Doubt: perft estimate averaging N MonteCarlo samples.

[Ajedrecista]

Hello:

I have been thinking about an idea that will be surely clumsy: using 'perftmc' command of GNU 5.07.173b (which gives different values in each try), could I do a good estimate averaging results? Here is a typical output:

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m=6.188431e+019 sd=5.191844e+015 ci(99%)=[6.187093e+019,6.189768e+019] n=2001154
971 sdn=2.322533e+020 t=37391.12s

It is an example of MonteCarlo Perft(14) for the initial position of standard chess. I thought about using NebiyuChess 1.42, which automatically interrupts MonteCarlo Perft at 5e+8 nodes more less... but always gives the same results in different tries, so I discarded it. This is the reason why I thought about GNU.

My question is the following: if I run N MonteCarlo samples of the same position and I stop all of them at the same point (with the same number of nodes ± a very little amount), can I average the results in this way?

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m_1, m_2, ..., m_N
(Average m) = <m> = (1/N)·(m_1 + m_2 + ... + m_N)

sd_1, sd_2, ... sd_N
(Average standard deviation) = <sd> = sqrt{(1/N)·[(sd_1)² + (sd_2)² + ... + (sd_N)²]}

Or, taking into account that different samples have different number of nodes:

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<m> = [(n_1)·(m_1) + (n_2)·(m_2) + ... + (n_N)·(m_N)]/(n_1 + n_2 + ... n_N)

<sd> = sqrt{[(sdn_1)² + (sdn_2)² + ... + (sdn_N)²]/(n_1 + n_2 + ... n_N)}

Where sdn_i = (sd_i)·sqrt(n_i) and GNU prints these numbers. I think that n_i ~ 1e+8 or 5e+8 nodes in each sample is accurate enough, but comments are welcome.

Are my assumptions correct or I have failure concepts? In the case that I am right (very unlikely), the estimate would be good/accurate or is it a waste of time because of the size of the standard deviation (or other issues)? Thanks in advance.

Regards from Spain.

Ajedrecita.

[Daniel Shawul]

Hello Jesus

I thought about using NebiyuChess 1.42, which automatically interrupts MonteCarlo Perft at 5e+8 nodes more less... but always gives the same results in different tries, so I discarded it. This is the reason why I thought about GNU.

You can set different random number seed before calling perft.

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seed 0              => sets the seed to time(NULL) and prints the number used so that it can be used to debug that specific game (sequence of random numbers)
seed N              => sets seed to that number N for N != 0 eg. 457632

I found reproduciblity very important in many situations, which is why i decided to make not setting to time a default.

regards,
Daniel

[Ajedrecista]

Hello:

Hello Jesus

I thought about using NebiyuChess 1.42, which automatically interrupts MonteCarlo Perft at 5e+8 nodes more less... but always gives the same results in different tries, so I discarded it. This is the reason why I thought about GNU.

You can set different random number seed before calling perft.

Code: Select all

seed 0              => sets the seed to time(NULL) and prints the number used so that it can be used to debug that specific game (sequence of random numbers)
seed N              => sets seed to that number N for N != 0 eg. 457632

I found reproduciblity very important in many situations, which is why i decided to make not setting to time a default.

regards,
Daniel

Thanks for your tip: it works, as expected. I had to search 'random number seed' in Google for little clarification, but you explained it quite well.

I finally used GNU instead of Nebiyu for avoiding the change of seed each time (I suppose I would set seed 1, seed 2, ..., seed N) because is easier for me. But using GNU should not be an offence for you, because I stop each MonteCarlo sample of GNU with Nebiyu criterion: as soon as number of nodes are greater than 5e+8.

I average the data taking into account the number of nodes of each sample, that is the second way I explained in the initial post of this topic; as nobody has commented about the validity of my idea, I will use it without changes.

I have ran 27 samples until now. Here are the results (hoping no typos in the whole post):

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perftmc 14 (GNU 5.07.173b w32):

 1) m=6.187678e+019 sd=9.750798e+015 ci(99%)=[6.185166e+019,6.190189e+019] n=501279094 sdn=2.183132e+020 t=9565.06s

 2) m=6.189193e+019 sd=1.051857e+016 ci(99%)=[6.186484e+019,6.191903e+019] n=501280285 sdn=2.355033e+020 t=2637.27s

 3) m=6.188427e+019 sd=1.006031e+016 ci(99%)=[6.185836e+019,6.191019e+019] n=501279965 sdn=2.252432e+020 t=2639.08s

 4) m=6.187349e+019 sd=1.007542e+016 ci(99%)=[6.184753e+019,6.189944e+019] n=501279854 sdn=2.255814e+020 t=2635.56s

 5) m=6.187708e+019 sd=1.032063e+016 ci(99%)=[6.185050e+019,6.190367e+019] n=501279004 sdn=2.310713e+020 t=1803.31s

 6) m=6.188005e+019 sd=1.020789e+016 ci(99%)=[6.185375e+019,6.190634e+019] n=501279218 sdn=2.285471e+020 t=1801.80s

 7) m=6.189288e+019 sd=1.071983e+016 ci(99%)=[6.186527e+019,6.192050e+019] n=501279423 sdn=2.400092e+020 t=1801.86s

 8) m=6.190143e+019 sd=1.049982e+016 ci(99%)=[6.187438e+019,6.192847e+019] n=501278163 sdn=2.350831e+020 t=1796.52s

 9) m=6.187719e+019 sd=1.072126e+016 ci(99%)=[6.184957e+019,6.190481e+019] n=501278534 sdn=2.400410e+020 t=1795.84s

10) m=6.188709e+019 sd=1.088681e+016 ci(99%)=[6.185904e+019,6.191513e+019] n=501280532 sdn=2.437481e+020 t=1796.27s

11) m=6.189915e+019 sd=9.883658e+015 ci(99%)=[6.187369e+019,6.192461e+019] n=501279126 sdn=2.212878e+020 t=1795.14s

12) m=6.187896e+019 sd=1.079972e+016 ci(99%)=[6.185114e+019,6.190678e+019] n=501281179 sdn=2.417983e+020 t=1795.41s

13) m=6.188828e+019 sd=1.063891e+016 ci(99%)=[6.186088e+019,6.191569e+019] n=501280070 sdn=2.381975e+020 t=1798.03s

14) m=6.188041e+019 sd=1.117936e+016 ci(99%)=[6.185161e+019,6.190921e+019] n=501276617 sdn=2.502971e+020 t=1790.55s

15) m=6.189834e+019 sd=1.103298e+016 ci(99%)=[6.186992e+019,6.192676e+019] n=501280169 sdn=2.470205e+020 t=1790.69s

