Unremovable ko  

In this position, white has an unremovable throw-in ko. White can, at any time, play b to start a ko for the corner. Black can do nothing to remove this ko.

It is not an unremovable ko the other way around. Although black can start the ko at any time by playing a, white can remove the ko by playing a himself, creating seki.

10,000 year ko  

Black cannot remove this ko by filling, as he will die. On the other hand, White can take and fill the ko for seki.

Unremovable kos  

These two positions are well known. See Sending three, returning one.

Implications for play

These positions are hyperactive. How to play them depends upon the ko threat situation. Often play revolves around creating and destroying ko threats.

When neither player is komaster, usually the player with fewer stones at stake (White in these examples), should start the ko. Even if he loses the ko, he will get compensation elsewhere in the ko exchange. The same is usually the case when Black is komaster. (The fact that Black cannot remove the ko is no disadvantage to Black then.)

When White is komaster, however, Black is at a serious disadvantage, because he has no effective play to remove the ko. The longer he waits to start the ko, the less he gets in compensation for losing it. Therefore, as paradoxical as it may seem, Black should usually start the ko as soon as possible.

Group status implications

If an unremovable ko remains at the end of the game, it may have implications for the status of groups (depending on the rule set):

Status?  

What is the status of the white stones?

Play-out  

Black claims: They are dead.

White says: Show me.

Play goes as shown. After , white can live with a move at , or retake the ko with a move at .

Since the ko is bigger in this position, black takes with at a and white lives with at .

So what is the status of the white stones in the upper right?

Seki  

In this situation, is optimal play by black to claim seki?

Bill: I think that (under area rules or certain territory rules) Black scores 1 pt. better by "killing" the right side group in exchange for the ko.

Encore  

For instance, under Spight territory rules Black can start the encore with .

Encore (cont.)  

Play could stop at this point by agreement that the White stones on the right are dead, and the score would be 25 - 24 in favor of Black. Or White could make Black capture those stones, for the same net score. If Black does not play in the encore the result is jigo.

Seki on 6×4  

BTW I'm curious if this was already a know rules-beast, or if I was actually the first to stumble upon it.

Herman: I had never seen it before, and I've seen a lot of rules beasts already, so I wouldn't be surprised if this is a new discovery.

Bill: It's new to me. :)

Herman: I found a similar position at: http://www.harryfearnley.com/go/bestiary/molasses_ko.html (third diagram)

Clarify  

Herman: I tried to build a position like this (because you told me you'd found it on 4x6), but failed. In the given positions, after and , black would capture with at a. So white should play at a, resulting in the following:

Clarify, cont'd  

Herman So now is the ko threat white needs.