Jesús Muñoz
Joined: 13 Jul 2011
Posts: 707
Location: Madrid, Spain.
|
 Post subject: Perft(14) estimate after averaging 96 MC perft samples. Posted: Thu Jan 26, 2012 4:44 pm |
  |
|
Hello:
It was totally unexpected, but I managed to run 42 more MonteCarlo samples of Perft(14) this week. I copy the results:
| Code: |
perftmc 14 (GNU 5.07.173b w32):
55) m=6.189126e+019 sd=1.025756e+016 ci(99%)=[6.186484e+019,6.191768e+019] n=501279326 sdn=2.296592e+020 t=1795.62s
56) m=6.189066e+019 sd=1.028560e+016 ci(99%)=[6.186416e+019,6.191716e+019] n=501280839 sdn=2.302874e+020 t=1799.20s
57) m=6.188512e+019 sd=1.023282e+016 ci(99%)=[6.185876e+019,6.191148e+019] n=501278469 sdn=2.291052e+020 t=1798.42s
58) m=6.187755e+019 sd=1.016845e+016 ci(99%)=[6.185136e+019,6.190375e+019] n=501281149 sdn=2.276645e+020 t=1798.14s
59) m=6.188874e+019 sd=1.071921e+016 ci(99%)=[6.186113e+019,6.191635e+019] n=501280297 sdn=2.399956e+020 t=1799.11s
60) m=6.188642e+019 sd=1.041763e+016 ci(99%)=[6.185959e+019,6.191326e+019] n=501279319 sdn=2.332430e+020 t=1804.00s
61) m=6.188827e+019 sd=1.107349e+016 ci(99%)=[6.185975e+019,6.191680e+019] n=501279766 sdn=2.479274e+020 t=1807.48s
62) m=6.187425e+019 sd=1.091419e+016 ci(99%)=[6.184613e+019,6.190236e+019] n=501278351 sdn=2.443606e+020 t=1808.16s
63) m=6.187935e+019 sd=1.041703e+016 ci(99%)=[6.185252e+019,6.190619e+019] n=501280432 sdn=2.332298e+020 t=1811.73s
64) m=6.188126e+019 sd=1.025338e+016 ci(99%)=[6.185484e+019,6.190767e+019] n=501279973 sdn=2.295658e+020 t=1817.97s
65) m=6.188444e+019 sd=1.081156e+016 ci(99%)=[6.185659e+019,6.191229e+019] n=501279716 sdn=2.420631e+020 t=1804.44s
66) m=6.187651e+019 sd=1.120478e+016 ci(99%)=[6.184764e+019,6.190537e+019] n=501278857 sdn=2.508666e+020 t=1805.70s
67) m=6.186686e+019 sd=9.913670e+015 ci(99%)=[6.184132e+019,6.189239e+019] n=501279446 sdn=2.219599e+020 t=1815.36s
68) m=6.190257e+019 sd=1.033446e+016 ci(99%)=[6.187595e+019,6.192919e+019] n=501278726 sdn=2.313809e+020 t=1806.02s
69) m=6.188596e+019 sd=1.104028e+016 ci(99%)=[6.185752e+019,6.191440e+019] n=501278991 sdn=2.471837e+020 t=1805.50s
70) m=6.190975e+019 sd=1.006684e+016 ci(99%)=[6.188382e+019,6.193568e+019] n=501279280 sdn=2.253892e+020 t=1806.19s
71) m=6.189794e+019 sd=1.075091e+016 ci(99%)=[6.187024e+019,6.192563e+019] n=501279168 sdn=2.407050e+020 t=1816.84s
72) m=6.187742e+019 sd=1.021332e+016 ci(99%)=[6.185111e+019,6.190372e+019] n=501279298 sdn=2.286688e+020 t=1806.98s
73) m=6.189354e+019 sd=1.071593e+016 ci(99%)=[6.186593e+019,6.192114e+019] n=501280695 sdn=2.399222e+020 t=1804.38s
74) m=6.189176e+019 sd=1.107339e+016 ci(99%)=[6.186323e+019,6.192028e+019] n=501280582 sdn=2.479254e+020 t=1804.09s
75) m=6.189556e+019 sd=1.080762e+016 ci(99%)=[6.186772e+019,6.192340e+019] n=501279602 sdn=2.419747e+020 t=1809.20s
76) m=6.186469e+019 sd=1.031877e+016 ci(99%)=[6.183811e+019,6.189127e+019] n=501279784 sdn=2.310298e+020 t=1804.23s
77) m=6.189422e+019 sd=1.006358e+016 ci(99%)=[6.186830e+019,6.192014e+019] n=501280566 sdn=2.253164e+020 t=1803.45s
78) m=6.188256e+019 sd=1.076320e+016 ci(99%)=[6.185483e+019,6.191028e+019] n=501277490 sdn=2.409797e+020 t=1801.77s
79) m=6.187859e+019 sd=1.060298e+016 ci(99%)=[6.185128e+019,6.190590e+019] n=501281395 sdn=2.373935e+020 t=1797.48s
80) m=6.187284e+019 sd=1.076798e+016 ci(99%)=[6.184511e+019,6.190058e+019] n=501280409 sdn=2.410875e+020 t=1793.48s
81) m=6.187718e+019 sd=1.072083e+016 ci(99%)=[6.184956e+019,6.190480e+019] n=501280975 sdn=2.400319e+020 t=1793.64s