16) m=6.187616e+019 sd=9.864250e+015 ci(99%)=[6.185075e+019,6.190157e+019] n=501279165 sdn=2.208533e+020 t=1792.44s

17) m=6.187847e+019 sd=1.005758e+016 ci(99%)=[6.185256e+019,6.190437e+019] n=501278458 sdn=2.251817e+020 t=1804.33s

18) m=6.189063e+019 sd=1.052264e+016 ci(99%)=[6.186352e+019,6.191774e+019] n=501278921 sdn=2.355941e+020 t=1801.36s

19) m=6.189348e+019 sd=9.871633e+015 ci(99%)=[6.186805e+019,6.191891e+019] n=501277767 sdn=2.210183e+020 t=1788.69s

20) m=6.187280e+019 sd=1.078500e+016 ci(99%)=[6.184502e+019,6.190058e+019] n=501280242 sdn=2.414684e+020 t=1789.23s

21) m=6.186935e+019 sd=1.068577e+016 ci(99%)=[6.184182e+019,6.189688e+019] n=501279639 sdn=2.392466e+020 t=1790.42s

22) m=6.188677e+019 sd=1.043255e+016 ci(99%)=[6.185990e+019,6.191365e+019] n=501280046 sdn=2.335774e+020 t=1779.53s

23) m=6.189836e+019 sd=1.067554e+016 ci(99%)=[6.187086e+019,6.192586e+019] n=501277372 sdn=2.390171e+020 t=1779.41s

24) m=6.187303e+019 sd=1.050259e+016 ci(99%)=[6.184598e+019,6.190009e+019] n=501280197 sdn=2.351455e+020 t=1778.72s

25) m=6.187547e+019 sd=1.011699e+016 ci(99%)=[6.184941e+019,6.190154e+019] n=501278694 sdn=2.265118e+020 t=1803.11s

26) m=6.188085e+019 sd=1.080187e+016 ci(99%)=[6.185303e+019,6.190868e+019] n=501278742 sdn=2.418458e+020 t=1802.89s

27) m=6.188734e+019 sd=9.995885e+015 ci(99%)=[6.186159e+019,6.191309e+019] n=501279495 sdn=2.238006e+020 t=1803.56s

The first sample was ran with an Intel Pentium D930 almost a month ago; the others are from today, running three simultaneous samples each time in an Intel i5-760.

I have averaged the data with Excel 2003, so you can expect some roundings. Here are the averages I get for these 27 samples:

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<m> ~ 61,884,075,552,228,100,000
<sd> ~ 10,437,106,444,028,200

<m>/<sd> ~ 5929.237

I add <m>/<sd> for a quick look of the quality of the standard deviation compared with the mean. I hope that all this data will be somewhat helpful in the future.

If I feel energized, I will continue growing the number of samples (at this moment: N = 27) and updating the data periodically, in the way that Steven J. Edwards upgrades his Perft(13) run (a very huge task).

Regards from Spain.

Ajedrecista.

[Ajedrecista]

Hello:

I have been running other 27 MonteCarlo Perft(14) samples and this is what I get:

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perftmc 14 (GNU 5.07.173b w32):

28) m=6.188011e+019 sd=9.946225e+015 ci(99%)=[6.185449e+019,6.190573e+019] n=501279154 sdn=2.226887e+020 t=1794.44s

29) m=6.187823e+019 sd=1.083952e+016 ci(99%)=[6.185030e+019,6.190615e+019] n=501280058 sdn=2.426891e+020 t=1793.56s

30) m=6.190087e+019 sd=1.062835e+016 ci(99%)=[6.187350e+019,6.192825e+019] n=501279242 sdn=2.379609e+020 t=1794.03s

31) m=6.186841e+019 sd=1.001161e+016 ci(99%)=[6.184262e+019,6.189420e+019] n=501282355 sdn=2.241533e+020 t=1803.33s

32) m=6.186260e+019 sd=1.058766e+016 ci(99%)=[6.183533e+019,6.188988e+019] n=501278370 sdn=2.370498e+020 t=1802.84s

33) m=6.187918e+019 sd=1.047857e+016 ci(99%)=[6.185219e+019,6.190617e+019] n=501278678 sdn=2.346074e+020 t=1808.39s

34) m=6.187713e+019 sd=1.089137e+016 ci(99%)=[6.184907e+019,6.190518e+019] n=501279776 sdn=2.438498e+020 t=1794.05s

35) m=6.188263e+019 sd=1.121174e+016 ci(99%)=[6.185375e+019,6.191151e+019] n=501280644 sdn=2.510231e+020 t=1794.03s

36) m=6.187222e+019 sd=1.063405e+016 ci(99%)=[6.184483e+019,6.189962e+019] n=501279318 sdn=2.380886e+020 t=1797.12s

37) m=6.187374e+019 sd=1.057575e+016 ci(99%)=[6.184650e+019,6.190099e+019] n=501279868 sdn=2.367833e+020 t=1794.12s

38) m=6.186556e+019 sd=9.809724e+015 ci(99%)=[6.184029e+019,6.189083e+019] n=501280175 sdn=2.196327e+020 t=1796.73s

39) m=6.187162e+019 sd=1.029827e+016 ci(99%)=[6.184510e+019,6.189815e+019] n=501277766 sdn=2.305705e+020 t=1793.00s

40) m=6.188765e+019 sd=1.113190e+016 ci(99%)=[6.185898e+019,6.191633e+019] n=501281045 sdn=2.492355e+020 t=1813.12s

41) m=6.187547e+019 sd=1.037987e+016 ci(99%)=[6.184874e+019,6.190221e+019] n=501280995 sdn=2.323981e+020 t=1814.27s

42) m=6.189318e+019 sd=1.031386e+016 ci(99%)=[6.186661e+019,6.191975e+019] n=501279435 sdn=2.309197e+020 t=1829.69s

43) m=6.188305e+019 sd=1.050592e+016 ci(99%)=[6.185598e+019,6.191011e+019] n=501279973 sdn=2.352199e+020 t=1787.39s

44) m=6.185973e+019 sd=9.954686e+015 ci(99%)=[6.183408e+019,6.188537e+019] n=501281580 sdn=2.228786e+020 t=1789.70s

45) m=6.185511e+019 sd=1.036460e+016 ci(99%)=[6.182841e+019,6.188181e+019] n=501277568 sdn=2.320555e+020 t=1789.03s

46) m=6.188931e+019 sd=1.069488e+016 ci(99%)=[6.186176e+019,6.191686e+019] n=501280008 sdn=2.394508e+020 t=1801.38s

47) m=6.188533e+019 sd=1.025258e+016 ci(99%)=[6.185892e+019,6.191174e+019] n=501279859 sdn=2.295478e+020 t=1796.28s

