Unremovable Ko Threat / Discussion

This position is seki as it stands. Black can play any of the 1-2 points as what seems to be a threat that loses nothing:

If Black plays (or ) as a ko threat and White resolves the ko, then Black captures a stone, turning the original seki into an 8 point territory.

If White answers, then Black hasn't lost points: the position is still seki.

White on the other hand doesn't even have a threat here: Black can safely resolve the presumable ko and the position is still seki. What's worse: White has now created a chance for Black to play A and turn this into a 10 point territory.

This is why Black's ko threat is "unremovable": Black can play the threat, White can't remove it.

Note however how Black's ko threat and White's answer results in a simple seki, where both now have a ko threat. The value of the threat is huge: Black can make 10 points and White can make 18.

How will this situation play out?

Suppose first the case where White has no ko threats, or more generally, Black is ko master.

Black should wait for the temperature to drop below before treating this as an unremovable ko threat.

If White wins the ko (value X) and Black executes his threat, Black gains 8-X. As long as the temperature Y is higher than 8, hence the value of the ko, Black can gain Y-X by letting White win the ko.

If WHite answers Black threat here, Black takes back the ko and now it's White to find a threat. The biggest threat on the board is the corner itself and White risks losing 10 points. The value of the ko should be close to the temperature on the board which was not higher than 8. So White has no good reason doing so. She needs to play a less valuable threat and Black can resolve the ko.

Suppose now White is ko master.

Then Black can use this as an extra threat, to topple White as ko master, still for kos that are smaller than 8.

-- Dieter