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Subject: Re: Mate in 15

Author: Tom Likens

Date: 06:30:14 04/22/04

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On April 22, 2004 at 05:04:36, Tord Romstad wrote:

>On April 21, 2004 at 22:23:53, Tom Likens wrote:
>
>>> 7    >=   #41     0.73     110603 Rf8+ Kh7 Qg8+ Kg6 Rf6+ Kxf6 Qf8+ Ke6 Qe8+
>>>                                   Kd6 Bxe5+ Kc5 Bd4+ Kd6 Qd8+ Ke6 Qd5+ Ke7
>>>                                   Bc5+ Ke8 Qe6+ Kd8 Be7+ Ke8 Bf6+
>>> 7         #15     1.06     172533 Rf8+ Kh7 Qg8+ Kg6 Rf6+ Kxf6 Qf8+ Ke6 Qe8+
>>>                                   Kd6 Bxe5+ Kc5 Bd4+ Kd6 Qd8+ Ke6 Qd5+ Ke7
>>>                                   Bc5+ Ke8 Qe6+ Kd8 Be7+ Ke8 Bf6+ Kf8 Qe7+
>>>                                   Kg8 Qxg7#
>>>
>>>Tord
>>>
>>
>>Hey Tord,
>>
>>I've been curious about this in the past.  When Gothmog announces a mate in
>>at most 41, does it actually see the mate (20+ moves!!).  And if not, what
>>is it using to bound the mate?
>
>Hi Tom,
>
>Believe it or not:  I have no clear idea why this happens.  Perhaps it is
>a result of a bug somewhere, but I haven't yet bothered to study the problem
>very closely, because it apparently is not very critical.
>
>At least I am 100% sure that Gothmog does not see any 41-move variation which
>ends in a mate.  The maximum search depth is only 60 plies.
>
>FWIW, here is the detailed search output for Gothmog in this position.
>A '>=' before a score means that the score is a lower bound, while '<='
>means an upper bound.  As you can see, the score climbs from mate in 41
>to mate in 15 very quickly (less than 2000 nodes).
>
> 1        1.62     0.00         94 Rf8+ Kh7 Qg8+
> 2        2.16     0.00        425 Rf8+ Kh7 Qg8+ Kg6 Rf2
> 3        0.00     0.07       7618 Rf8+ Kh7 Qg8+ Kg6 Qe6+ Kh7
> 4        0.00     0.12      12331 Rf8+ Kh7 Qg8+ Kg6 Qe6+ Kh7
> 5        0.00     0.24      27645 Rf8+ Kh7 Qg8+ Kg6 Qe6+ Kh7
> 6    >=  0.00     0.24      27656 Rf8+ Kh7 Qg8+ Kg6 Qe6+ Kh7
> 6    >=  0.03     0.47      63834 Rf8+ Kh7 Qg8+ Kg6 Rf6+ Kxf6 Qf8+ Ke6 Qe8+
>                                   Kd6 Bxe5+ Kc5 Bd4+ Kd6 Qd8+ Ke6 Qd5+ Ke7
>                                   Bc5+ Ke8 Qe6+ Kd8 Be7+ Ke8 Ba3+ Kd8
> 6    >=  0.19     0.48      63883 Rf8+ Kh7 Qg8+ Kg6 Rf6+ Kxf6 Qf8+ Ke6 Qe8+
>                                   Kd6 Bxe5+ Kc5 Bd4+ Kd6 Qd8+ Ke6 Qd5+ Ke7
>                                   Bc5+ Ke8 Qe6+ Kd8 Be7+ Ke8 Ba3+ Kd8
> 6    <=  0.44     0.58      80306 Rf8+ Kh7 Qg8+ Kg6 Rf6+ Kxf6 Qf8+ Ke6 Qe8+