48) m=6.188584e+019 sd=1.024875e+016 ci(99%)=[6.185944e+019,6.191225e+019] n=501280494 sdn=2.294622e+020 t=1796.48s

49) m=6.187672e+019 sd=1.142710e+016 ci(99%)=[6.184729e+019,6.190616e+019] n=501278206 sdn=2.558442e+020 t=1806.58s

50) m=6.187417e+019 sd=1.029176e+016 ci(99%)=[6.184766e+019,6.190068e+019] n=501280296 sdn=2.304251e+020 t=1802.50s

51) m=6.187121e+019 sd=1.047623e+016 ci(99%)=[6.184422e+019,6.189819e+019] n=501280150 sdn=2.345552e+020 t=1810.09s

52) m=6.188088e+019 sd=1.113788e+016 ci(99%)=[6.185219e+019,6.190957e+019] n=501279478 sdn=2.493689e+020 t=1804.67s

53) m=6.189411e+019 sd=1.098293e+016 ci(99%)=[6.186581e+019,6.192240e+019] n=501278721 sdn=2.458996e+020 t=1803.09s

54) m=6.188640e+019 sd=1.065530e+016 ci(99%)=[6.185896e+019,6.191385e+019] n=501280051 sdn=2.385646e+020 t=1804.02s

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Averages after N = 54 MonteCarlo perft samples:

 <m> ~ 61,881,120,367,616,500,000
<sd> ~     10,495,306,430,406,300

<m>/<sd> ~ 5896.076

<n> ~ 501,279,504.33

I have included <n> (the average number of nodes per sample) which should be around 5.0128e+8 nodes. I am not an expert, but these results do not seem unreasonable.

I will be very busy for running more samples until mid February, so I postpone this Perft(14) estimate experiment for a while. I hope to exceed 100 samples, trying to get more accurate results.

Regards from Spain.

Ajedrecista.

[Ajedrecista]

Hello:

In the output of GNU appears sdn, which is by definition (sd)·sqrt(n) for each sample. I said in my first post that I would use (sdn_i)² for averaging the standard deviation, but actually I am using (n_i)·(sd_i)² for two reasons:

a) More accurate results: I assume that both m_i and sd_i are rounded, but also sdn_i is rounded; so I suppose that the output of (n_i)·(sd_i)² is a little more exact than the output of (sdn_i)².

b) Save time: for each sample, I do three 'copy & paste' (m_i, sd_i and n_i) from a notepad to Excel instead of four (m_i, sd_i, n_i and sdn_i). I save N 'copy & paste' in N samples.

So, the method of averaging the data is now fully explained. I have just realized that Peter Österlund did a similar thing with Perft(13) averaging lots of samples, but he averaged around 180,000 samples! His relative error with the true Perft(13) value was ~ 0.000449%! I have done 54 until the moment, the 0.03%, and with much larger standard deviations (that is why I compare <m>/<sd>, for viewing the quality of the average standard deviation against the average mean). Something is something...

I see that GNU gives a confidence interval with 99% confidence. I knew that this level of confidence is reached between m ± (2.57)sd and m ± (2.58)sd in a normal distribution; so, m ± k·sd has 99% confidence, where k ~ 2.575829303 according to Derive 6. I can give now a minimum value and a maximum value for Perft(14) estimate:

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Averages after N = 54 MonteCarlo perft samples: 

 <m> ~ 61,881,120,367,616,500,000 
<sd> ~     10,495,306,430,406,300

(Minimum value with 99% confidence) ~ <m> - (2.575829303)<sd> ~ 61,854,086,249,769,100,000
(Maximum value with 99% confidence) ~ <m> + (2.575829303)<sd> ~ 61,908,154,485,463,900,000

<m>/<sd> ~ 5,896.076 

<n> ~ 501,279,504.33

I remember that Excel also rounds its results. In view of the evolution of my tiny experiment, I expect that <sd> will be around 1.05e+16 (with the criterion of stop GNU at more less 5.0128e+8 nodes).

I have done a little search of Perft(14) estimates of people of this forum (except Mr. Labelle), and here are the estimates that I consider more accurate:

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.

Each person uses his own estimate method: this is the reason why I give the links. The more different estimates (Joshua's and Reinhard's) differ in less than 0.16%!

Regards from Spain.

Ajedrecista.

[Ajedrecista]

Hello:

It was totally unexpected, but I managed to run 42 more MonteCarlo samples of Perft(14) this week. I copy the results:

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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: Select all

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.

[Ajedrecista]

Hello:

As I promised some weeks ago, I resumed this experiment in mid February; I have ran other 24 MonteCarlo samples:

Code: Select all

perftmc 14 (GNU 5.07.173b w32):

 97) m=6.189968e+019 sd=9.968961e+015 ci(99%)=[6.187400e+019,6.192536e+019] n=501276978 sdn=2.231972e+020 t=1817.47s

 98) m=6.187422e+019 sd=1.047597e+016 ci(99%)=[6.184724e+019,6.190121e+019] n=501280763 sdn=2.345497e+020 t=1805.58s

 99) m=6.187648e+019 sd=1.095249e+016 ci(99%)=[6.184826e+019,6.190469e+019] n=501280884 sdn=2.452187e+020 t=1807.66s

100) m=6.188386e+019 sd=1.081047e+016 ci(99%)=[6.185602e+019,6.191171e+019] n=501278574 sdn=2.420383e+020 t=1804.91s

101) m=6.188416e+019 sd=1.081914e+016 ci(99%)=[6.185629e+019,6.191203e+019] n=501278937 sdn=2.422324e+020 t=1805.38s

102) m=6.188435e+019 sd=1.033910e+016 ci(99%)=[6.185771e+019,6.191098e+019] n=501279884 sdn=2.314851e+020 t=1805.92s

103) m=6.188559e+019 sd=1.117139e+016 ci(99%)=[6.185682e+019,6.191437e+019] n=501279281 sdn=2.501193e+020 t=1808.84s

104) m=6.189134e+019 sd=1.133385e+016 ci(99%)=[6.186215e+019,6.192054e+019] n=501279579 sdn=2.537567e+020 t=1815.66s

105) m=6.187967e+019 sd=1.013839e+016 ci(99%)=[6.185356e+019,6.190579e+019] n=501278569 sdn=2.269909e+020 t=1804.41s

106) m=6.187396e+019 sd=9.922992e+015 ci(99%)=[6.184839e+019,6.189952e+019] n=501279194 sdn=2.221685e+020 t=1818.95s

107) m=6.187536e+019 sd=1.101518e+016 ci(99%)=[6.184699e+019,6.190374e+019] n=501279098 sdn=2.466218e+020 t=1804.69s

