[Retros] Happy New Hebrew Year

Noam D. Elkies elkies at math.harvard.edu
Thu Sep 21 15:39:14 EDT 2017

I wrote:

>> With such a fakakte stipulation :-) one shouldn't have to also resort to
>> three promoted Bishops.  I think this position works in 17.0 (BTM)
>> and without having to keep track of the current convention for
>> "dead reckoning":

>> https://www.janko.at/Retros/d.php?ff=2k5/P7/1P6/p7/P5pp/4p1P1/4P1KP/n2B2b1

andrew buchanan <andrew at anselan.com> replies:

> That's really delightful. The stipulation form is basically about
> turning endgames into enumeration problems, and I think that will
> play to your strengths as an endgamer. [...]

Thanks.  Yes, I think I'm thus also entitled to kvetch [sic] about
the stipulation . . .

> So Black must play Kb7 very soon, because otherwise White will promote
> and win. But 1. Kb7? gxh4! 2. Bf2 h5 3. Be1/Bh4 f6 4. Bc3/Bf6 Kg3
> (4... h7? 5. Be5!) and Black has no defensive line. bPg4 falls,
> and Black cannot take wPh2 without allowing wPh6 to promote,
> as wK can cover e5.

Basically yes, though I think even the 4 ... h7 5 Be5 line is a White win:
h3 6 g3 h4 7 Ka8 h5 8 Kb7 h6 9 Ka8 h8Q+ 10 Bxh8 Kxg3 and 11 ... h7
and White is basically a King up, and can win by capturing e3,
or marching to g8 and playing h8Q, or just going straight to d7
and then ...Kc8 (after ...a8Q+ if necessary) and b7+.

> Thus play must begin 1. h3! Kf1/Kxg1/Kh1 2. Kb7 Kxg1/Kf1-Kh1/Kxg1.
> Critically, not 2... Kxe1? Bf2+! 3. Kf1 and is trapped.

2... Ke1? (not a capture) Bxh2 3 Kf1 Bxg3 is even simpler.

> So after White's second turn there are 0,1,2,1 ways for wK to have
> reached e1,f1,g1,h1. This adds to 4, which is L_3 = 3rd Lucas Number [...]
> turn 17 we hit the magic value 5778.


> I wonder only if it might be possible to lighten the pawns on the
> right hand side. Perhaps you tried remove the g-pawns before.

Yes I did, also with other variations (e3+ instead of h3+,
wN instead of wB, other ways to block d1).  I didn't find
anything more economical.

> At the very least try to remove bPh4 & move sPg3 to h3.

I'm worried that then 1 ... Kxh3 2 Kb7 Kg3 3 Bf2+ Kf4 or Kg4
may then be at least good enough to draw, and even if it
turns out that Black has a forced win I think it's worth an extra
pawn or two to avoid that distraction.


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