>                                   Kd6 Bxe5+ Kc5 Bd4+ Kd6 Qd8+ Ke6 Qd5+ Ke7
>                                   Bc5+ Ke8 Qe6+ Kd8 Be7+ Ke8 Ba3+ Kd8
> 6    <=  0.41     0.59      80682 Rf8+ Kh7 Qg8+ Kg6 Rf6+ Kxf6 Qf8+ Ke6 Qe8+
>                                   Kd6 Bxe5+ Kc5 Bd4+ Kd6 Qd8+ Ke6 Qd5+ Ke7
>                                   Bc5+ Ke8 Qe6+ Kd8 Be7+ Ke8 Ba3+ Kd8
> 6    <=  0.31     0.61      81238 Rf8+ Kh7 Qg8+ Kg6 Rf6+ Kxf6 Qf8+ Ke6 Qe8+
>                                   Kd6 Bxe5+ Kc5 Bd4+ Kd6 Qd8+ Ke6 Qd5+ Ke7
>                                   Bc5+ Ke8 Qe6+ Kd8 Be7+ Ke8 Ba3+ Kd8
> 6    <=  0.19     0.62      82200 Rf8+ Kh7 Qg8+ Kg6 Rf6+ Kxf6 Qf8+ Ke6 Qe8+
>                                   Kd6 Bxe5+ Kc5 Bd4+ Kd6 Qd8+ Ke6 Qd5+ Ke7
>                                   Bc5+ Ke8 Qe6+ Kd8 Be7+ Ke8 Ba3+ Kd8
> 6        0.19     0.64      82200 Rf8+ Kh7 Qg8+ Kg6 Rf6+ Kxf6 Qf8+ Ke6 Qe8+
>                                   Kd6 Bxe5+ Kc5 Bd4+ Kd6 Qd8+ Ke6 Qd5+ Ke7
>                                   Bc5+ Ke8 Qe6+ Kd8 Be7+ Ke8 Ba3+ Kd8
> 7    >=  0.19     0.65      82293 Rf8+ Kh7 Qg8+ Kg6 Rf6+ Kxf6 Qf8+ Ke6 Qe8+
>                                   Kd6 Bxe5+ Kc5 Bd4+ Kd6 Qd8+ Ke6 Qd5+ Ke7
>                                   Bc5+ Ke8 Qe6+ Kd8 Be7+ Ke8 Ba3+ Kd8 Qg8+
> 7    >=  0.22     0.66      82365 Rf8+ Kh7 Qg8+ Kg6 Rf6+ Kxf6 Qf8+ Ke6 Qe8+
>                                   Kd6 Bxe5+ Kc5 Bd4+ Kd6 Qd8+ Ke6 Qd5+ Ke7
>                                   Bc5+ Ke8 Qe6+ Kd8 Be7+ Ke8 Ba3+ Kd8 Qg8+
> 7    >=  0.59     0.66      82430 Rf8+ Kh7 Qg8+ Kg6 Rf6+ Kxf6 Qf8+ Ke6 Qe8+
>                                   Kd6 Bxe5+ Kc5 Bd4+ Kd6 Qd8+ Ke6 Qd5+ Ke7
>                                   Bc5+ Ke8 Qe6+ Kd8 Be7+ Ke8 Ba3+ Kd8 Qg8+
> 7    >=  1.09     0.66      83052 Rf8+ Kh7 Qg8+ Kg6 Rf6+ Kxf6 Qf8+ Ke6 Qe8+
>                                   Kd6 Bxe5+ Kc5 Bd4+ Kd6 Qd8+ Ke6 Qd5+ Ke7
>                                   Bc5+ Ke8 Qe6+ Kd8 Be7+ Ke8 Bf6+
> 7    >=  1.62     0.66      83419 Rf8+ Kh7 Qg8+ Kg6 Rf6+ Kxf6 Qf8+ Ke6 Qe8+
>                                   Kd6 Bxe5+ Kc5 Bd4+ Kd6 Qd8+ Ke6 Qd5+ Ke7
>                                   Bc5+ Ke8 Qe6+ Kd8 Be7+ Ke8 Bf6+
> 7    >=  2.44     0.67      84318 Rf8+ Kh7 Qg8+ Kg6 Rf6+ Kxf6 Qf8+ Ke6 Qe8+
>                                   Kd6 Bxe5+ Kc5 Bd4+ Kd6 Qd8+ Ke6 Qd5+ Ke7
>                                   Bc5+ Ke8 Qe6+ Kd8 Be7+ Ke8 Bf6+
> 7    >=  3.44     0.77     100635 Rf8+ Kh7 Qg8+ Kg6 Rf6+ Kxf6 Qf8+ Ke6 Qe8+
>                                   Kd6 Bxe5+ Kc5 Bd4+ Kd6 Qd8+ Ke6 Qd5+ Ke7
>                                   Bc5+ Ke8 Qe6+ Kd8 Be7+ Ke8 Bf6+