108) m=6.187363e+019 sd=1.109060e+016 ci(99%)=[6.184506e+019,6.190220e+019] n=501280477 sdn=2.483108e+020 t=1806.41s

109) m=6.186728e+019 sd=1.111241e+016 ci(99%)=[6.183865e+019,6.189590e+019] n=501280536 sdn=2.487991e+020 t=1808.86s

110) m=6.187670e+019 sd=1.072955e+016 ci(99%)=[6.184907e+019,6.190434e+019] n=501278981 sdn=2.402266e+020 t=1811.28s

111) m=6.186937e+019 sd=1.113884e+016 ci(99%)=[6.184068e+019,6.189806e+019] n=501278139 sdn=2.493902e+020 t=1808.75s

112) m=6.188844e+019 sd=1.005461e+016 ci(99%)=[6.186254e+019,6.191434e+019] n=501276761 sdn=2.251148e+020 t=1837.12s

113) m=6.189127e+019 sd=1.050394e+016 ci(99%)=[6.186421e+019,6.191833e+019] n=501280428 sdn=2.351758e+020 t=1829.86s

114) m=6.188861e+019 sd=1.064436e+016 ci(99%)=[6.186119e+019,6.191603e+019] n=501279647 sdn=2.383195e+020 t=1837.08s

115) m=6.188280e+019 sd=1.089486e+016 ci(99%)=[6.185473e+019,6.191086e+019] n=501277456 sdn=2.439274e+020 t=1787.16s

116) m=6.188394e+019 sd=1.041013e+016 ci(99%)=[6.185712e+019,6.191075e+019] n=501279502 sdn=2.330752e+020 t=1786.92s

117) m=6.188412e+019 sd=1.011535e+016 ci(99%)=[6.185806e+019,6.191018e+019] n=501278484 sdn=2.264750e+020 t=1787.61s

118) m=6.187346e+019 sd=1.024464e+016 ci(99%)=[6.184707e+019,6.189985e+019] n=501278990 sdn=2.293699e+020 t=1788.97s

119) m=6.187020e+019 sd=1.016764e+016 ci(99%)=[6.184401e+019,6.189639e+019] n=501279750 sdn=2.276461e+020 t=1788.77s

120) m=6.188485e+019 sd=1.097793e+016 ci(99%)=[6.185657e+019,6.191313e+019] n=501278229 sdn=2.457876e+020 t=1788.67s

It is not easy for me find the requested time for running those samples, so the number of them will grow, but (very) slowly. I do not know the number of samples I will run until I finish this experiment.

Averaging the accumulated data with Excel:

Code: Select all

Averages after N = 120 MonteCarlo perft samples:

 <m> ~ 61,882,166,247,766,000,000
<sd> ~     10,532,596,445,177,000

(Minimum value with 99% confidence) ~ <m> - (2.575829303)<sd> ~ 61,855,036,077,205,900,000
(Maximum value with 99% confidence) ~ <m> + (2.575829303)<sd> ~ 61,909,296,418,326,200,000

<m>/<sd> ~ 5,875.300

<n> ~ 501,279,506.50

Results seem credible IMHO.

Regards from Spain.

Ajedrecista.

[Ajedrecista]

Hello:

I have ran 54 more MonteCarlo Perft(14) samples during the last two weeks (39 of them in this current week). Here are the results:

Code: Select all

perftmc 14 (GNU 5.07.173b w32):

121) m=6.189284e+019 sd=1.008047e+016 ci(99%)=[6.186688e+019,6.191881e+019] n=501278987 sdn=2.256944e+020 t=1794.00s

122) m=6.187890e+019 sd=1.123685e+016 ci(99%)=[6.184995e+019,6.190785e+019] n=501279826 sdn=2.515849e+020 t=1797.20s

123) m=6.188323e+019 sd=1.055339e+016 ci(99%)=[6.185604e+019,6.191041e+019] n=501279158 sdn=2.362827e+020 t=1796.28s

124) m=6.188984e+019 sd=1.047161e+016 ci(99%)=[6.186286e+019,6.191681e+019] n=501278865 sdn=2.344515e+020 t=1809.95s

125) m=6.188092e+019 sd=1.007806e+016 ci(99%)=[6.185496e+019,6.190688e+019] n=501277680 sdn=2.256399e+020 t=1810.48s

126) m=6.190602e+019 sd=1.012834e+016 ci(99%)=[6.187993e+019,6.193211e+019] n=501279540 sdn=2.267661e+020 t=1809.20s

127) m=6.189542e+019 sd=9.590962e+015 ci(99%)=[6.187071e+019,6.192012e+019] n=501279403 sdn=2.147346e+020 t=1793.72s

128) m=6.189455e+019 sd=1.003952e+016 ci(99%)=[6.186869e+019,6.192042e+019] n=501279233 sdn=2.247775e+020 t=1797.50s

129) m=6.187941e+019 sd=1.052887e+016 ci(99%)=[6.185229e+019,6.190653e+019] n=501278958 sdn=2.357335e+020 t=1794.56s

130) m=6.188222e+019 sd=9.940390e+015 ci(99%)=[6.185662e+019,6.190783e+019] n=501280319 sdn=2.225583e+020 t=1789.98s

131) m=6.188558e+019 sd=1.040922e+016 ci(99%)=[6.185876e+019,6.191239e+019] n=501279962 sdn=2.330550e+020 t=1788.97s

132) m=6.187640e+019 sd=1.007706e+016 ci(99%)=[6.185045e+019,6.190236e+019] n=501278639 sdn=2.256179e+020 t=1789.83s

133) m=6.188719e+019 sd=1.103660e+016 ci(99%)=[6.185876e+019,6.191562e+019] n=501280461 sdn=2.471017e+020 t=1789.38s

134) m=6.187670e+019 sd=8.907128e+015 ci(99%)=[6.185375e+019,6.189964e+019] n=501279361 sdn=1.994241e+020 t=1788.58s

135) m=6.190021e+019 sd=1.031477e+016 ci(99%)=[6.187364e+019,6.192678e+019] n=501280856 sdn=2.309405e+020 t=1789.97s

136) m=6.186606e+019 sd=1.070175e+016 ci(99%)=[6.183850e+019,6.189363e+019] n=501279708 sdn=2.396046e+020 t=1779.16s

137) m=6.187397e+019 sd=1.159761e+016 ci(99%)=[6.184410e+019,6.190385e+019] n=501279745 sdn=2.596622e+020 t=1782.75s

138) m=6.187630e+019 sd=9.482699e+015 ci(99%)=[6.185187e+019,6.190072e+019] n=501280498 sdn=2.123109e+020 t=1779.52s

