Guide/Analysis - Defense Techniques: Kabe and One-Chance

Another common defense technique is kabe, or in English, wall or blockade. When you can see four of a tile, the player can't have that ryanmen, and sometimes it also removes the chance of kanchan. There's also one-chance, when you can see three of a tile. Let's check out how safe they are.

This data was gathered from 1,246,147 Houou games. Every time a player discarded a tile against a riichi player, I checked how many nearby visible tiles there were (+/- 2 from the discarded tile) and counted it and whether it dealt in.

This led to some fairly hostile data. For each tile, there are five options: 0, 1, 2, 3, or 4 visible. With a middle tile, such as a 4, five different tile counts get checked (the 2, 3, 4, 5, and 6). So, that means that there are around 5^5, or 3125 rows in the dataset for every middle tile. In total, there are 54,744 rows. So, rather than throw spreadsheets around, I'm going to condense them into graphs.

Let's look at kabe first, starting from when a 1 is walled off. To be specific, this data is for when you can see X ones, 4 twos, and 1 three, and the one is not suji. Being able to see all the twos means they couldn't have a 23 ryanmen, so, does that make the 1 as safe as suji? For comparison, I'll also include the non-suji and suji deal-in rates as dotted lines.

When it's the first 1, it's not quite safe. That makes sense. When you can see all the twos, the ones are very hard to use. So, if you can't see them, where are they? But, if you can see another 1 somewhere, then it's about as safe as suji, and if you can see two, then a shanpon is impossible and it would need to be a hell wait tanki, making it very safe.

As mentioned, another strength of kabe is its ability to deny other shapes. If you can see all the threes, then they can't have a 34 ryanmen to wait on a 2, but they also can't have a 13 kanchan waiting on a 2. In situations like these, the kabe can make the tile safer than suji, since it's denying two wait types.

Let's look at a chart for discarding a two when you can see 4 threes and 1 four. For this, I added up all the counts for different amounts of ones visible from 0 to 3, as the data would be very thin looking at only one.

Even if it's the first 2, it's usually safer than suji. You can't even see the musuji line on this graph. For comparison, let's look at the chart for when you can see 1 three and 4 fours. It's also kabe, but it doesn't deny the kanchan like the 3 kabe does.

This more resembles the kabe 1 graph. The first one isn't safe, but the later ones are. There are just under twenty thousand instances of this happening, which is why the lines are so jaggy.

Now, how about one-chance? When you can see three of a tile, there's only one left for the opponent to be using for that shape. Logically, this should reduce the chance of them having that shape. If you can see 3 twos, then they'd need the last two to have a 23 ryanmen. What are the chances of them having it, and it not being in the wall or the other players' hands?

Let's look at the ones again. This chart is for when you can see 3 twos and 1 three.

Early on, it is a bit safer, but as the game progresses, it can become even more dangerous than a non-suji tile. Not something you should rely on if you have any other options. Note that the fourth tile's deal in rate is about the same as the third tile. If included on the graph, the lines would mostly overlap.

How about for the two, where having 3 threes visible makes it harder to have both the ryanmen and the kanchan?

These are safer for longer compared to the ones, but still quickly become unreliable in the mid to late game. In summary, keep an eye out for kabe, but don't fret too much about looking for one-chances unless you're truly desperate.

For a taste of how unreadable the data is, here's all the possible one-chance shapes for a 1.

Click the image to make it bigger, if you really want to. The numbers on the left say how many tiles are visible. For example, 132 means there is 1 one visible (the one being discarded), 3 twos visible, and 2 threes visible. If you want to see ALL the data for some reason, you can find it in this spreadsheet.