Jesús Muñoz
Joined: 13 Jul 2011
Posts: 687
Location: Madrid, Spain.
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 Post subject: Perft(14) estimate after averaging 315 MC perft samples. Posted: Fri Mar 23, 2012 3:22 pm |
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Hello:
45 new MonteCarlo Perft(14) samples are added to my tiny experiment:
| Code: |
perftmc 14 (GNU 5.07.173b w32):
271) m=6.187703e+019 sd=1.022980e+016 ci(99%)=[6.185068e+019,6.190339e+019] n=501279212 sdn=2.290376e+020 t=1791.41s
272) m=6.188890e+019 sd=9.762461e+015 ci(99%)=[6.186375e+019,6.191405e+019] n=501279043 sdn=2.185743e+020 t=1793.02s
273) m=6.188354e+019 sd=1.171300e+016 ci(99%)=[6.185336e+019,6.191371e+019] n=501279522 sdn=2.622456e+020 t=1794.09s
274) m=6.188518e+019 sd=9.710792e+015 ci(99%)=[6.186016e+019,6.191019e+019] n=501279032 sdn=2.174175e+020 t=1811.61s
275) m=6.188275e+019 sd=1.081107e+016 ci(99%)=[6.185490e+019,6.191060e+019] n=501279633 sdn=2.420520e+020 t=1804.62s
276) m=6.188114e+019 sd=1.154080e+016 ci(99%)=[6.185141e+019,6.191087e+019] n=501280716 sdn=2.583904e+020 t=1812.86s
277) m=6.186353e+019 sd=1.037373e+016 ci(99%)=[6.183681e+019,6.189026e+019] n=501280701 sdn=2.322605e+020 t=1804.95s
278) m=6.188124e+019 sd=1.124615e+016 ci(99%)=[6.185227e+019,6.191021e+019] n=501280034 sdn=2.517932e+020 t=1820.50s
279) m=6.187463e+019 sd=1.065921e+016 ci(99%)=[6.184717e+019,6.190209e+019] n=501280977 sdn=2.386524e+020 t=1804.78s
280) m=6.188229e+019 sd=1.034120e+016 ci(99%)=[6.185566e+019,6.190893e+019] n=501277905 sdn=2.315316e+020 t=1811.45s
281) m=6.189107e+019 sd=1.066118e+016 ci(99%)=[6.186360e+019,6.191853e+019] n=501280574 sdn=2.386963e+020 t=1808.11s
282) m=6.187324e+019 sd=1.092642e+016 ci(99%)=[6.184509e+019,6.190138e+019] n=501278662 sdn=2.446344e+020 t=1815.91s
283) m=6.190766e+019 sd=1.076427e+016 ci(99%)=[6.187993e+019,6.193539e+019] n=501281010 sdn=2.410046e+020 t=1810.98s
284) m=6.189784e+019 sd=1.000495e+016 ci(99%)=[6.187207e+019,6.192361e+019] n=501280602 sdn=2.240038e+020 t=1806.45s
285) m=6.189188e+019 sd=1.126369e+016 ci(99%)=[6.186287e+019,6.192090e+019] n=501278402 sdn=2.521855e+020 t=1822.22s
286) m=6.188322e+019 sd=1.110273e+016 ci(99%)=[6.185462e+019,6.191182e+019] n=501277954 sdn=2.485816e+020 t=1792.09s
287) m=6.187042e+019 sd=9.691154e+015 ci(99%)=[6.184545e+019,6.189538e+019] n=501278905 sdn=2.169778e+020 t=1796.23s
288) m=6.187912e+019 sd=1.057190e+016 ci(99%)=[6.185189e+019,6.190635e+019] n=501280806 sdn=2.366975e+020 t=1793.84s
289) m=6.188722e+019 sd=1.045064e+016 ci(99%)=[6.186030e+019,6.191414e+019] n=501281028 sdn=2.339825e+020 t=1801.59s
290) m=6.189998e+019 sd=1.082594e+016 ci(99%)=[6.187210e+019,6.192787e+019] n=501281116 sdn=2.423852e+020 t=1799.88s
291) m=6.188632e+019 sd=1.071780e+016 ci(99%)=[6.185871e+019,6.191393e+019] n=501278404 sdn=2.399634e+020 t=1799.17s
292) m=6.186374e+019 sd=1.039383e+016 ci(99%)=[6.183697e+019,6.189052e+019] n=501278058 sdn=2.327099e+020 t=1795.94s
293) m=6.187128e+019 sd=1.097441e+016 ci(99%)=[6.184301e+019,6.189955e+019] n=501278505 sdn=2.457089e+020 t=1795.03s
294) m=6.189723e+019 sd=9.517460e+015 ci(99%)=[6.187272e+019,6.192175e+019] n=501279077 sdn=2.130889e+020 t=1794.38s