139) m=6.189303e+019 sd=1.103679e+016 ci(99%)=[6.186460e+019,6.192146e+019] n=501280212 sdn=2.471058e+020 t=1796.73s

140) m=6.188546e+019 sd=1.137474e+016 ci(99%)=[6.185616e+019,6.191476e+019] n=501279468 sdn=2.546721e+020 t=1799.14s

141) m=6.187604e+019 sd=1.004837e+016 ci(99%)=[6.185016e+019,6.190193e+019] n=501278151 sdn=2.249755e+020 t=1800.30s

142) m=6.187485e+019 sd=1.011928e+016 ci(99%)=[6.184878e+019,6.190092e+019] n=501279472 sdn=2.265633e+020 t=1798.12s

143) m=6.188353e+019 sd=9.887368e+015 ci(99%)=[6.185806e+019,6.190900e+019] n=501277751 sdn=2.213706e+020 t=1795.67s

144) m=6.188995e+019 sd=9.882406e+015 ci(99%)=[6.186449e+019,6.191541e+019] n=501279360 sdn=2.212599e+020 t=1798.36s

145) m=6.188272e+019 sd=9.780943e+015 ci(99%)=[6.185752e+019,6.190791e+019] n=501282312 sdn=2.189888e+020 t=1800.72s

146) m=6.187672e+019 sd=1.084942e+016 ci(99%)=[6.184877e+019,6.190467e+019] n=501277682 sdn=2.429101e+020 t=1798.41s

147) m=6.188110e+019 sd=1.053987e+016 ci(99%)=[6.185394e+019,6.190825e+019] n=501277514 sdn=2.359796e+020 t=1797.59s

148) m=6.187031e+019 sd=1.014276e+016 ci(99%)=[6.184418e+019,6.189644e+019] n=501281110 sdn=2.270894e+020 t=1798.31s

149) m=6.187199e+019 sd=1.117055e+016 ci(99%)=[6.184321e+019,6.190076e+019] n=501278954 sdn=2.501003e+020 t=1797.16s

150) m=6.188504e+019 sd=1.115479e+016 ci(99%)=[6.185631e+019,6.191378e+019] n=501279919 sdn=2.497477e+020 t=1802.39s

151) m=6.186887e+019 sd=1.062790e+016 ci(99%)=[6.184149e+019,6.189625e+019] n=501279154 sdn=2.379509e+020 t=1794.09s

152) m=6.188174e+019 sd=9.944726e+015 ci(99%)=[6.185612e+019,6.190736e+019] n=501279662 sdn=2.226552e+020 t=1790.56s

153) m=6.188554e+019 sd=1.041242e+016 ci(99%)=[6.185872e+019,6.191237e+019] n=501279522 sdn=2.331265e+020 t=1794.12s

154) m=6.190050e+019 sd=9.932023e+015 ci(99%)=[6.187491e+019,6.192608e+019] n=501278635 sdn=2.223706e+020 t=1798.81s

155) m=6.189155e+019 sd=1.149098e+016 ci(99%)=[6.186195e+019,6.192115e+019] n=501279808 sdn=2.572747e+020 t=1793.88s

156) m=6.189017e+019 sd=1.005289e+016 ci(99%)=[6.186427e+019,6.191606e+019] n=501278928 sdn=2.250768e+020 t=1794.17s

157) m=6.187382e+019 sd=1.033040e+016 ci(99%)=[6.184721e+019,6.190044e+019] n=501279086 sdn=2.312901e+020 t=1800.12s

158) m=6.189066e+019 sd=1.103952e+016 ci(99%)=[6.186223e+019,6.191910e+019] n=501280079 sdn=2.471670e+020 t=1804.23s

159) m=6.189075e+019 sd=1.044283e+016 ci(99%)=[6.186385e+019,6.191765e+019] n=501280564 sdn=2.338075e+020 t=1801.02s

160) m=6.187843e+019 sd=1.125054e+016 ci(99%)=[6.184944e+019,6.190741e+019] n=501279519 sdn=2.518915e+020 t=1819.77s

161) m=6.187819e+019 sd=1.075871e+016 ci(99%)=[6.185048e+019,6.190591e+019] n=501280569 sdn=2.408799e+020 t=1819.33s

162) m=6.188285e+019 sd=1.081494e+016 ci(99%)=[6.185499e+019,6.191071e+019] n=501279010 sdn=2.421386e+020 t=1813.84s

163) m=6.188064e+019 sd=1.086191e+016 ci(99%)=[6.185266e+019,6.190862e+019] n=501279776 sdn=2.431903e+020 t=1794.53s

164) m=6.186738e+019 sd=1.015982e+016 ci(99%)=[6.184121e+019,6.189355e+019] n=501279864 sdn=2.274711e+020 t=1798.00s

165) m=6.189776e+019 sd=1.036952e+016 ci(99%)=[6.187105e+019,6.192447e+019] n=501280786 sdn=2.321662e+020 t=1805.20s

166) m=6.187368e+019 sd=1.017968e+016 ci(99%)=[6.184746e+019,6.189991e+019] n=501279713 sdn=2.279156e+020 t=1806.56s

167) m=6.187860e+019 sd=1.142511e+016 ci(99%)=[6.184916e+019,6.190803e+019] n=501280526 sdn=2.558001e+020 t=1816.75s

168) m=6.189199e+019 sd=1.053784e+016 ci(99%)=[6.186485e+019,6.191914e+019] n=501280494 sdn=2.359347e+020 t=1804.31s

169) m=6.188049e+019 sd=1.104201e+016 ci(99%)=[6.185204e+019,6.190893e+019] n=501280569 sdn=2.472228e+020 t=1801.94s

170) m=6.188333e+019 sd=1.055069e+016 ci(99%)=[6.185615e+019,6.191050e+019] n=501280229 sdn=2.362224e+020 t=1804.25s

171) m=6.188742e+019 sd=1.044487e+016 ci(99%)=[6.186051e+019,6.191433e+019] n=501278692 sdn=2.338529e+020 t=1802.48s

172) m=6.187370e+019 sd=1.010134e+016 ci(99%)=[6.184768e+019,6.189973e+019] n=501279299 sdn=2.261615e+020 t=1803.36s

173) m=6.188538e+019 sd=1.209636e+016 ci(99%)=[6.185422e+019,6.191654e+019] n=501278304 sdn=2.708284e+020 t=1800.78s

174) m=6.189349e+019 sd=1.093528e+016 ci(99%)=[6.186533e+019,6.192166e+019] n=501279202 sdn=2.448329e+020 t=1804.97s

Averaging the accumulated data with Excel:

Code: Select all

Averages after N = 174 MonteCarlo perft samples:

 <m> ~ 61,882,548,159,772,100,000
<sd> ~     10,527,431,703,577,400

(Minimum value with 99% confidence) ~ <m> - (2.575829303)<sd> ~ 61,855,431,292,704,700,000
(Maximum value with 99% confidence) ~ <m> + (2.575829303)<sd> ~ 61,909,665,026,839,500,000

<m>/<sd> ~ 5,878.219

<n> ~ 501,279,516.52

The average (weighted by the number of nodes of each sample) of the mean values (<m>) still remains between 6.1882e+19 and 6.1883e+19.

