Jesús Muñoz
Joined: 13 Jul 2011
Posts: 690
Location: Madrid, Spain.
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 Post subject: Final Perft(14) estimate after averaging 400 MC samples. Posted: Tue Apr 10, 2012 7:21 pm |
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Hello!
I finally end my experiment running the last thirteen MonteCarlo Perft(14) samples this afternoon:
| Code: |
perftmc 14 (GNU 5.07.173b w32):
388) m=6.189325e+019 sd=1.107188e+016 ci(99%)=[6.186473e+019,6.192177e+019] n=501281536 sdn=2.478919e+020 t=1804.30s
389) m=6.189283e+019 sd=1.104337e+016 ci(99%)=[6.186438e+019,6.192127e+019] n=501279684 sdn=2.472531e+020 t=1818.23s
390) m=6.187348e+019 sd=1.046049e+016 ci(99%)=[6.184653e+019,6.190043e+019] n=501279868 sdn=2.342028e+020 t=1808.17s
391) m=6.189113e+019 sd=1.061620e+016 ci(99%)=[6.186378e+019,6.191848e+019] n=501279281 sdn=2.376889e+020 t=1804.75s
392) m=6.191932e+019 sd=1.046622e+016 ci(99%)=[6.189236e+019,6.194628e+019] n=501279929 sdn=2.343312e+020 t=1780.16s
393) m=6.187486e+019 sd=1.030452e+016 ci(99%)=[6.184832e+019,6.190141e+019] n=501278686 sdn=2.307106e+020 t=1782.14s
394) m=6.188057e+019 sd=1.080277e+016 ci(99%)=[6.185274e+019,6.190839e+019] n=501279847 sdn=2.418662e+020 t=1781.14s
395) m=6.189902e+019 sd=1.096645e+016 ci(99%)=[6.187077e+019,6.192727e+019] n=501280143 sdn=2.455311e+020 t=1772.08s
396) m=6.188374e+019 sd=1.113740e+016 ci(99%)=[6.185505e+019,6.191243e+019] n=501279887 sdn=2.493584e+020 t=1773.70s
397) m=6.187808e+019 sd=1.082125e+016 ci(99%)=[6.185021e+019,6.190596e+019] n=501278916 sdn=2.422797e+020 t=1772.61s
398) m=6.185479e+019 sd=1.093808e+016 ci(99%)=[6.182661e+019,6.188297e+019] n=501279320 sdn=2.448957e+020 t=1778.66s
399) m=6.187071e+019 sd=1.044383e+016 ci(99%)=[6.184381e+019,6.189761e+019] n=501278671 sdn=2.338296e+020 t=1778.38s
400) m=6.189027e+019 sd=1.034538e+016 ci(99%)=[6.186362e+019,6.191692e+019] n=501279784 sdn=2.316256e+020 t=1778.52s |
Averaging the accumulated data with Excel:
| Code: |
Averages after N = 400 MonteCarlo perft samples:
<m> ~ 61,882,684,824,777,700,000
<sd> ~ 10,585,166,354,801,500
(Minimum value with 99% confidence) ~ <m> - (2.575829303)<sd> ~ 61,855,419,243,103,900,000
(Maximum value with 99% confidence) ~ <m> + (2.575829303)<sd> ~ 61,909,950,406,451,500,000
<m>/<sd> ~ 5,846.170
<n> ~ 501,279,616.08 |
Once I said that I run three simultaneous samples each time: the whole truth is that sometimes I run four simultaneous samples. Given that fact, the elapsed time of running samples should be around 64 or 65 hours (a great amount of time for me); taking in mind that I lost some samples (wasted time), and also counting the time of processing the data manually, I estimate that the total elapsed time should be around a little over 70 hours: an important effort for me!
I recover the estimates of other people from this post:
| Quote: |
61,803,489,628,662,504,195 by Joshua Haglund.
6.187e+19 by François Labelle.
61,886,459,822,115,294,738 by myself.
6.188925e+19 by H.G.Muller.
6.19009592e+19 by Reinhard Scharnagl. |
According with my experiment, only Haglund's estimate is out of the confidence interval for 99% confidence. Calculating the relative errors of all these five estimates respect <m> ~ 61,882,684,824,777,700,000 (hoping no typos):
| Quote: |
(Haglund's estimate) ~ <m> - 0.127976%
(Labelle's estimate) ~ <m> - 0.020498%
(My own estimate) ~ <m> + 0.0061%
(Muller's estimate) ~ <m> + 0.010609%
(Scharnagl's estimate) ~ <m> + 0.029531% |
Thanks to the people that try their best for doing accurate estimates. I hope that this experiment will be somewhat useful in the future. I was lucky this time and my estimate has the lowest relative error (in absolute value, of course). But logically, this means nothing until the real Perft(14) value for the starting position of the game of chess will be known... we can wait some years. 
Regards from Spain.
Ajedrecista.
_________________
Six Fortran 95 tools.
Chess will never be solved. |
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