counted as overflows, though some of the overflows could still be folds against non-riichi hands.

A hand will be looked at if their calls are "flushy." This means that the hand has at least one suited call, and all their calls are either that suit or honors. A hand that has called a chii with circles and a pon of dragons will be counted, while a hand that has ponned two winds will not be. A hand that has called a chii of circles and a chii of bamboo will also obviously not be counted. Closed kans will be counted as calls, so, for example a player with only a closed kan of circles will be counted as having flushy calls.

An overflow is counted when a flushy hand discards the first tile from their suit.

That's enough about methodology, so let's get into the data.

First, let's look at the chance that their hand is a flush, if they haven't discarded any tiles of their suit, or have just overflowed. Overflows will be separated into tedashi and tsumogiri. Karagiri will be counted as tsumogiri.

With one call, an overflow actually reduces the chance of a flush, but let's wait until we see the tenpai data.

With two calls, the chance of a flush after an overflow still goes down, but not as drastically as with one call. This data could be from hands that have one honor call and one suited call, or two suited calls.

With three calls, we now see the chance of a flush going up after a tedashi.

Now, how often are they tenpai? We'll look at two separate numbers. The chance they are tenpai at all, and the chance that they're tenpai for a flush specifically. Let's start with one call.

 

I've looked at tenpai chance after calling a while ago, in Analysis - Shanten After Calling. Feel free to compare those charts. This chart isn't the moment of calling, so the numbers are quite different.

Something interesting here is that if the overflow is tedashi, the flush tenpai chance is higher when compared to tsumogiri, while for any tenpai, the tenpai chance is higher with tsumogiri.

Next, two calls.

 

These follow the same patterns as the previous charts, but the numbers are higher. Now, the three call data.

 

Very high tenpai chances for three calls, as you would expect.

These charts show that overflow does indeed make tenpai more likely. It's interesting that it also greatly increases the chance of tenpai for non-flush hands. Let's compare the chance of a flush with two calls to the chance of it being tenpai for the flush. We've seen these charts already, I'm just putting them side by side for ease of use.

 

If we look at say, turn 10, the chance of a flush after a tedashi overflow is about 15%. The chance of it being a flush tenpai is about 10%. So, about 66% of two-call flushes that overflow on turn 10 will be tenpai.

The raw data is separated into three different spreadsheets. The data for the flush tenpai chance can be found here, the data for any tenpai chance is here, and the data for the chance of a hand being a flush is here.