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Subject: Re: Mate in 38.

Author: Uri Blass

Date: 19:31:33 01/25/01

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On January 25, 2001 at 21:48:06, Heiner Marxen wrote:

>On January 25, 2001 at 20:41:50, Paul wrote:
>
>>On January 25, 2001 at 20:31:55, Heiner Marxen wrote:
>>
>>>On January 25, 2001 at 19:40:58, Paul wrote:
>>>
>>>>On January 24, 2001 at 19:39:52, Dan Andersson wrote:
>>>>
>>>>>[D]1R6/6pK/5p2/4p3/1B1p3n/8/p1p1pp2/1k3b2 w - - 0 1
>>>>>Krabbé (1985)
>>>>
>>>>I just tried this position with my program Pretz, after having unsuccesfully
>>>>grappled with the mate in 16/20 positions by José Antônio Fabiano Mendes
>>>>(I ran out of patience :) and indeed get a mate in 38! It's amazing!
>>>>
>>>>02:17 WM38 09 1. Ba3+ Ka1 2. Bb2+ Kb1 3. Bxd4+ Kc1 4. Be3+ Kd1 5. Rd8+ Ke1 6.
>>>>Bd2+ Kd1 7. Bb4+ Kc1 8. Ba3+ Kb1 9. Rb8+ Ka1 10. Bb2+ Kb1 11. Bxe5+ Kc1 12. Bf4+
>>>>Kd1 13. Rd8+ Ke1 14. Bd2+ Kd1 15. Bb4+ Kc1 16. Ba3+ Kb1 17. Rb8+ Ka1 18. Bb2+
>>>>Kb1 19. Bxf6+ Kc1 20. Bg5+ Kd1 21. Rd8+ Ke1 22. Bd2+ Kd1 23. Bb4+ Kc1 24. Ba3+
>>>>Kb1 25. Rb8+ Ka1 26. Bb2+ Kb1 27. Bxg7+ Kc1 28. Bh6+ Kd1 29. Rd8+ Ke1 30. Bd2+
>>>>Kd1 31. Bb4+ Kc1 32. Ba3+ Kb1 33. Rb8+ Ka1 34. Be7 c1=Q 35. Bf6+ Qb2 36. Rxb2
>>>>e1=Q 37. Rb8+ Qe5 38. Bxe5x
>>>>
>>>>I used 96MB hash and full ply extensions on check and one-rep, and some
>>>>other tricks :) Does this look ok? Has anyone else tried this position?
>>>>
>>>>Groetjes,
>>>>Paul
>>>
>>>That looks ok to me.
>>>From a 1993 posting of Dennis Breuker:
>>>
>>>An implementation of proof-number search (a kind of conspiracy-number
>>>search) finds the intended solution in 225752 nodes (86 seconds)
>>>on a SPARC-2.
>>>
>>>He gives the exact same solution as you do.
>>>
>>>Heiner
>>
>>Thanks for checking that for me. I couldn't believe it at first!!
>>
>>I really hope some other programmer will also try this, coz I don't use
>>proofnumber search, just 'plain' alpha-beta. Didn't know it was possible.
>
>Since the solution line is nearly completely forced, that does not
>look so impossible to me.  I would expect that some programs do find this one,
>depending on the nature of extensions they do.
>
>>Heiner, is it out of reach for Chest? What do you think?
>>
>>Paul
>
>Yes, that is absolutely out of reach for Chest.  The problem is not to find
>the solution, but to prove all the non-solutions up to a depth of 38.
>For depth 9 Chest needs 111 seconds, and increasing the depth by one,
>multiplies the search time by 4.  Do the math and be shocked.  ;-)

The assumption of branching factor of 4 is not always correct.

In order to prove that the mate in 38 is the shortest mate you need only to
prove that white has no alternatives.

I do not know if it is possible to do it in this case but it may be possible

In order to do it it is enough to prove that after every alternative of white
except 1.Ba3 black can force a mate or a repetition(proving a mate or repetition
can be easier than proving only mate).

It is possible that you need an hour to prove for every move of white in the
first 29 moves that it is singular and in this case you need only 30 hours to
prove the mate(I guess that you can prove the last mate in 9 in an hour).

Uri



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