Broken Keima = Empty Triangle? | Tewari Delight #2

Tewari (手割り) has been one of my favorite concepts in Go for a long time, especially due to its usefulness in helping us avoid mistakes and inefficient moves.

In case you're wondering, Tewari Delight #1 doesn't exist as an article yet, it was actually a video originally .

As a teaching aid, about a year and a half ago, I found myself wanting an example of how not to do it though. After a bit of searching through the web, I ended up on the How to lie with tewari page, on Sensei's Library.

In it, a discussion about the following shape popped up:

Dia. 1.

An adaptation of the board position on the "How to lie with tewari" page, causing a heated discussion on Sensei's Library.

The original diagram had move 2 at B, the stone at 2 would already be in place. One of the first arguments in the discussion was that, if 2 were already there, then Black should play at A. Which is actually not true, it's still better to play at B, having a clean broken keima is better in that case.

Anyway, it's much more common for us to see that shape as the peep on the tiger's mouth, with the solid connection at 2 as a supposedly inevitable follow-up.

If that sequence were to happen as in Dia. 1, what would you think? Optimal for both sides? Better for Black? Better for White?

One point of view would be White ending up with with a broken keima shape, evidenced by the square stones cutting through the triangle keima:

Dia. 2.

White ends up with a broken keima.

However, it's also true that Black arrives at an empty triangle:

Dia. 3.

Black arrives at an empty triangle.

In this case, two things are true at the same time. The local board position is still slightly better for Black — after all, White has two very damaged stones — but it could have been worse for White. Overall, by playing suboptimally here, Black incurred a near-point loss.

Let's analyze this a bit further. Shifting this pattern to the 4-4 will make things clearer for now:

Dia. 4.

The same problem, but transposed to a modern, post-AI joseki.

If we apply tewari to the similar position in Dia. 4, we can easily see that move number 6 should have been B instead. White 5 is clear nonsense; and the post-AI, modern joseki is for White to play at A instead.

Similarly, if Black were to connect from the direct peep, White would try to revert back to Dia. 4:

Dia. 5.

White tries to get back to the subpar version of the post-AI joseki.

Through that joseki analysis, it's more obvious that the end result isn't ideal for Black. But how should Black better play then?

Unexpectedly, globally, even if Black plays the correct punishment, AI's evaluation is B+1.5 only. Black connecting at 2 gets us back to an even game, at B+0.5. Apparently, a broken keima evens out with the empty triangle at the beginning of the game.

Black should then strive for a more efficient shape. Instead of connecting at 4, maybe we could try capturing the A stone directly:

Dia. 6.

Black tries to justify connecting at 4.

White shouldn't give Black a clean ponnuki here, but it is nonetheless a surprising move to descend at 3, considering that we will eventually arrive at the broken keima shape from 1 to A. From Black's perspective, it is finally satisfactory to connect at 4, since White invested another stone at 3.

Locally, White would follow things up with C, going back to the familiar modern joseki once again. White 3 might seem like a near total waste, but the aji around the 3-3 at B, or D, has increased a lot.

What happens if we move this pattern back to the center of the board?

Dia. 7.

The same pattern, but now in the center of the board. Black should now atari at 2 instead of 3.

The same rationale still applies. However, AI now recommends ataring from 2 instead of 3. Both Black and White should prioritize the corners though, if they are empty.

Last year, I converted this analysis into a video on my English YouTube channel, in a partnership with Go Magic:

Towards the end of the video, unfortunately, I accidentally mixed some things up, and said that, in the case of a broken keima in the center, if the corners are open, both players should still go for them, instead of completing or preventing the broken shape.

Dia. 8.

Should we play at A or go for open corners?

Black should absolutely complete the broken keima at A. It is a bit surprising that not doing so is only a 2-point loss, however. What I meant to say in the video was that Black shouldn't play at A and go for corners if we had a stone at B already.

Comparatively, a broken jump is much worse than a broken keima. But by how much?

Dia. 9.

What's the cost of not playing at A?

If Black plays for a corner this time, instead of a 2-point loss, we get into a near 6-point deficit.

So there you go:

• Broken Keima = Empty Triangle
• Broken Jump = Broken Keima - 4
• Broken Jump = Empty Triangle - 4

That's simple math for you. Relatively true. Absolute nonsense.