Doubt: perft estimate averaging N MonteCarlo samples.

[Ajedrecista]

Hello:

45 new MonteCarlo Perft(14) samples are added to my tiny experiment:

Code: Select all

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: Select all

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.

[Ajedrecista]

Hello:

I made a great effort this week and I managed to run 72 new MonteCarlo Perft(14) samples:

Code: Select all

perftmc 14 (GNU 5.07.173b w32):

316) m=6.189098e+019 sd=1.110376e+016 ci(99%)=[6.186238e+019,6.191959e+019] n=501279682 sdn=2.486053e+020 t=1815.70s

317) m=6.187335e+019 sd=1.092277e+016 ci(99%)=[6.184522e+019,6.190149e+019] n=501280104 sdn=2.445531e+020 t=1808.05s

318) m=6.189883e+019 sd=1.075027e+016 ci(99%)=[6.187113e+019,6.192652e+019] n=501280166 sdn=2.406908e+020 t=1804.05s

319) m=6.187476e+019 sd=1.032256e+016 ci(99%)=[6.184817e+019,6.190135e+019] n=501280720 sdn=2.311149e+020 t=1806.30s

320) m=6.188253e+019 sd=1.062659e+016 ci(99%)=[6.185516e+019,6.190991e+019] n=501280300 sdn=2.379218e+020 t=1804.80s

321) m=6.187461e+019 sd=1.023809e+016 ci(99%)=[6.184824e+019,6.190099e+019] n=501280820 sdn=2.292236e+020 t=1816.36s

322) m=6.185577e+019 sd=1.079434e+016 ci(99%)=[6.182796e+019,6.188358e+019] n=501279170 sdn=2.416774e+020 t=1808.05s

323) m=6.186658e+019 sd=1.030075e+016 ci(99%)=[6.184004e+019,6.189311e+019] n=501278519 sdn=2.306260e+020 t=1804.92s

324) m=6.185466e+019 sd=1.141046e+016 ci(99%)=[6.182527e+019,6.188406e+019] n=501278548 sdn=2.554717e+020 t=1805.81s

325) m=6.188838e+019 sd=1.020840e+016 ci(99%)=[6.186208e+019,6.191467e+019] n=501279172 sdn=2.285585e+020 t=1803.83s

326) m=6.187637e+019 sd=1.032392e+016 ci(99%)=[6.184977e+019,6.190296e+019] n=501280986 sdn=2.311454e+020 t=1805.41s

327) m=6.188798e+019 sd=1.050154e+016 ci(99%)=[6.186093e+019,6.191503e+019] n=501278942 sdn=2.351216e+020 t=1816.25s

328) m=6.188280e+019 sd=1.033611e+016 ci(99%)=[6.185617e+019,6.190943e+019] n=501279881 sdn=2.314181e+020 t=1778.20s

329) m=6.187395e+019 sd=1.106646e+016 ci(99%)=[6.184544e+019,6.190245e+019] n=501278366 sdn=2.477698e+020 t=1779.67s

330) m=6.189515e+019 sd=1.077388e+016 ci(99%)=[6.186740e+019,6.192291e+019] n=501279786 sdn=2.412193e+020 t=1781.33s

331) m=6.189894e+019 sd=1.057547e+016 ci(99%)=[6.187169e+019,6.192618e+019] n=501279074 sdn=2.367770e+020 t=1805.75s

332) m=6.187619e+019 sd=1.151239e+016 ci(99%)=[6.184654e+019,6.190585e+019] n=501278709 sdn=2.577539e+020 t=1804.94s

333) m=6.189264e+019 sd=1.078235e+016 ci(99%)=[6.186487e+019,6.192042e+019] n=501278426 sdn=2.414088e+020 t=1805.48s

334) m=6.190254e+019 sd=1.056393e+016 ci(99%)=[6.187533e+019,6.192975e+019] n=501278771 sdn=2.365185e+020 t=1816.62s

335) m=6.188394e+019 sd=1.110800e+016 ci(99%)=[6.185533e+019,6.191256e+019] n=501280251 sdn=2.487002e+020 t=1810.36s

336) m=6.187046e+019 sd=1.090335e+016 ci(99%)=[6.184237e+019,6.189854e+019] n=501278914 sdn=2.441179e+020 t=1805.94s

337) m=6.188791e+019 sd=1.041909e+016 ci(99%)=[6.186107e+019,6.191475e+019] n=501279998 sdn=2.332760e+020 t=1807.41s

338) m=6.186743e+019 sd=1.076001e+016 ci(99%)=[6.183971e+019,6.189515e+019] n=501278902 sdn=2.409087e+020 t=1810.19s

339) m=6.188028e+019 sd=1.006258e+016 ci(99%)=[6.185436e+019,6.190621e+019] n=501279413 sdn=2.252938e+020 t=1815.36s

340) m=6.188271e+019 sd=1.069434e+016 ci(99%)=[6.185516e+019,6.191026e+019] n=501280643 sdn=2.394388e+020 t=1806.36s

