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May 1998's Go Answer of the Month

I recently requested readers to send me any non life_and_death problems that they would be happy for me to use here. Andre Engles sent me this endgame problem.

Dia 1 & 2 - What is the best move for Black? What is the best move for White?

Dia 1   Dia 2

When this problem was originally presented, it was posted with Dia 2. The presence of the lower of the two black stones on the right in that diagram inhibits the tesuji-ness of the correct answer! Dia 1 is therefore the one primarily discussed in the answers. For completeness I also explain why Dia 2 prevents the tesuji being effective.

Apparently this is a well-known endgame problem which most 1 kyu players get wrong when they meet it in a game. At 2 kyu I would have got it wrong!

If anyone disagrees with these answers, please email me .

Dia 3 - The area counted for comparisons.

Dia 3

In order to get relative counts, I'm counting territory and prisoners in the 18 point area marked here. Also, arbitrarily, I am scoring everything from White's point of view.

First let's look at the problem with Black to play.

Dia 4 - Black's obvious but incorrect move.

Dia 4 Black 3 takes sente elsewhere.

Generally, we assume that a sente sequence such as this is better than a gote sequence. Here Black tenukied with 3 to take sente elsewhere.
We observe here that White can push with 4 and 6 and end up with 5 white points to 2 black ones, a white surplus of +3 points in sente for Black.

Had Black played 3' at 4 in gote, then the white surplus would have been -1, 4 points better for Black. When it gets to the stage in the game that there are no other Black sente moves worth 2 points or more (half the 4 point difference here) and all the gote moves are smaller than 4 points then Black should play this way with 3'.
Not that Black should have reached here in the first place.

Dia 5 - The correct black move.

Dia 5 Black 3 takes sente elsewhere.

The only difference between Dias 4 & 5 is that White has pushed two points further into Black's territory in Dia 4. So, pointwise, Dia 5 is better for Black and it is equally sente for him.

The jump to the first line, 1, is the tesuji here.

Now let's look at the problem with White to play. We obviously expect a different result to the 'Black plays first' situation.

Dia 6 - White's obvious and incorrect move.

Dia 6 White 3 takes sente elsewhere.

The key thing in an endgame sequence is knowing when to stop. Generally sente is worth having, and a small move that becomes gote should be avoided. Playing 3' at 4 is one point better (7) but is gote. Playing 3' at 6 is sente but doesn't alter the score in the end.
Here, in Dia 6, 1 forces 2 and 4 forces 5. 6 and 7 are dame, shown for completeness of the diagram. The result - a white surplus of +1 with sente for White.

Dia 7 - The right white move.

Dia 7 White 5 takes sente elsewhere.

Playing the tesuji move of 1 here, still permits White to take sente, as was the case in Dia 6. However Black's border is remains incomplete. If Black gets to play here first, descending to the edge then the score is the same as Dia 6. But if White manages to play here first, he can push further into Black's territory forcing Black to play on the two points marked '?'.

What is first move here worth?

Both correct sequences are sente, so this is a double sente situation and should be played as soon as the yose move value gets to the relevant level.
If Black plays first, white's surplus is +1. If White plays first, it is either +1 or +3 (call it +2, a difference of 1 point).
This suggests to me that if both players play correctly, then these moves are worth very little and should not to be played until the one point border pushes occur.

Now to review the problem of Dia 2.

Dia 8 - If Black plays the 'wrong' move.

Dia 8 Black 3 and 9 take sente elsewhere.

The presence of the lower stone on the right means that after this sequence, Black has no need to connect above 7, he therefore gets one extra point and he gets yet another sente move.
In this circumstance, White should push once with 4 and refrain from pushing again with 6.

And if White plays in Dia 2.

Then the result should be similar to Dia 7, except White would not attempt to gain the '?' points as Black again has no need to connect and the one point extra for White is gote.


None of these answers were what I was expecting when I presented the problem. The value of the moves are all much smaller than I thought they would be.

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