Regards from Spain.

Ajedrecista.

[Ajedrecista]

Hello:

I managed to run 48 MonteCarlo Perft(14) samples this week:

Code: Select all

perftmc 14 (GNU 5.07.173b w32):

175) m=6.188097e+019 sd=1.088038e+016 ci(99%)=[6.185294e+019,6.190900e+019] n=501280604 sdn=2.436040e+020 t=1798.61s

176) m=6.189682e+019 sd=1.140451e+016 ci(99%)=[6.186745e+019,6.192620e+019] n=501278241 sdn=2.553384e+020 t=1804.20s

177) m=6.188218e+019 sd=1.073110e+016 ci(99%)=[6.185454e+019,6.190983e+019] n=501279423 sdn=2.402616e+020 t=1799.52s

178) m=6.189257e+019 sd=1.079571e+016 ci(99%)=[6.186476e+019,6.192038e+019] n=501278349 sdn=2.417079e+020 t=1792.98s

179) m=6.186884e+019 sd=1.019336e+016 ci(99%)=[6.184259e+019,6.189510e+019] n=501279827 sdn=2.282221e+020 t=1796.72s

180) m=6.187771e+019 sd=9.683364e+015 ci(99%)=[6.185277e+019,6.190266e+019] n=501279426 sdn=2.168035e+020 t=1794.55s

181) m=6.189102e+019 sd=1.074193e+016 ci(99%)=[6.186335e+019,6.191869e+019] n=501279002 sdn=2.405039e+020 t=1808.94s

182) m=6.188231e+019 sd=1.175920e+016 ci(99%)=[6.185202e+019,6.191260e+019] n=501280331 sdn=2.632802e+020 t=1811.45s

183) m=6.187141e+019 sd=1.053201e+016 ci(99%)=[6.184428e+019,6.189854e+019] n=501279393 sdn=2.358041e+020 t=1803.80s

184) m=6.189440e+019 sd=1.080515e+016 ci(99%)=[6.186657e+019,6.192224e+019] n=501281193 sdn=2.419199e+020 t=1787.52s

185) m=6.189122e+019 sd=1.054490e+016 ci(99%)=[6.186406e+019,6.191839e+019] n=501278700 sdn=2.360924e+020 t=1789.36s

186) m=6.188205e+019 sd=1.076295e+016 ci(99%)=[6.185433e+019,6.190978e+019] n=501281325 sdn=2.409750e+020 t=1787.95s

187) m=6.190043e+019 sd=1.084941e+016 ci(99%)=[6.187248e+019,6.192838e+019] n=501279658 sdn=2.429105e+020 t=1818.27s

188) m=6.187634e+019 sd=9.958161e+015 ci(99%)=[6.185069e+019,6.190199e+019] n=501280099 sdn=2.229561e+020 t=1809.98s

189) m=6.188988e+019 sd=1.046943e+016 ci(99%)=[6.186291e+019,6.191685e+019] n=501280212 sdn=2.344030e+020 t=1808.45s

190) m=6.188849e+019 sd=1.113586e+016 ci(99%)=[6.185981e+019,6.191718e+019] n=501279431 sdn=2.493237e+020 t=1808.48s

191) m=6.187719e+019 sd=1.096988e+016 ci(99%)=[6.184893e+019,6.190545e+019] n=501278973 sdn=2.456076e+020 t=1819.70s

192) m=6.187995e+019 sd=9.954302e+015 ci(99%)=[6.185431e+019,6.190560e+019] n=501279573 sdn=2.228696e+020 t=1809.52s

193) m=6.186921e+019 sd=9.928545e+015 ci(99%)=[6.184364e+019,6.189479e+019] n=501278751 sdn=2.222927e+020 t=1818.11s

194) m=6.187739e+019 sd=1.092481e+016 ci(99%)=[6.184925e+019,6.190553e+019] n=501279477 sdn=2.445985e+020 t=1810.14s

195) m=6.190203e+019 sd=1.064405e+016 ci(99%)=[6.187461e+019,6.192944e+019] n=501279422 sdn=2.383126e+020 t=1814.94s

196) m=6.188280e+019 sd=1.097746e+016 ci(99%)=[6.185452e+019,6.191108e+019] n=501280748 sdn=2.457775e+020 t=1819.36s

197) m=6.186709e+019 sd=1.052132e+016 ci(99%)=[6.183999e+019,6.189419e+019] n=501277695 sdn=2.355643e+020 t=1817.78s

198) m=6.189555e+019 sd=9.757581e+015 ci(99%)=[6.187041e+019,6.192069e+019] n=501281256 sdn=2.184655e+020 t=1882.45s

199) m=6.188959e+019 sd=1.064004e+016 ci(99%)=[6.186218e+019,6.191700e+019] n=501279547 sdn=2.382228e+020 t=1793.67s

200) m=6.186608e+019 sd=1.074596e+016 ci(99%)=[6.183840e+019,6.189376e+019] n=501279334 sdn=2.405943e+020 t=1793.77s

201) m=6.188662e+019 sd=1.071486e+016 ci(99%)=[6.185901e+019,6.191422e+019] n=501279648 sdn=2.398980e+020 t=1793.83s

202) m=6.187063e+019 sd=1.161566e+016 ci(99%)=[6.184071e+019,6.190056e+019] n=501279135 sdn=2.600660e+020 t=1793.48s

203) m=6.188481e+019 sd=1.041675e+016 ci(99%)=[6.185797e+019,6.191164e+019] n=501280223 sdn=2.332237e+020 t=1791.39s

204) m=6.188920e+019 sd=1.035624e+016 ci(99%)=[6.186252e+019,6.191588e+019] n=501279765 sdn=2.318687e+020 t=1791.20s

205) m=6.188009e+019 sd=9.863987e+015 ci(99%)=[6.185468e+019,6.190550e+019] n=501279443 sdn=2.208475e+020 t=1811.45s

206) m=6.188296e+019 sd=1.117885e+016 ci(99%)=[6.185417e+019,6.191176e+019] n=501279363 sdn=2.502862e+020 t=1808.45s