> 7    >=  4.44     0.79     103186 Rf8+ Kh7 Qg8+ Kg6 Rf6+ Kxf6 Qf8+ Ke6 Qe8+
>                                   Kd6 Bxe5+ Kc5 Bd4+ Kd6 Qd8+ Ke6 Qd5+ Ke7
>                                   Bc5+ Ke8 Qe6+ Kd8 Be7+ Ke8 Bf6+
> 7    >=  5.84     0.81     103882 Rf8+ Kh7 Qg8+ Kg6 Rf6+ Kxf6 Qf8+ Ke6 Qe8+
>                                   Kd6 Bxe5+ Kc5 Bd4+ Kd6 Qd8+ Ke6 Qd5+ Ke7
>                                   Bc5+ Ke8 Qe6+ Kd8 Be7+ Ke8 Bf6+
> 7    >=  7.12     0.82     103995 Rf8+ Kh7 Qg8+ Kg6 Rf6+ Kxf6 Qf8+ Ke6 Qe8+
>                                   Kd6 Bxe5+ Kc5 Bd4+ Kd6 Qd8+ Ke6 Qd5+ Ke7
>                                   Bc5+ Ke8 Qe6+ Kd8 Be7+ Ke8 Bf6+
> 7    >=  8.16     0.83     104286 Rf8+ Kh7 Qg8+ Kg6 Rf6+ Kxf6 Qf8+ Ke6 Qe8+
>                                   Kd6 Bxe5+ Kc5 Bd4+ Kd6 Qd8+ Ke6 Qd5+ Ke7
>                                   Bc5+ Ke8 Qe6+ Kd8 Be7+ Ke8 Bf6+
> 7    >=  9.22     0.85     104376 Rf8+ Kh7 Qg8+ Kg6 Rf6+ Kxf6 Qf8+ Ke6 Qe8+
>                                   Kd6 Bxe5+ Kc5 Bd4+ Kd6 Qd8+ Ke6 Qd5+ Ke7
>                                   Bc5+ Ke8 Qe6+ Kd8 Be7+ Ke8 Bf6+
> 7    >= 10.75     0.86     104620 Rf8+ Kh7 Qg8+ Kg6 Rf6+ Kxf6 Qf8+ Ke6 Qe8+
>                                   Kd6 Bxe5+ Kc5 Bd4+ Kd6 Qd8+ Ke6 Qd5+ Ke7
>                                   Bc5+ Ke8 Qe6+ Kd8 Be7+ Ke8 Bf6+
> 7    >= 11.75     0.87     105201 Rf8+ Kh7 Qg8+ Kg6 Rf6+ Kxf6 Qf8+ Ke6 Qe8+
>                                   Kd6 Bxe5+ Kc5 Bd4+ Kd6 Qd8+ Ke6 Qd5+ Ke7
>                                   Bc5+ Ke8 Qe6+ Kd8 Be7+ Ke8 Bf6+
> 7    >= 12.75     0.90     109251 Rf8+ Kh7 Qg8+ Kg6 Rf6+ Kxf6 Qf8+ Ke6 Qe8+
>                                   Kd6 Bxe5+ Kc5 Bd4+ Kd6 Qd8+ Ke6 Qd5+ Ke7
>                                   Bc5+ Ke8 Qe6+ Kd8 Be7+ Ke8 Bf6+
> 7    >= 13.75     0.92     110005 Rf8+ Kh7 Qg8+ Kg6 Rf6+ Kxf6 Qf8+ Ke6 Qe8+
>                                   Kd6 Bxe5+ Kc5 Bd4+ Kd6 Qd8+ Ke6 Qd5+ Ke7
>                                   Bc5+ Ke8 Qe6+ Kd8 Be7+ Ke8 Bf6+
> 7    >= 14.88     0.92     110548 Rf8+ Kh7 Qg8+ Kg6 Rf6+ Kxf6 Qf8+ Ke6 Qe8+
>                                   Kd6 Bxe5+ Kc5 Bd4+ Kd6 Qd8+ Ke6 Qd5+ Ke7
>                                   Bc5+ Ke8 Qe6+ Kd8 Be7+ Ke8 Bf6+
> 7    >=   #41     0.94     110603 Rf8+ Kh7 Qg8+ Kg6 Rf6+ Kxf6 Qf8+ Ke6 Qe8+
>                                   Kd6 Bxe5+ Kc5 Bd4+ Kd6 Qd8+ Ke6 Qd5+ Ke7
>                                   Bc5+ Ke8 Qe6+ Kd8 Be7+ Ke8 Bf6+
> 7    >=   #39     0.94     110634 Rf8+ Kh7 Qg8+ Kg6 Rf6+ Kxf6 Qf8+ Ke6 Qe8+
