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Subject: Re: Number of legal positions for KQk (hello Dieter)

Author: Guido

Date: 15:53:59 03/10/02

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On March 10, 2002 at 13:38:10, Dieter Buerssner wrote:

>On March 10, 2002 at 04:23:21, Rafael Andrist wrote:
>
>>On March 10, 2002 at 02:29:18, Les Fernandez wrote:
>>
>>>Sometime ago Dieter had provided me the following info regarding number of legal
>>>KRk positions:   wtm = 175,168     btm = 223,944
>>>
>>>Does anyone know the same figures for KQk for wtm and btm ?
>>
>>KQK:
>>phyically distinct positions:
>>wtm: 144508
>>btm: 223944
>
>I get the same number here. The later is easy to calculate: 3620 legal KK
>positions times 62 squares for the Q.
>
>>logically distict positions:
>>wtm: 22589
>>btm: 34968
>
>But for this, I get different numbers. Perhaps, I do not understand your meaning
>of logically distinct. The easier case is btm, because all positions with legal
>KK are legal. There are 462 "logically distinct" legal KK positions (with the
>idea of Nalimov, to restrict one K to a triangle, for example a1-d1-d4, and when
>the K is on the diagonal, restrict the other K to a big triangle a1-h1-h8).
>There will be 62 squares for the Q left, which makes 62*462=28644 different
>positions. For white to move, not all positions are legal, and I get 18492
>different legal positions.
>
>My numbers are also different to those Guido has posted ...
>
>Regards,
>Dieter

I follow the same logic, but the value you obtain 462*62=28644 doesn't take into
account that positions of the Queen/Rook are not 62 when the two Kings are on
the diagonal a1h8. There are 21 of such positions for the Kings, and in these
cases the Queen/Rook has only 34 square. Therefore:

28644 - 21*(62-34) = 28056

Using the same reduction it is possible that you obtain the same number as me
also for wtm.

Ciao
Guido




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