207) m=6.186660e+019 sd=1.151582e+016 ci(99%)=[6.183694e+019,6.189627e+019] n=501280529 sdn=2.578311e+020 t=1808.88s

208) m=6.188055e+019 sd=1.052447e+016 ci(99%)=[6.185344e+019,6.190767e+019] n=501279637 sdn=2.356352e+020 t=1804.09s

209) m=6.188877e+019 sd=1.021727e+016 ci(99%)=[6.186246e+019,6.191509e+019] n=501282237 sdn=2.287579e+020 t=1802.30s

210) m=6.188829e+019 sd=1.007519e+016 ci(99%)=[6.186234e+019,6.191425e+019] n=501279869 sdn=2.255762e+020 t=1804.25s

211) m=6.188321e+019 sd=9.848306e+015 ci(99%)=[6.185784e+019,6.190858e+019] n=501280406 sdn=2.204966e+020 t=1806.23s

212) m=6.188375e+019 sd=1.071925e+016 ci(99%)=[6.185613e+019,6.191136e+019] n=501279255 sdn=2.399961e+020 t=1805.22s

213) m=6.189752e+019 sd=1.053322e+016 ci(99%)=[6.187039e+019,6.192466e+019] n=501279910 sdn=2.358313e+020 t=1815.97s

214) m=6.187089e+019 sd=1.079322e+016 ci(99%)=[6.184309e+019,6.189870e+019] n=501279030 sdn=2.416522e+020 t=1784.67s

215) m=6.187456e+019 sd=9.834222e+015 ci(99%)=[6.184923e+019,6.189989e+019] n=501279505 sdn=2.201811e+020 t=1788.14s

216) m=6.188619e+019 sd=1.160983e+016 ci(99%)=[6.185629e+019,6.191610e+019] n=501280097 sdn=2.599358e+020 t=1784.86s

217) m=6.188617e+019 sd=1.053039e+016 ci(99%)=[6.185904e+019,6.191330e+019] n=501280732 sdn=2.357681e+020 t=1795.52s

218) m=6.189534e+019 sd=1.122056e+016 ci(99%)=[6.186643e+019,6.192424e+019] n=501280484 sdn=2.512205e+020 t=1789.41s

219) m=6.188727e+019 sd=1.029030e+016 ci(99%)=[6.186076e+019,6.191378e+019] n=501279376 sdn=2.303923e+020 t=1792.22s

220) m=6.187117e+019 sd=1.125649e+016 ci(99%)=[6.184217e+019,6.190017e+019] n=501279734 sdn=2.520247e+020 t=1809.67s

221) m=6.189189e+019 sd=1.032011e+016 ci(99%)=[6.186531e+019,6.191848e+019] n=501278415 sdn=2.310594e+020 t=1806.98s

222) m=6.188647e+019 sd=9.984144e+015 ci(99%)=[6.186075e+019,6.191219e+019] n=501279959 sdn=2.235378e+020 t=1812.36s

Averaging the accumulated data with Excel:

Code: Select all

Averages after N = 222 MonteCarlo perft samples:

 <m> ~ 61,882,747,071,807,300,000
<sd> ~     10,550,127,986,642,200

(Minimum value with 99% confidence) ~ <m> - (2.575829303)<sd> ~ 61,855,571,742,988,900,000
(Maximum value with 99% confidence) ~ <m> + (2.575829303)<sd> ~ 61,909,922,400,625,700,000

<m>/<sd> ~ 5,865.592

<n> ~ 501,279,561.33

I still get 6.1882e+19 < (<m>) < 6.1883e+19; OTOH, the average standard deviation is raising slowly because I obtain some samples with high standard deviations, and those ones raise <sd> (the smaller standard deviations can not compensate the higher ones).

Regards from Spain.

Ajedrecista.

[Ajedrecista]

Hello:

48 MonteCarlo Perft(14) samples were ran this week:

Code: Select all

perftmc 14 (GNU 5.07.173b w32):

223) m=6.189385e+019 sd=1.084110e+016 ci(99%)=[6.186592e+019,6.192178e+019] n=501279642 sdn=2.427243e+020 t=1789.30s

224) m=6.187004e+019 sd=1.073432e+016 ci(99%)=[6.184239e+019,6.189769e+019] n=501281449 sdn=2.403341e+020 t=1792.52s

225) m=6.188099e+019 sd=1.015489e+016 ci(99%)=[6.185483e+019,6.190715e+019] n=501280191 sdn=2.273608e+020 t=1790.08s

226) m=6.185762e+019 sd=1.039561e+016 ci(99%)=[6.183085e+019,6.188440e+019] n=501280644 sdn=2.327503e+020 t=1803.44s

227) m=6.185942e+019 sd=1.058966e+016 ci(99%)=[6.183214e+019,6.188670e+019] n=501279804 sdn=2.370948e+020 t=1817.53s

228) m=6.186120e+019 sd=1.062726e+016 ci(99%)=[6.183382e+019,6.188857e+019] n=501279393 sdn=2.379367e+020 t=1805.62s

229) m=6.189011e+019 sd=9.831376e+015 ci(99%)=[6.186479e+019,6.191544e+019] n=501279881 sdn=2.201174e+020 t=1809.88s

230) m=6.188422e+019 sd=9.893324e+015 ci(99%)=[6.185873e+019,6.190970e+019] n=501279402 sdn=2.215043e+020 t=1804.72s

231) m=6.188332e+019 sd=1.016738e+016 ci(99%)=[6.185713e+019,6.190951e+019] n=501279672 sdn=2.276402e+020 t=1808.75s

232) m=6.188688e+019 sd=9.999232e+015 ci(99%)=[6.186112e+019,6.191264e+019] n=501278999 sdn=2.238754e+020 t=1803.78s

233) m=6.189257e+019 sd=1.023457e+016 ci(99%)=[6.186620e+019,6.191893e+019] n=501281044 sdn=2.291449e+020 t=1815.62s

234) m=6.188391e+019 sd=1.134061e+016 ci(99%)=[6.185470e+019,6.191313e+019] n=501279113 sdn=2.539079e+020 t=1804.88s

235) m=6.188103e+019 sd=1.046489e+016 ci(99%)=[6.185407e+019,6.190799e+019] n=501278920 sdn=2.343011e+020 t=1806.86s

236) m=6.188196e+019 sd=9.812251e+015 ci(99%)=[6.185668e+019,6.190724e+019] n=501279864 sdn=2.196892e+020 t=1803.61s

237) m=6.187069e+019 sd=1.072360e+016 ci(99%)=[6.184307e+019,6.189831e+019] n=501280988 sdn=2.400939e+020 t=1815.00s

