Your estimates are in the range of others I have seen here, so congratulations. Of all of these numbers, I only understand the number of plies (13 and 14), the estimates (1.9801...e+18 and 6.1803...e+19) and the branching factors (31.5031... and 31.2118...). What are the other numbers?
Almost a month ago, Reinhard Scharnagl did estimates using inverse interpolation and the output of the results is similar to yours. I guess you have done one kind of interpolation or extrapolation, but could you confirm this, please? Thanks in advance.
Ajedrecista wrote:... Almost a month ago, Reinhard Scharnagl did estimates using inverse interpolation and the output of the results is similar to yours. ...
The idea of my calculation using inverse interpolation has been based upon:
a) switching to the natural logarithm, because Perft seems to me mainly a growth function
b) the growth factor seems to have an asymptotic behavior for about the next hundreds of ply levels,
thus using continued fractions seems to be more appropriate than to follow a polynomial approach.
just curious: how did you come to the conclusion that the value "-2587,643803" for n=12 in the rightmost column of your second table (for even levels) could be seen as "constant" so that you could assume it as a base for all remaining calculations with n>12 ?
Ajedrecista wrote:... Almost a month ago, Reinhard Scharnagl did estimates using inverse interpolation and the output of the results is similar to yours. ...
The idea of my calculation using inverse interpolation has been based upon:
a) switching to the natural logarithm, because Perft seems to me mainly a growth function
b) the growth factor seems to have an asymptotic behavior for about the next hundreds of ply levels,
thus using continued fractions seems to be more appropriate than to follow a polynomial approach.
Hi Reinhard:
I see that you put a table of your calculations, but this table had a little bug in odd values of n, as you said:
The changes are minimum but they exist. Regarding your points:
a) I agree, it seems a good way for me; I also use logarithms (in base 10) for my intermedial calculations just before my polynomials.
b) (Sven was faster than me). I agree with the issue of the asymptotic behaviour, but I disagree (slightly) with your point 'blaming' polynomials: the polynomials can be adjust when more true perft values will be known. You have to do the same with the last column of values that will not be constant although you suppose they are constant because is the simplest way I see for interpolating (and maybe it is the only way). I am sure that if we ignore, for example, Perft(11) and Perft(12) values (as they were unknown), using your method of inverse interpolation, for estimating Perft(11) you would get different values on those columns of continuous fractions than the true ones.
I think our methods are not better or worse than the other, only they are different but also valid (the relative error in Perft(13) will be 'small'). If I take your last value you got: 1.98112079e+18; and mine: 1.980468096e+18 (the central value of my given interval), the relative error between them is less than 0.033%.
Sven Schüle wrote:... just curious: how did you come to the conclusion that the value "-2587,643803" for n=12 in the rightmost column of your second table (for even levels) could be seen as "constant" so that you could assume it as a base for all remaining calculations with n>12 ?
Well, this is not a constant. It is the best value available for this level. This has been taken to be repeated for to interpolate/extrapolate results for higher plies.
Despite of the different base value levels for even and odd plies both interpolations describe the same function, for which I presume the properties will converge. Therefore I "freely" took the last calculated inverse factor, not having anything better.
Nevertheless slightly changing that value at this outmost level will not have that big impact to the finally interpolated Perft13 or Perft14 result as you might expect.
Sven Schüle wrote:... just curious: how did you come to the conclusion that the value "-2587,643803" for n=12 in the rightmost column of your second table (for even levels) could be seen as "constant" so that you could assume it as a base for all remaining calculations with n>12 ?
Well, this is not a constant. It is the best value available for this level. This has been taken to be repeated for to interpolate/extrapolate results for higher plies.
Despite of the different base value levels for even and odd plies both interpolations describe the same function, for which I presume the properties will converge. Therefore I "freely" took the last calculated inverse factor, not having anything better.
Nevertheless slightly changing that value at this outmost level will not have that big impact to the finally interpolated Perft13 or Perft14 result as you might expect.
Hi Reinhard,
actually it seems that the perft(13) estimate in your table is "almost independent" from that number "-2587,643803". Nearly always I get a result of approximately 1,98E+18 regardless whether I change that "-2587,..." number into -1000, +1000000000, or to -33333. The differences seem to affect the less significant digits beyond "1,98" only. I can't explain why, maybe you have an explanation?
Your estimates are in the range of others I have seen here, so congratulations. Of all of these numbers, I only understand the number of plies (13 and 14), the estimates (1.9801...e+18 and 6.1803...e+19) and the branching factors (31.5031... and 31.2118...). What are the other numbers?
Almost a month ago, Reinhard Scharnagl did estimates using inverse interpolation and the output of the results is similar to yours. I guess you have done one kind of interpolation or extrapolation, but could you confirm this, please? Thanks in advance.
Regards from Spain.
Ajedrecista.
I used the same methods as Julien Marcel (See page 2), but I took it a little further with a couple more calculations. Reversing the process arrived at the new data points.
The other numbers are differences and percentages of increases and decreases.
Bottom_line, I manually crunched numbers for 6 hours, on my "NASA" calculator. I guess I lost track of time or maybe time lost track of me? Both? I crunched so many numbers I might have time traveled.
I see, thanks for replying; until this momment, my estimates were usually the lowest of all here... but it has changed! It is very hard to find a serious estimate not starting by 1.980...e+18 or 1.981...e+18. If true Perft(13) value is among this range, then estimates will be a total success.
