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Subject: Re: Mathematical impossibilities regarding Deep Blue statements by Bob

Author: Ricardo Gibert

Date: 08:23:35 01/31/02

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On January 31, 2002 at 08:38:31, Uri Blass wrote:

>On January 31, 2002 at 08:33:32, Ricardo Gibert wrote:
>
>>On January 30, 2002 at 12:11:16, Robert Hyatt wrote:
>>
>>>On January 30, 2002 at 11:00:58, Alexander Kure wrote:
>>>
>>>>On January 30, 2002 at 10:25:41, Robert Hyatt wrote:
>>>>
>>>>[..]
>>>>
>>>>>You can make up all the math you want, but it doesn't prove anything.  I
>>>>>_know_ that DB's branching factor was roughly 4.0, as was discussed _here_
>>>>>a few years ago after several of us looked carefully at their logs.
>>>>>
>>>>>to go to depth 18 requires 4^17 as many nodes as searching to one ply.
>>>>>4^17 = 2^18, = 262,000 roughly.
>>>>
>>>>4^17 = 2^34
>>>>
>>>>[..]
>>>>
>>>>
>>>>Greetings
>>>>Alex
>>>
>>>
>>>You are right.  Wasn't thinking clearly at the time, obviously.
>>>:)
>>>
>>>Bob
>>
>>But at the time, you must have thought you were thinking clearly or you surely
>>would not have made the post. This raises the question of, "How do you know you
>>are thinking clearly now?" ;-)
>>
>>Nothing "obvious" about it, yes?
>>
>>Setting aside my stupid jokes, the serious question now is: "Isn't 2^34 a bit
>>too big for Deep Blue?"
>
>200M nodes/second*180 seconds=36*10^9>2^34

2^34 figure is how many times more nodes must be searched than a 1 ply search
(see http://www.icdchess.com/forums/1/message.shtml?210884). If we make the very
generous assumption that the BF at the root is only 4 (at least 30 actually. RH
assumed 100 for example), then the inequality becomes 3.6E10 < 6.4E10.

When you factor in that this assumes iterative deepening is not employed, then
it is not even close. I will admit that it is closer than I originally thought,
however.

>
>2^34 nodes is not too big for a machine that can calculate 200M nodes per
>second.
>
>Uri



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