295) m=6.190489e+019 sd=1.076681e+016 ci(99%)=[6.187715e+019,6.193262e+019] n=501279919 sdn=2.410611e+020 t=1812.94s
296) m=6.186754e+019 sd=1.142993e+016 ci(99%)=[6.183810e+019,6.189699e+019] n=501278122 sdn=2.559075e+020 t=1811.58s
297) m=6.188869e+019 sd=1.034916e+016 ci(99%)=[6.186203e+019,6.191535e+019] n=501278471 sdn=2.317098e+020 t=1821.31s
298) m=6.187789e+019 sd=1.095595e+016 ci(99%)=[6.184967e+019,6.190611e+019] n=501281214 sdn=2.452961e+020 t=1795.03s
299) m=6.187978e+019 sd=1.064639e+016 ci(99%)=[6.185235e+019,6.190720e+019] n=501279974 sdn=2.383651e+020 t=1795.73s
300) m=6.188218e+019 sd=1.150266e+016 ci(99%)=[6.185255e+019,6.191181e+019] n=501280378 sdn=2.575363e+020 t=1799.58s
301) m=6.187109e+019 sd=1.132928e+016 ci(99%)=[6.184190e+019,6.190027e+019] n=501280215 sdn=2.536546e+020 t=1795.03s
302) m=6.184447e+019 sd=1.041555e+016 ci(99%)=[6.181764e+019,6.187130e+019] n=501280496 sdn=2.331969e+020 t=1794.45s
303) m=6.188917e+019 sd=1.101121e+016 ci(99%)=[6.186080e+019,6.191753e+019] n=501278705 sdn=2.465328e+020 t=1794.27s
304) m=6.185893e+019 sd=1.048003e+016 ci(99%)=[6.183194e+019,6.188593e+019] n=501280586 sdn=2.346405e+020 t=1800.91s
305) m=6.188042e+019 sd=1.127879e+016 ci(99%)=[6.185136e+019,6.190947e+019] n=501279138 sdn=2.525238e+020 t=1798.70s
306) m=6.188263e+019 sd=1.083797e+016 ci(99%)=[6.185471e+019,6.191055e+019] n=501279155 sdn=2.426541e+020 t=1801.02s
307) m=6.188198e+019 sd=1.109769e+016 ci(99%)=[6.185340e+019,6.191057e+019] n=501280959 sdn=2.484695e+020 t=1792.19s
308) m=6.187836e+019 sd=1.099590e+016 ci(99%)=[6.185003e+019,6.190668e+019] n=501278964 sdn=2.461900e+020 t=1791.69s
309) m=6.189149e+019 sd=1.140495e+016 ci(99%)=[6.186211e+019,6.192087e+019] n=501280410 sdn=2.553487e+020 t=1796.25s
310) m=6.188610e+019 sd=1.166440e+016 ci(99%)=[6.185605e+019,6.191615e+019] n=501279878 sdn=2.611576e+020 t=1797.19s
311) m=6.186480e+019 sd=1.104451e+016 ci(99%)=[6.183635e+019,6.189325e+019] n=501279800 sdn=2.472786e+020 t=1800.94s
312) m=6.189211e+019 sd=1.023432e+016 ci(99%)=[6.186575e+019,6.191848e+019] n=501278552 sdn=2.291388e+020 t=1801.70s
313) m=6.186605e+019 sd=1.012123e+016 ci(99%)=[6.183998e+019,6.189212e+019] n=501279781 sdn=2.266070e+020 t=1788.22s
314) m=6.188615e+019 sd=1.053339e+016 ci(99%)=[6.185901e+019,6.191328e+019] n=501280943 sdn=2.358353e+020 t=1788.61s
315) m=6.187519e+019 sd=1.006749e+016 ci(99%)=[6.184926e+019,6.190112e+019] n=501278945 sdn=2.254037e+020 t=1791.83s |
Averaging the accumulated data with Excel:
| Code: |
Averages after N = 315 MonteCarlo perft samples:
<m> ~ 61,882,395,047,298,300,000
<sd> ~ 10,578,099,735,512,300
(Minimum value with 99% confidence) ~ <m> - (2.575829303)<sd> ~ 61,855,147,668,029,500,000
(Maximum value with 99% confidence) ~ <m> + (2.575829303)<sd> ~ 61,909,642,426,567,000,000
<m>/<sd> ~ 5,850.048
<n> ~ 501,279,602.07 |
The average standard deviation has grown a lot, and the average mean has decreased a little, so <m>/<sd> has decreased notably. But <m> is still between 6.1882e+19 and 6.1883e+19: it does not leave this range for weeks (now, <m> is more less 6.18824e+19 with 315 MonteCarlo perft samples).
Regards from Spain.
Ajedrecista.
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