238) m=6.187368e+019 sd=1.140424e+016 ci(99%)=[6.184430e+019,6.190306e+019] n=501279699 sdn=2.553328e+020 t=1803.89s

239) m=6.188927e+019 sd=1.040781e+016 ci(99%)=[6.186246e+019,6.191608e+019] n=501279894 sdn=2.330233e+020 t=1803.70s

240) m=6.186939e+019 sd=1.027641e+016 ci(99%)=[6.184292e+019,6.189586e+019] n=501280089 sdn=2.300815e+020 t=1803.33s

241) m=6.187985e+019 sd=1.172311e+016 ci(99%)=[6.184965e+019,6.191005e+019] n=501281215 sdn=2.624724e+020 t=1799.59s

242) m=6.187433e+019 sd=1.007750e+016 ci(99%)=[6.184837e+019,6.190029e+019] n=501280722 sdn=2.256282e+020 t=1800.05s

243) m=6.187623e+019 sd=1.080829e+016 ci(99%)=[6.184839e+019,6.190407e+019] n=501279819 sdn=2.419898e+020 t=1800.81s

244) m=6.190023e+019 sd=1.095258e+016 ci(99%)=[6.187201e+019,6.192844e+019] n=501281380 sdn=2.452207e+020 t=1795.69s

245) m=6.189770e+019 sd=1.046610e+016 ci(99%)=[6.187074e+019,6.192466e+019] n=501279274 sdn=2.343283e+020 t=1797.91s

246) m=6.186297e+019 sd=1.071092e+016 ci(99%)=[6.183538e+019,6.189057e+019] n=501277786 sdn=2.398093e+020 t=1794.33s

247) m=6.186454e+019 sd=1.017963e+016 ci(99%)=[6.183832e+019,6.189076e+019] n=501279566 sdn=2.279145e+020 t=1792.36s

248) m=6.188582e+019 sd=1.017347e+016 ci(99%)=[6.185961e+019,6.191202e+019] n=501279996 sdn=2.277768e+020 t=1793.11s

249) m=6.188076e+019 sd=1.124135e+016 ci(99%)=[6.185180e+019,6.190972e+019] n=501280860 sdn=2.516860e+020 t=1790.23s

250) m=6.188355e+019 sd=1.048577e+016 ci(99%)=[6.185654e+019,6.191056e+019] n=501277895 sdn=2.347685e+020 t=1804.52s

251) m=6.188824e+019 sd=1.029093e+016 ci(99%)=[6.186173e+019,6.191475e+019] n=501279094 sdn=2.304063e+020 t=1803.67s

252) m=6.187363e+019 sd=1.036214e+016 ci(99%)=[6.184694e+019,6.190033e+019] n=501281214 sdn=2.320011e+020 t=1806.84s

253) m=6.188831e+019 sd=1.068899e+016 ci(99%)=[6.186077e+019,6.191584e+019] n=501279391 sdn=2.393187e+020 t=1796.05s

254) m=6.189269e+019 sd=1.088491e+016 ci(99%)=[6.186465e+019,6.192073e+019] n=501278684 sdn=2.437051e+020 t=1802.28s

255) m=6.190091e+019 sd=1.077227e+016 ci(99%)=[6.187316e+019,6.192866e+019] n=501279952 sdn=2.411834e+020 t=1799.67s

256) m=6.187218e+019 sd=1.046309e+016 ci(99%)=[6.184523e+019,6.189914e+019] n=501279390 sdn=2.342609e+020 t=1818.70s

257) m=6.190159e+019 sd=1.040234e+016 ci(99%)=[6.187479e+019,6.192838e+019] n=501280509 sdn=2.329011e+020 t=1828.83s

258) m=6.188909e+019 sd=9.918563e+015 ci(99%)=[6.186354e+019,6.191464e+019] n=501279475 sdn=2.220694e+020 t=1828.77s

259) m=6.188671e+019 sd=1.080453e+016 ci(99%)=[6.185888e+019,6.191454e+019] n=501280379 sdn=2.419058e+020 t=1811.81s

260) m=6.187343e+019 sd=1.001726e+016 ci(99%)=[6.184762e+019,6.189923e+019] n=501280529 sdn=2.242794e+020 t=1809.36s

261) m=6.187563e+019 sd=1.028033e+016 ci(99%)=[6.184915e+019,6.190211e+019] n=501279734 sdn=2.301692e+020 t=1811.84s

262) m=6.188912e+019 sd=1.055022e+016 ci(99%)=[6.186194e+019,6.191629e+019] n=501278057 sdn=2.362113e+020 t=1806.97s

263) m=6.191272e+019 sd=1.040150e+016 ci(99%)=[6.188592e+019,6.193951e+019] n=501278618 sdn=2.328818e+020 t=1804.91s

264) m=6.188305e+019 sd=1.015731e+016 ci(99%)=[6.185689e+019,6.190922e+019] n=501279604 sdn=2.274148e+020 t=1809.97s

265) m=6.187664e+019 sd=1.071063e+016 ci(99%)=[6.184905e+019,6.190423e+019] n=501278320 sdn=2.398029e+020 t=1791.80s

266) m=6.187710e+019 sd=1.030565e+016 ci(99%)=[6.185056e+019,6.190365e+019] n=501280355 sdn=2.307363e+020 t=1790.69s

267) m=6.188167e+019 sd=1.189517e+016 ci(99%)=[6.185103e+019,6.191231e+019] n=501278054 sdn=2.663237e+020 t=1792.86s

268) m=6.188379e+019 sd=1.079089e+016 ci(99%)=[6.185599e+019,6.191159e+019] n=501278845 sdn=2.416001e+020 t=1818.69s

269) m=6.188676e+019 sd=1.132908e+016 ci(99%)=[6.185758e+019,6.191594e+019] n=501281072 sdn=2.536502e+020 t=1818.06s

270) m=6.188484e+019 sd=1.064403e+016 ci(99%)=[6.185742e+019,6.191226e+019] n=501279075 sdn=2.383119e+020 t=1822.56s

Averaging the accumulated data with Excel:

Code: Select all

Averages after N = 270 MonteCarlo perft samples: 

 <m> ~ 61,882,607,703,086,900,000
<sd> ~     10,551,871,275,442,700

(Minimum value with 99% confidence) ~ <m> - (2.575829303)<sd> ~ 61,855,427,883,854,100,000
(Maximum value with 99% confidence) ~ <m> + (2.575829303)<sd> ~ 61,909,787,522,319,600,000

<m>/<sd> ~ 5,864.610

<n> ~ 501,279,593.21

The average results have not varied so much from last week.

Regards from Spain.

Ajedrecista.