Forum for Multi-stage ko

In principle, there can be very long multi-stage kos... [#2720]

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tapir: In principle, there can be very long multi-stage kos... (2011-12-21 11:55) [#9152]

As there are two eyes at stake in the three stage ko already, I wonder whether there are any examples of more stages, where those additional stages have to be fought. I have a little trouble imagining that.

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RobertJasiek: Re: In principle, there can be very long multi-stage kos... (2011-12-21 12:46) [#9153]

Imagine two hell kos: one is the colour-inverse of the other.

tapir: Re: In principle, there can be very long multi-stage kos... (2011-12-21 13:55) [#9154]

One hell is enough for me. My imagination is limited, an example would be easier for me.

RobertJasiek: Re: In principle, there can be very long multi-stage kos... (2011-12-21 14:26) [#9155]

To repeat, a hell ko is a simple multi-stage ko so that only the successive (current or potential) ko shapes are affected while the surrounding groups are independently alive. Put one such long hell ko on the board. Then copy it but swap colours in the duplicate.

68.124.184.174: Re: In principle, there can be very long multi-stage kos... (2011-12-21 16:18) [#9156]

Bill:

[Diagram]
Multi-stage ko  
RobertJasiek: Re: In principle, there can be very long multi-stage kos... (2011-12-21 16:56) [#9158]
[Diagram]
Two hell kos  


Now, if one player plays in the one hell ko, the opponent can play in the other hell ko. "hell ko" because either side's single stones can all die if the a player may make successive captures.

MrTenuki: Re: In principle, there can be very long multi-stage kos... (2011-12-21 20:13) [#9159]

Now the hard part: What's the optimal play for both sides in this position under Ing Rules? (Sorry, couldn't resist ;-)

tapir: Re: In principle, there can be very long multi-stage kos... (2011-12-21 20:41) [#9160]

What I meant was a long multi-stage ko where both sides are committed to play it as such. Given you evaluate the threat situation correctly, there likely will be a point in the "five stage" ko of Bill where it is correct play to just connect instead of fighting the ko further. As opposed to that in the clearer examples of three stage kos, one or both sides have their life at stake and are committed to playing the ko until the end, without an option for compromise. As winning three stages already includes two eyes, I indeed have trouble to imagine longer multi-stage kos w/ both sides committed to playing it to the final stage.

In Roberts example, there is no ko fight because the situation is miai, then indeed one side will play all moves in one ko, the other in the other one. But this isn't really different from two standard kos being miai.

107.210.159.110: Re: In principle, there can be very long multi-stage kos... (2019-12-21 01:51) [#11463]

Professor Berlekamp studied long multi-stage kos back in the 1980s. Assuming no large payoff at either end, then as long as the play is at least four ko mouths from each end, connecting a ko is not the hottest play. The gain from taking a ko asymptotes to 3 pts. of territory.

 
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