82) m=6.188221e+019 sd=1.118553e+016 ci(99%)=[6.185339e+019,6.191102e+019] n=501278295 sdn=2.504355e+020 t=1803.11s
83) m=6.188124e+019 sd=1.075494e+016 ci(99%)=[6.185353e+019,6.190894e+019] n=501280270 sdn=2.407955e+020 t=1803.45s
84) m=6.186572e+019 sd=1.005592e+016 ci(99%)=[6.183982e+019,6.189162e+019] n=501279188 sdn=2.251447e+020 t=1811.27s
85) m=6.188960e+019 sd=1.038603e+016 ci(99%)=[6.186284e+019,6.191635e+019] n=501280925 sdn=2.325359e+020 t=1792.14s
86) m=6.188382e+019 sd=1.053394e+016 ci(99%)=[6.185668e+019,6.191095e+019] n=501280516 sdn=2.358475e+020 t=1788.02s
87) m=6.186771e+019 sd=9.579151e+015 ci(99%)=[6.184304e+019,6.189239e+019] n=501278125 sdn=2.144699e+020 t=1786.83s
88) m=6.187624e+019 sd=1.029300e+016 ci(99%)=[6.184972e+019,6.190275e+019] n=501280503 sdn=2.304530e+020 t=1780.06s
89) m=6.188133e+019 sd=9.987345e+015 ci(99%)=[6.185561e+019,6.190706e+019] n=501281412 sdn=2.236098e+020 t=1779.09s
90) m=6.188588e+019 sd=1.124572e+016 ci(99%)=[6.185691e+019,6.191485e+019] n=501280892 sdn=2.517839e+020 t=1780.97s
91) m=6.188649e+019 sd=1.087649e+016 ci(99%)=[6.185848e+019,6.191451e+019] n=501279350 sdn=2.435167e+020 t=1818.27s
92) m=6.188796e+019 sd=1.003571e+016 ci(99%)=[6.186211e+019,6.191381e+019] n=501279124 sdn=2.246922e+020 t=1811.00s
93) m=6.188901e+019 sd=1.107146e+016 ci(99%)=[6.186049e+019,6.191753e+019] n=501278422 sdn=2.478817e+020 t=1810.81s
94) m=6.188876e+019 sd=9.339720e+015 ci(99%)=[6.186470e+019,6.191282e+019] n=501281744 sdn=2.091100e+020 t=1794.28s
95) m=6.189020e+019 sd=1.054152e+016 ci(99%)=[6.186305e+019,6.191736e+019] n=501276286 sdn=2.360162e+020 t=1795.55s
96) m=6.188467e+019 sd=1.074019e+016 ci(99%)=[6.185700e+019,6.191233e+019] n=501280472 sdn=2.404652e+020 t=1797.77s |
Averaging the accumulated data with Excel (hoping no typos):
| Code: |
Averages after N = 96 MonteCarlo perft samples:
<m> ~ 61,882,464,686,162,800,000
<sd> ~ 10,506,880,305,211,500
(Minimum value with 99% confidence) ~ <m> - (2.575829303)<sd> ~ 61,855,400,755,989,600,000
(Maximum value with 99% confidence) ~ <m> + (2.575829303)<sd> ~ 61,909,528,616,336,100,000
<m>/<sd> ~ 5,889.709
<n> ~ 501,279,600.61 |
Three simultaneous samples take around half an hour in an Intel i5-760 (at 2.8 GHz). So, a rough time estimate for this experiment is N/6 hours. At this moment, 96/6 = 16 hours is a good estimate of the effective spent time (spread over several days).
I have updated my data (IIRC) for N = 60, 75, 78 and 90 (without posting the intermediate results in TalkChess) and the average mean value <m> ranged from ~ 6.188211e+19 to ~ 6.188279e+19 more less... I could be lucky (very likely) or a slight sort of convergence is appearing around <m>, probably indicating that the first four numbers of Perft(14) are 6188. But I know that 96 samples is not a big amount of data, and the average standard deviation <sd> is more less 0.017% of <m> (quite large, but it is my criterion stopping around 500 millions of nodes per sample). <sd> increased up to ~ 1.0514e+16 (for N = 75) and now has decreased a little. The amount <m>/<sd> almost has not varied from N = 54 to N = 96.
I will not be able of resume this experiment until mid February. However, I do not know the number of samples that I will run until I finish the experiment (I guess that N will not be very large). I hope that all these averages will be helpful in the future.
Regards from Spain.
Ajedrecista.
_________________
Six Fortran 95 tools.
Chess will never be solved. |
|
FAQ
Search
Memberlist
Usergroups
Register
Profile
Log in to check your private messages
Log in