>                                   Kd6 Bxe5+ Kc5 Bd4+ Kd6 Qd8+ Ke6 Qd5+ Ke7
>                                   Bc5+ Ke8 Qe6+ Kd8 Be7+ Ke8 Bf6+
> 7    >=   #36     0.94     110680 Rf8+ Kh7 Qg8+ Kg6 Rf6+ Kxf6 Qf8+ Ke6 Qe8+
>                                   Kd6 Bxe5+ Kc5 Bd4+ Kd6 Qd8+ Ke6 Qd5+ Ke7
>                                   Bc5+ Ke8 Qe6+ Kd8 Be7+ Ke8 Bf6+
> 7    >=   #35     0.94     110731 Rf8+ Kh7 Qg8+ Kg6 Rf6+ Kxf6 Qf8+ Ke6 Qe8+
>                                   Kd6 Bxe5+ Kc5 Bd4+ Kd6 Qd8+ Ke6 Qd5+ Ke7
>                                   Bc5+ Ke8 Qe6+ Kd8 Be7+ Ke8 Bf6+
> 7    >=   #32     0.94     110763 Rf8+ Kh7 Qg8+ Kg6 Rf6+ Kxf6 Qf8+ Ke6 Qe8+
>                                   Kd6 Bxe5+ Kc5 Bd4+ Kd6 Qd8+ Ke6 Qd5+ Ke7
>                                   Bc5+ Ke8 Qe6+ Kd8 Be7+ Ke8 Bf6+
> 7    >=   #31     0.94     110799 Rf8+ Kh7 Qg8+ Kg6 Rf6+ Kxf6 Qf8+ Ke6 Qe8+
>                                   Kd6 Bxe5+ Kc5 Bd4+ Kd6 Qd8+ Ke6 Qd5+ Ke7
>                                   Bc5+ Ke8 Qe6+ Kd8 Be7+ Ke8 Bf6+
> 7    >=   #28     0.94     110854 Rf8+ Kh7 Qg8+ Kg6 Rf6+ Kxf6 Qf8+ Ke6 Qe8+
>                                   Kd6 Bxe5+ Kc5 Bd4+ Kd6 Qd8+ Ke6 Qd5+ Ke7
>                                   Bc5+ Ke8 Qe6+ Kd8 Be7+ Ke8 Bf6+
> 7    >=   #27     0.94     110925 Rf8+ Kh7 Qg8+ Kg6 Rf6+ Kxf6 Qf8+ Ke6 Qe8+
>                                   Kd6 Bxe5+ Kc5 Bd4+ Kd6 Qd8+ Ke6 Qd5+ Ke7
>                                   Bc5+ Ke8 Qe6+ Kd8 Be7+ Ke8 Bf6+
> 7    >=   #26     0.94     111081 Rf8+ Kh7 Qg8+ Kg6 Rf6+ Kxf6 Qf8+ Ke6 Qe8+
>                                   Kd6 Bxe5+ Kc5 Bd4+ Kd6 Qd8+ Ke6 Qd5+ Ke7
>                                   Bc5+ Ke8 Qe6+ Kd8 Be7+ Ke8 Bf6+
> 7    >=   #25     0.96     111259 Rf8+ Kh7 Qg8+ Kg6 Rf6+ Kxf6 Qf8+ Ke6 Qe8+
>                                   Kd6 Bxe5+ Kc5 Bd4+ Kd6 Qd8+ Ke6 Qd5+ Ke7
>                                   Bc5+ Ke8 Qe6+ Kd8 Be7+ Ke8 Bf6+
> 7    >=   #24     0.96     111461 Rf8+ Kh7 Qg8+ Kg6 Rf6+ Kxf6 Qf8+ Ke6 Qe8+
>                                   Kd6 Bxe5+ Kc5 Bd4+ Kd6 Qd8+ Ke6 Qd5+ Ke7
>                                   Bc5+ Ke8 Qe6+ Kd8 Be7+ Ke8 Bf6+
> 7    >=   #23     0.96     111705 Rf8+ Kh7 Qg8+ Kg6 Rf6+ Kxf6 Qf8+ Ke6 Qe8+
>                                   Kd6 Bxe5+ Kc5 Bd4+ Kd6 Qd8+ Ke6 Qd5+ Ke7
>                                   Bc5+ Ke8 Qe6+ Kd8 Be7+ Ke8 Bf6+
> 7    >=   #22     0.96     111955 Rf8+ Kh7 Qg8+ Kg6 Rf6+ Kxf6 Qf8+ Ke6 Qe8+
>                                   Kd6 Bxe5+ Kc5 Bd4+ Kd6 Qd8+ Ke6 Qd5+ Ke7
>                                   Bc5+ Ke8 Qe6+ Kd8 Be7+ Ke8 Bf6+
