> Black can the make x false, but that allows White to make y true, after which 
> she can successfully escape in a ladder.

I think you are right and the solution is W takes at z, B is forced to
take at x, W is forced to take at y and no matter what B does next W
escapes from one of the ladders and makes the group alive.

Now the question is how hard is to program a tsumego solver for this
(kind of) problem.

Cheers,
Marcel

On 19 June 2018 at 11:35, John Tromp <john.tr...@gmail.com> wrote:
> 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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