Hanezeki

    Keywords: Life & Death

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Table of contents

Introduction

[Diagram]
Hanezeki  

Both sides have a string in atari, but for either side, capturing starts a capturing race that the other side can win. Best play is to leave this, therefore it's seki.


Why is hanezeki a seki

Neither player can win the capturing race by playing first. The explanation on why this is so follows.

[Diagram]
Black first (W2 at white+circle)  

Suppose Black captures at B1. Then W2 captures the Black stones in a snapback.

[Diagram]
Black first (W6 at white+circle)  

Black has no better move than to play B3 to reduce White's liberties. But W4 and W6 clearly wins the capturing race by three liberties to two.

[Diagram]
White first (B2 at black+circle)  

Suppose W1 captures, then B2 makes a placement.

Note that both players have a big eye each. By capturing the three Black stones, White has made his own eye small. See big eye - small eye for more.

[Diagram]
White first (W5 at white+circle)  

W3 makes an approach move, forcing B4 to capture three White stones. However, when W5 makes the necessary placement, B6 wins the capturing race by two liberties to one.

[Diagram]
White first (W3 and W5 elsewhere, W7 at white+circle)  

Now suppose W3 plays elsewhere. To prove that Black still can win this capturing race, B4 can play inside White's eye. Later, B6 captures, forcing the placement at W7, and B8 again wins the capturing race by one move.



To conclude, the player who starts the capturing race first loses it instead. Therefore, the hanezeki is effectively a seki.

The Most Difficult Problem Ever has a beautiful example from the Igo Hatsuyoron of a (maybe temporary) Hanezeki, involving the sacrifice of 20 stones to make even more stones live!

In summer 2011, Harry Fearnley, working on variations of this problem, discovered a new type of seki :

[Diagram]
Circular hanezeki  



This situation is especially counterintuitive: the main semeai is me-ari me-nashi (one eye vs no eye), but it is nevertheless a complete seki, with 5 unplayable mutual liberties.


Terminology

The locus classicus of the term hanezeki is Volume 3 of Hayashi Genbi's Gokyo Seimyo (folio 9, verso). He gives one example.

That alone makes the attribution to Kaise Takaaki (though I'm not at all sure that Ikeda says that anyway) wrong by a century, but in fact the earliest known case of hanezeki is the problem called Zheng Li (Wrestling) in the Xuanxuan Qijing (Gateway to All Marvels), so that puts the date back to 1347 straightaway!

Hanezeki is also sometimes wrongly called itazeki from confusion with the first character.

Note: elsewhere, hanezeki may be referred to by the terms, haneseki, or hane seki.

Also known as hanazeki or hana seki. (For the latter see the GokyoSeimyo, vol. 3, p. 18. The former is a common elision, where s becomes z.)


See also


Hanezeki last edited by 194.78.35.195 on November 28, 2013 - 10:22
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