> 7    >=   #21     0.97     112213 Rf8+ Kh7 Qg8+ Kg6 Rf6+ Kxf6 Qf8+ Ke6 Qe8+
>                                   Kd6 Bxe5+ Kc5 Bd4+ Kd6 Qd8+ Ke6 Qd5+ Ke7
>                                   Bc5+ Ke8 Qe6+ Kd8 Be7+ Ke8 Bf6+
> 7    >=   #20     0.97     112485 Rf8+ Kh7 Qg8+ Kg6 Rf6+ Kxf6 Qf8+ Ke6 Qe8+
>                                   Kd6 Bxe5+ Kc5 Bd4+ Kd6 Qd8+ Ke6 Qd5+ Ke7
>                                   Bc5+ Ke8 Qe6+ Kd8 Be7+ Ke8 Bf6+
> 7    >=   #19     0.97     112777 Rf8+ Kh7 Qg8+ Kg6 Rf6+ Kxf6 Qf8+ Ke6 Qe8+
>                                   Kd6 Bxe5+ Kc5 Bd4+ Kd6 Qd8+ Ke6 Qd5+ Ke7
>                                   Bc5+ Ke8 Qe6+ Kd8 Be7+ Ke8 Bf6+
> 7    >=   #18     0.97     113099 Rf8+ Kh7 Qg8+ Kg6 Rf6+ Kxf6 Qf8+ Ke6 Qe8+
>                                   Kd6 Bxe5+ Kc5 Bd4+ Kd6 Qd8+ Ke6 Qd5+ Ke7
>                                   Bc5+ Ke8 Qe6+ Kd8 Be7+ Ke8 Bf6+
> 7    >=   #17     0.97     113468 Rf8+ Kh7 Qg8+ Kg6 Rf6+ Kxf6 Qf8+ Ke6 Qe8+
>                                   Kd6 Bxe5+ Kc5 Bd4+ Kd6 Qd8+ Ke6 Qd5+ Ke7
>                                   Bc5+ Ke8 Qe6+ Kd8 Be7+ Ke8 Bf6+
> 7    >=   #16     0.98     113891 Rf8+ Kh7 Qg8+ Kg6 Rf6+ Kxf6 Qf8+ Ke6 Qe8+
>                                   Kd6 Bxe5+ Kc5 Bd4+ Kd6 Qd8+ Ke6 Qd5+ Ke7
>                                   Bc5+ Ke8 Qe6+ Kd8 Be7+ Ke8 Bf6+
> 7    >=   #15     0.98     114327 Rf8+ Kh7 Qg8+ Kg6 Rf6+ Kxf6 Qf8+ Ke6 Qe8+
>                                   Kd6 Bxe5+ Kc5 Bd4+ Kd6 Qd8+ Ke6 Qd5+ Ke7
>                                   Bc5+ Ke8 Qe6+ Kd8 Be7+ Ke8 Bf6+
> 7    <=   #15     1.27     172533 Rf8+ Kh7 Qg8+ Kg6 Rf6+ Kxf6 Qf8+ Ke6 Qe8+
>                                   Kd6 Bxe5+ Kc5 Bd4+ Kd6 Qd8+ Ke6 Qd5+ Ke7
>                                   Bc5+ Ke8 Qe6+ Kd8 Be7+ Ke8 Bf6+ Kf8 Qe7+
>                                   Kg8 Qxg7#
> 7         #15     1.28     172533 Rf8+ Kh7 Qg8+ Kg6 Rf6+ Kxf6 Qf8+ Ke6 Qe8+
>                                   Kd6 Bxe5+ Kc5 Bd4+ Kd6 Qd8+ Ke6 Qd5+ Ke7
>                                   Bc5+ Ke8 Qe6+ Kd8 Be7+ Ke8 Bf6+ Kf8 Qe7+
>                                   Kg8 Qxg7#
>
>Tord

It's possible (probable) that this is an artifact of the hash table.
Gothmog *could* be grafting on large sub-trees via the TT so that
the apparent depth really is 41 etc. (I'm guessing like the rest of
us you adjust the depth of all mates retrieved from the hash table).

Interesting anyway, like you, I wouldn't worry too much if it isn't
causing you any real problems and it's actually kinda cool.

--tom



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