341) m=6.189357e+019 sd=1.071024e+016 ci(99%)=[6.186598e+019,6.192116e+019] n=501279611 sdn=2.397945e+020 t=1809.88s

342) m=6.186805e+019 sd=1.098051e+016 ci(99%)=[6.183976e+019,6.189634e+019] n=501280148 sdn=2.458458e+020 t=1806.08s

343) m=6.188561e+019 sd=9.367953e+015 ci(99%)=[6.186148e+019,6.190975e+019] n=501279484 sdn=2.097416e+020 t=1805.59s

344) m=6.190626e+019 sd=1.064836e+016 ci(99%)=[6.187883e+019,6.193369e+019] n=501278501 sdn=2.384087e+020 t=1819.44s

345) m=6.188636e+019 sd=1.144078e+016 ci(99%)=[6.185689e+019,6.191583e+019] n=501280317 sdn=2.561510e+020 t=1807.05s

346) m=6.187950e+019 sd=1.105576e+016 ci(99%)=[6.185102e+019,6.190798e+019] n=501281120 sdn=2.475309e+020 t=1791.09s

347) m=6.188679e+019 sd=1.063989e+016 ci(99%)=[6.185938e+019,6.191420e+019] n=501278165 sdn=2.382190e+020 t=1787.62s

348) m=6.188965e+019 sd=1.070164e+016 ci(99%)=[6.186208e+019,6.191722e+019] n=501278544 sdn=2.396017e+020 t=1788.41s

349) m=6.187044e+019 sd=1.042571e+016 ci(99%)=[6.184359e+019,6.189730e+019] n=501281466 sdn=2.334246e+020 t=1794.22s

350) m=6.188965e+019 sd=1.042406e+016 ci(99%)=[6.186280e+019,6.191650e+019] n=501279440 sdn=2.333872e+020 t=1794.53s

351) m=6.189307e+019 sd=1.005459e+016 ci(99%)=[6.186717e+019,6.191897e+019] n=501278525 sdn=2.251148e+020 t=1797.67s

352) m=6.188376e+019 sd=1.100634e+016 ci(99%)=[6.185541e+019,6.191211e+019] n=501279426 sdn=2.464238e+020 t=1784.94s

353) m=6.189820e+019 sd=1.065391e+016 ci(99%)=[6.187076e+019,6.192565e+019] n=501279682 sdn=2.385333e+020 t=1782.67s

354) m=6.189423e+019 sd=1.079883e+016 ci(99%)=[6.186642e+019,6.192205e+019] n=501278159 sdn=2.417776e+020 t=1783.08s

355) m=6.188607e+019 sd=1.128164e+016 ci(99%)=[6.185701e+019,6.191513e+019] n=501280193 sdn=2.525878e+020 t=1782.67s

356) m=6.186525e+019 sd=9.880073e+015 ci(99%)=[6.183980e+019,6.189071e+019] n=501279312 sdn=2.212076e+020 t=1783.89s

357) m=6.187448e+019 sd=1.085169e+016 ci(99%)=[6.184653e+019,6.190243e+019] n=501280786 sdn=2.429618e+020 t=1786.39s

358) m=6.189461e+019 sd=1.045605e+016 ci(99%)=[6.186768e+019,6.192155e+019] n=501279864 sdn=2.341034e+020 t=1805.47s

359) m=6.188247e+019 sd=9.961796e+015 ci(99%)=[6.185681e+019,6.190813e+019] n=501279764 sdn=2.230374e+020 t=1806.86s

360) m=6.187392e+019 sd=9.346828e+015 ci(99%)=[6.184984e+019,6.189799e+019] n=501280156 sdn=2.092688e+020 t=1815.72s

361) m=6.188313e+019 sd=1.027136e+016 ci(99%)=[6.185667e+019,6.190959e+019] n=501278292 sdn=2.299681e+020 t=1806.08s

362) m=6.189396e+019 sd=9.644964e+015 ci(99%)=[6.186912e+019,6.191881e+019] n=501281254 sdn=2.159441e+020 t=1804.73s

363) m=6.190889e+019 sd=1.124874e+016 ci(99%)=[6.187992e+019,6.193787e+019] n=501279972 sdn=2.518511e+020 t=1808.19s

364) m=6.186984e+019 sd=1.050565e+016 ci(99%)=[6.184278e+019,6.189690e+019] n=501281051 sdn=2.352142e+020 t=1815.98s

365) m=6.188480e+019 sd=1.088246e+016 ci(99%)=[6.185677e+019,6.191283e+019] n=501279702 sdn=2.436504e+020 t=1805.66s

366) m=6.188059e+019 sd=1.104004e+016 ci(99%)=[6.185215e+019,6.190902e+019] n=501279774 sdn=2.471786e+020 t=1806.34s

367) m=6.188091e+019 sd=1.164047e+016 ci(99%)=[6.185092e+019,6.191089e+019] n=501279568 sdn=2.606217e+020 t=1809.44s

368) m=6.188450e+019 sd=1.093652e+016 ci(99%)=[6.185633e+019,6.191267e+019] n=501278959 sdn=2.448607e+020 t=1816.70s

