Parity seki

  Difficulty: Advanced   Keywords: Life & Death

A parity seki is a special kind of seki where one of the players can remove any of the common liberties in sente so that the other player must reply by removing another one of the common liberties.

The status of the groups is decided by the parity of the common liberties: if there are an even number of common liberties, the situation is a seki, otherwise it is possible for the side with the sente moves to kill.

Parity Seki

[Diagram]

Parity seki example

This is a parity seki. White can remove any pair of liberties in sente, but finally the groups will have two common liberties, and the result is a seki.

[Diagram]

Pairs of common liberties

The liberties come in pairs so that whenever white plays at one of the lettered points, black must respond at the other same lettered point.

[Diagram]

Even parity: white cannot kill

White can remove any pair of liberties whenever she wants. However, after each black response, the liberty count is restored to an even number, and finally, there are only two common liberties left, and the result is a "regular" seki.

Actually, any white play here is an unremovable ko threat that does not lose points. To see why, let's take a look at what happens if black tries to play here.


Odd parity

[Diagram]

Parity "seki", odd parity

If black were to remove one of the liberties, the parity now becomes odd. White can now kill, because after each white threat and black response, the parity of the common liberties is odd. This means that black would have to play a self atari at the end.

[Diagram]

Odd parity: white can kill

After W3, black cannot connect because of a lack of liberties.


Restoring parity

[Diagram]

W2 elsewhere, parity seki restored

If white does not kill black immediately, black can restore parity, and the position is a parity seki again. So, it could, in theory, be possible for black to play here all alone, and the status of the group would alternate between seki and killable.

In reality, black should of course not play this way.

[Diagram]

W2 elsewhere, parity seki avoided

If black got two moves in a row here, then he'd better make a regular seki instead. While white still has two ko threats, now one of them is removable, and the unremovable one will cause a big loss if black responds.


Other parity seki shapes

[Diagram]

Parity seki with three groups

[Diagram]

Parity seki with bamboo joints

[Diagram]

Parity seki with extended bamboo joints

Kudos to asmobia for this shape.


See Also


This is a copy of the living page "Parity seki" at Sensei's Library.
(OC) 2014 the Authors, published under the OpenContent License V1.0.
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