Author: blass uri
Date: 09:31:23 07/28/98
Go up one level in this thread
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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