369) m=6.190593e+019 sd=1.010070e+016 ci(99%)=[6.187991e+019,6.193195e+019] n=501279866 sdn=2.261474e+020 t=1807.02s

370) m=6.187797e+019 sd=1.030323e+016 ci(99%)=[6.185143e+019,6.190451e+019] n=501279701 sdn=2.306818e+020 t=1774.66s

371) m=6.188279e+019 sd=1.022259e+016 ci(99%)=[6.185646e+019,6.190913e+019] n=501280436 sdn=2.288766e+020 t=1774.97s

372) m=6.190268e+019 sd=1.078192e+016 ci(99%)=[6.187491e+019,6.193045e+019] n=501279802 sdn=2.413995e+020 t=1775.95s

373) m=6.188535e+019 sd=1.010918e+016 ci(99%)=[6.185931e+019,6.191140e+019] n=501281397 sdn=2.263376e+020 t=1805.97s

374) m=6.186664e+019 sd=1.019719e+016 ci(99%)=[6.184037e+019,6.189291e+019] n=501278518 sdn=2.283075e+020 t=1805.08s

375) m=6.188788e+019 sd=1.021323e+016 ci(99%)=[6.186157e+019,6.191418e+019] n=501279644 sdn=2.286669e+020 t=1810.45s

376) m=6.188848e+019 sd=1.000131e+016 ci(99%)=[6.186272e+019,6.191425e+019] n=501279536 sdn=2.239220e+020 t=1815.75s

377) m=6.188625e+019 sd=1.049028e+016 ci(99%)=[6.185923e+019,6.191327e+019] n=501280015 sdn=2.348698e+020 t=1809.28s

378) m=6.188681e+019 sd=1.126207e+016 ci(99%)=[6.185780e+019,6.191582e+019] n=501280377 sdn=2.521498e+020 t=1805.72s

379) m=6.187769e+019 sd=1.015868e+016 ci(99%)=[6.185152e+019,6.190386e+019] n=501280438 sdn=2.274456e+020 t=1812.66s

380) m=6.188703e+019 sd=1.021894e+016 ci(99%)=[6.186070e+019,6.191335e+019] n=501280185 sdn=2.287948e+020 t=1808.80s

381) m=6.188282e+019 sd=9.887869e+015 ci(99%)=[6.185735e+019,6.190829e+019] n=501280103 sdn=2.213823e+020 t=1813.31s

382) m=6.188363e+019 sd=1.055788e+016 ci(99%)=[6.185643e+019,6.191083e+019] n=501281333 sdn=2.363837e+020 t=1806.05s

383) m=6.189435e+019 sd=1.020903e+016 ci(99%)=[6.186805e+019,6.192065e+019] n=501277001 sdn=2.285722e+020 t=1807.41s

384) m=6.187464e+019 sd=1.055538e+016 ci(99%)=[6.184745e+019,6.190183e+019] n=501279924 sdn=2.363274e+020 t=1814.06s

385) m=6.188342e+019 sd=1.096265e+016 ci(99%)=[6.185518e+019,6.191166e+019] n=501279200 sdn=2.454456e+020 t=1779.03s

386) m=6.187623e+019 sd=1.065845e+016 ci(99%)=[6.184878e+019,6.190369e+019] n=501280562 sdn=2.386351e+020 t=1778.92s

387) m=6.187855e+019 sd=1.093253e+016 ci(99%)=[6.185039e+019,6.190672e+019] n=501278692 sdn=2.447713e+020 t=1778.67s

Averaging the accumulated data with Excel:

Code: Select all

Averages after N = 387 MonteCarlo perft samples: 

 <m> ~ 61,882,614,676,427,000,000
<sd> ~     10,580,326,385,712,700

(Minimum value with 99% confidence) ~ <m> - (2.575829303)<sd> ~ 61,855,361,561,687,400,000
(Maximum value with 99% confidence) ~ <m> + (2.575829303)<sd> ~ 61,909,867,791,166,700,000

<m>/<sd> ~ 5,848.838

<n> ~ 501,279,614.67

<m> has grown a little; <sd>, <m>/<sd> and <n> are almost unchanged compared with the results of last week.

My experiment is not endless and I have fixed a goal: 400 MC perft samples. I stop the experiment due to Easter... once I resume it, I estimate another week for reach the 400 samples.

In this post I collected some estimates, and I will calculate the relative errors as if <m> (with N = 400) were the true Perft(14) value for the game of chess (which is not correct).

Regards from Spain.

Ajedrecista.

[Ajedrecista]

Hello!

I finally end my experiment running the last thirteen MonteCarlo Perft(14) samples this afternoon:

Code: Select all

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: Select all

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:

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):

(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.

[petero2]

Hello!

I finally end my experiment running the last thirteen MonteCarlo Perft(14) samples this afternoon:

Averaging the accumulated data with Excel:

Code: Select all

Averages after N = 400 MonteCarlo perft samples: 
 <m> ~ 61,882,684,824,777,700,000

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.

Here is what I got after about 196 core hours:

Code: Select all

m = 6.18847822079403e+19
s = 0.00002368654103e+19