Author: Tom Kerrigan
Date: 11:50:47 07/28/98
Go up one level in this thread
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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