A puzzling endgame ko fight

[hexahedron]

Here’s a fun position I discovered today when playing with a game variation for 8x8.

White has just captured the final endgame ko. Black is entirely out of threats, except for the local move at A. White currently also has no threats. If both players play the best moves from here…

• What will the result be under Chinese rules?
• What will the result be under Japanese rules?

For reference if you want to score, komi is 9, which is the fair value for 8x8 under Japanese rules, and if you count stones on the board you will find that white has net captured 3 more black stones than black has captured white stones.

Hint:

After black plays A3, white can respond with G6. G6 is not a threat, but...

Also posted on reddit:

r/baduk - A puzzling endgame ko fight

[yebellz]

Thoughts

It seems that the top-right having some aji is essential here. I’m not sure if I’ve read this correctly.

So, after Black at A3, the move by White at G6 is not an immediate threat, but it gives White the ability to play a ko threat in that area (like at H5, maybe?). So, if Black then continues by taking the ko at A5, White can play a threat in the top-right to take that ko back.

However, does White have enough threats to eventually win the ko fight on the left? I guess the answer must be yes for this position to be interesting. It seems that Black can continue to resist by extending their stone out at A2? White also needs to either capture A3 first or connect at B4 before being able to win the ko by finally filling A5.

[jlt]

Thoughts

I don’t see how White can win the ko.

[hexahedron]

@yebellz

You're close.

You can assume that when white spends a move in the ko at a free moment when black has no threat, white will always connect B4, rather than capture at A2. As long the group still has plenty of liberties so that it doesn’t enable more black ko threats and White doesn’t need the eyes - both true in this case - then connecting B4 instead of capture at A2 is the standard good shape because it means that white will lose less the future if black somehow still wins the ko (because now there’s no followup capture for black if black is winning the ko). Of course, that doesn’t matter here because white is planning to win the ko outright, but it’s still a good instinct and means there’s no reason to even consider white capturing at A2 - does that make sense?

Obviously, this then means you can entirely disregard black extending at A2. Black A2 is a waste of a move because if white hasn’t connected B4 yet, then it doesn’t do any better job of delaying white from winning the ko than A3 already does alone, and if white has connected B4 already, then it’s just a dead stone and doesn’t even create any ko threats.

Does that help? With those variations out of the way, is it easier to read?

@jlt

Try a different ko threat for W4, one that doesn't leave black a way to then eliminate all ko threats.

Hint for the last ko threat in one of the variations:

If black had an extra eye somewhere, then white could do nothing. But black's only eyespace is the upper left.

[antonTobi]

Thoughts

I thought this white 4 was promising:

In this variation, white could continue by connecting at B4 and then there is a ko threat at C8.

But this 5 is an issue:

So maybe this 4 instead?

It’s actually not threatening to live outright, but white can ignore the B2 ko threat and win this ko:

(or even respond to B2 and use H8 as a local ko threat!)

But I don’t see any followup here:

This 4 almost works…

It looks like white has a threat at D8, but reducing black to one eye is not enough here since after black cuts at H6 it’s eye vs no eye:

So how about this 4, taking a liberty from G7 so that if black cuts at H6 in the future F8 still keeps an eye?

Then this continuation is working for white, because D8 is a real threat (with B8 being the followup to create seki):

This move slightly confuses things, but I think white can just respond at F8 and black didn’t change anything:

This 4 is perhaps clearer, not even giving the option of E8:

Continuation is same as before, white can win the ko thanks to D8 threat:

Final area score is black 36 - white 28, with 9 komi white wins by 1 point

Did I stumble upon the correct solution? (I started this post just wanting to share my failed solution, but then I got some new ideas while making the variation diagrams )

Edit: I think correct play looks the same under Japanese rules? White loses by 1 point if she gives up the ko, and makes jigo if she wins the ko. At first I thought that since white spends two moves in a row inside the black territory (2 and 4 in the second to last diagram) this would lose one point, making the ko meaningless to fight. But it’s made up for by the fact that black also spends two moves in a row (5 and 7 in the last diagram).

Edit 2: Wait a minute… I guess that means that black should not play 7 under Japanese rules, but just pass. Supposing then that white still has to fill B4 and A5, black still wins by 1 point!

[hexahedron]

Very nice!

There is actually a learnable lesson from this puzzle. Occasionally, your opponent may play a local “ko threat” that isn’t actually a threat. Black A in this puzzle is an example of such a move. It doesn’t threaten anything or have any immediate followup for black, or directly help black themselves win the ko. It solely stops white from winning the ko until responding to it (and also increases the temperature of the ko by making it a bit more costly for white to lose). Basically it makes it into an approach ko for white.

So white has a free moment to generate ko threats. If white can generate sufficient threats in one move, then instead of fighting a direct ko where white has no threats left, white will be fighting an approach ko where they do have many threats left, and the latter can be better!

Here’s another example of a position where you can make multiple ko threats in one move

Black in this position has no ko threats at all. However, if black plays A, even though this move is dead in gote, now black has 4 big threats B-E. If black was fighting a critical approach ko or preparing for a thousand year ko, A might be a good move, and correspondingly if there is an ongoing approach ko or a thousand year ko on the board, it might be good for white to play A themselves to stop black from generating these threats.

---

In the original puzzle for this thread, it works for white in Chinese rules because dead in gote moves don’t have a cost, if it is the very last thing on the board.

Under Japanese rules it doesn’t work, because the ko is tiny. White is hoping to do only 1 point better than normal. A dead in gote move to generate threats is always going to cost at least 1 point, so it doesn’t help.

But even in Japanese rules, if you are fighting an approach ko or a thousand year ko worth more than one point, then dead in gote moves to generate threats can become good.

Or, you maybe you can find moves that generate threats that don’t cost any points at all. Here’s a contrived example where white can do so with a dame move, losing nothing, while generating 3 new ko threats.

Under Japanese rules, at the moment black plays the “local-threat-that-isn’t-a-threat” move of A to win the final win half-point (1/3-point) ko fight, depending on the board white may be able to win the game by playing the dame move of B, which threatens nothing in gote, but creates 3 new threats at C, D, E.

[antonTobi]

I made a video talking through some of the variations

Can white win this ko?

It includes some extra variations that I missed in my first post above (what happens if black doesn’t immediately recapture the ko after white sets up ko threats?).