HermanHiddema/Shapenaji - Aguilar - analysis

Initial position  

This extremely interesting position is (simplified) from a game between shapenaji and aguilar, presented on GoDiscussions

Table of contents Black forces direct ko, black takes first White makes four step ko Black avoids and makes double ko seki White forces double ko seki with two step ko Conclusion

Table of diagrams Initial position Black starts, W2 @ WW Symmetrical situation Exchange internal threats Black takes first White starts (B4 @ BB) Exchange ko's (B8 @ WW) B12 @ BB, W13 @ WW Ko position White starts (B4 @ BB) Exchange ko's (B8 tenuki) Exchange ko's (B8 tenuki) B4 @ BB, W5 @ WW, B6 takes ko The earlier ko (W7 ko threat, B10 ignored, B12 @ BB) Double ko seki (W13 ko threat, B14 ignored)

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Black forces direct ko, black takes first

Black starts, @

Symmetrical situation

Exchange internal threats

Black takes first

Black has the option of playing -, making a direct ko which he takes first.

White makes four step ko

White starts ( @ )

Exchange ko's ( @ )

@ , @

Ko position

White can make ko like this. This is a very difficult ko for white, white will need at least four more ko threats than black to successfully win this ko due to the approach moves required!

Black avoids and makes double ko seki

White starts ( @ )

Exchange ko's ( tenuki)

Exchange ko's ( tenuki)

If white actualy has the ko threats for this, then black can avoid the variation by not playing , but like this, making double ko seki. In this case, black gets one free move elsewhere with .

White forces double ko seki with two step ko

@ , @ , takes ko

The earlier ko ( ko threat, ignored, @ )

Double ko seki ( ko threat, ignored)

If white does not have four, but has two more ko threats, White can fight the earlier ko and can make double ko seki.

Conclusion

Black is in no hurry to play this position, the worst that can happen to him is double ko seki in exchange for a free move elsewhere. White cannot force anything until he feels he can ignore two ko threats in order to force double ko seki.

If the position remains on the board until the end of the game, then under Japanese rules white is dead, while under Chinese rules it must be played out. Since black will win the ko if there are no ko threats, black will usually win in that case as well. If, however, there is one unremovable ko threat for white elsewhere (eg: due to seki), then black can choose not to play, in which case the position ends up as seki. Since black can always force double ko seki, there is never any point for white in starting the ko after the game, no matter how many unremovable ko threats.