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Subject: Re: computer calculations of number of ways to play first 10-ply

Author: Tom Kerrigan

Date: 11:50:47 07/28/98

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You're right. Your suggestion has downgraded the problem from impossible to
slightly less impossible. :)

Cheers,
Tom

On July 28, 1998 at 12:31:23, blass uri wrote:

>
>On July 28, 1998 at 12:15:54, Tom Kerrigan wrote:
>
>>Based on the name of this thread, I assumed we were counting the "number of ways
>>to play first 10-ply" instead of the number of possible positions.
>
>You are right but in order to compute the number of ways to play the first 10
>plies you do not have to count everything
>if you computed the number of ways to play after 1.a3 a6 b3
>you know the number of ways to play after 1.b3 a6 2.a3 is the same
>and you can save time by this way.
>
>Cheers,
>Uri
>>
>>Cheers,
>>Tom
>>
>>On July 28, 1998 at 09:34:47, blass uri wrote:
>>
>>>
>>>On July 28, 1998 at 09:17:42, Tom Kerrigan wrote:
>>>
>>>>I know that the number of 4-ply variations is 206,604 because I use that as a
>>>>first sign that my move generator is working correctly.
>>>>
>>>>The 4th root (the approx. branching factor) of 206,604 is 21.31, so the number
>>>>of 10 ply variations is ~ 1.931232214271e+13. The real number is probably
>>>>actually much higher, because mobility for the first few ply is very limited, so
>>>>the branching factor will generally increase as the game goes on.
>>>>
>>>>Assuming this [probably very low] number of positions and the ability to visit
>>>>1,000,000 positions per second (a pretty good clip...) it would take about 36
>>>>years to visit all of these positions.
>>>
>>>The same position can be reached in more than 1 way so the number of positions
>>>should be smaller for example if we look in the position after
>>>a3 a6 b3 b6 c3 c6 d3 d6 e3 e6 white have 120 options to play in another order
>>>and black has 120 option so the position can be reaced in 120*120=14400
>>>ways.
>>>If you have unlimited hash table you can decreae the time by a factor of
>>>thousands.
>>>
>>>Uri
>>>>
>>>>In other words, you're not going to get an exact answer anytime soon.
>>>>
>>>>Cheers,
>>>>Tom
>>>>
>>>>On July 28, 1998 at 04:17:57, Neil Carlson wrote:
>>>>
>>>>>Please forgive a stranger/beginner if I am breaching any rules of etiquette or I
>>>>>missed something in the archives or FAQ (I did look).
>>>>>
>>>>>Can anyone help or suggest a source for information on the following?
>>>>>
>>>>>Although computer chess is only effective if the programs focus on the
>>>>>"sensible" moves to make in a given position, I'm trying to find out if anyone
>>>>>has looked into the question of the huge numbers of ways to play a chess game -
>>>>>specifically, the number of ways that the first ten ply (first 20 half-moves)
>>>>>can be played; or the possible number of move combinations for a whole game
>>>>>(with some kind of sensible limit - 40 or 60 moves).
>>>>>
>>>>>I thought this might be the sort of thing that could have some significance for
>>>>>computer chess, so someone might have done this or know of someone who has.
>>>>>
>>>>>Thanks for your time and attention,
>>>>>
>>>>>Neil



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