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Jesús Muñoz
Joined: 13 Jul 2011
Posts: 690
Location: Madrid, Spain.
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 Post subject: Doubt: perft estimate averaging N MonteCarlo samples. Posted: Sun Jan 15, 2012 12:27 pm |
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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:
| Code: |
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?
| Code: |
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:
| Code: |
<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.
_________________
Six Fortran 95 tools.
Chess will never be solved. |
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| Subject |
Author |
Date/Time |
 Doubt: perft estimate averaging N MonteCarlo samples. |
Jesús Muñoz |
Sun Jan 15, 2012 12:27 pm |
| Re: Doubt: perft estimate averaging N MonteCarlo samples. |
Daniel Shawul |
Sun Jan 15, 2012 1:31 pm |
| Averages with 27 MonteCarlo samples. |
Jesús Muñoz |
Mon Jan 16, 2012 8:35 pm |
| Perft(14) estimate after averaging 54 MC perft samples. |
Jesús Muñoz |
Fri Jan 20, 2012 3:27 pm |
| Some explanations. |
Jesús Muñoz |
Sun Jan 22, 2012 4:09 pm |
| Perft(14) estimate after averaging 96 MC perft samples. |
Jesús Muñoz |
Thu Jan 26, 2012 4:44 pm |
| Perft(14) estimate after averaging 120 MC perft samples. |
Jesús Muñoz |
Fri Feb 17, 2012 8:00 pm |
| Perft(14) estimate after averaging 174 MC perft samples. |
Jesús Muñoz |
Fri Mar 02, 2012 5:26 pm |
| Perft(14) estimate after averaging 222 MC perft samples. |
Jesús Muñoz |
Fri Mar 09, 2012 3:50 pm |
| Perft(14) estimate after averaging 270 MC perft samples. |
Jesús Muñoz |
Fri Mar 16, 2012 4:57 pm |
| Perft(14) estimate after averaging 315 MC perft samples. |
Jesús Muñoz |
Fri Mar 23, 2012 3:22 pm |
| Perft(14) estimate after averaging 387 MC perft samples. |
Jesús Muñoz |
Fri Mar 30, 2012 3:11 pm |
| Final Perft(14) estimate after averaging 400 MC samples. |
Jesús Muñoz |
Tue Apr 10, 2012 7:21 pm |
| Re: Final Perft(14) estimate after averaging 400 MC samples. |
Peter Österlund |
Tue Apr 10, 2012 9:24 pm |
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