PJTraill: This article should start with a definition (and perhaps an overview) before plunging into details; I infer the above from the rest of the article, although it is not explicitly stated. If someone has access to an authoritative source (e.g. Gokyo Seimyo), would they please correct the definition if necessary, perhaps add another sentence of summary, and remove this annotation?
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Neither player can win the capturing race by playing first. The explanation on why this is so follows.
Suppose Black captures at . Then captures the Black stones in a snapback.
Black has no better move than to play to reduce White's liberties. But and clearly wins the capturing race by three liberties to two.
Suppose captures, then makes a placement.
makes an approach move, forcing to capture three White stones. However, when makes the necessary placement, wins the capturing race by two liberties to one.
Now suppose plays elsewhere. To prove that Black still can win this capturing race, can play inside White's eye. Later, captures, forcing the placement at , and 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.
In summer 2011, Harry Fearnley, working on variations of this problem, discovered a new type of seki :
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.
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.)