On Tue, Jun 19, 2018 at 12:03 PM, Marcel Crasmaru <crasma...@gmail.com> wrote:
>> White can start one ladder as a ko threat to take back the middle ko, and 
>> black will then take the top ko.

> I claim that White cannot  use the ladders as a ko thread because:
> - if W plays R4 as a ko threat then B responds with S4
> - if next W takes a ko back on the board then B kills the group
> locally by playing S6: the left ladder is no longer a ladder and if W
> gets out of the right ladder then the bottom W group ends in 2
> liberties and B can capture it
>
> Is the above reasoning sound?

Thanks for correcting me. You're right White can't use the ladders as
ko threats.

I also seem to have confused the formula expressed by the choice gadgets.
If we call the three kos x,y,z from top to bottom, then a succesfull
White ladder amounts to
(x || y) && (y || z). Which is equivalent to y || (x && z).
So with y currently false, and White unable to flip it, White should
take the bottom ko to make z true.
Black can the make x false, but that allows White to make y true,
after which she can successfully escape
in a ladder.

regards,
-John
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