Perft(14) estimates thread

[smrf]

Well, let me give a more recent estimation for Perft(14) actually based on an inverse interpolation now including Perft(13):

Perft(14) ≈ 6.18997E+19

[ibid]

For the ply 4 position:
[d]rnbqkbnr/ppp2ppp/8/3pp3/3PP3/8/PPP2PPP/RNBQKBNR w KQkq - 0 3[/d]
The perft(10) is: 5,029,284,456,467,481

Confirmed:

Code: Select all

1511172255/5029284456467481 positions.  16342 seconds.  done.

[smrf]

There could be a further refinement, I found:

Perft(14) ≈ 6.18986e+19

[petero2]

For the ply 4 position:
[d]rnbqkbnr/ppp2ppp/8/3pp3/3PP3/8/PPP2PPP/RNBQKBNR w KQkq - 0 3[/d]
The perft(10) is: 5,029,284,456,467,481

Confirmed:

Code: Select all

1511172255/5029284456467481 positions.  16342 seconds.  done.

I can confirm this too. The number of unique positions up to ply 7 are 1 38 1405 29256 598246 8815285 128870228 1511172255 and perft(10) is 5029284456467481.

The computation took 57466 seconds + about 1.5 hours to compute the unique positions at ply 7. The perft(14) computation was running at the same time though, which likely slowed things down by at least a factor of 2.

By the way, the perft 14 calculation has now been running for 9.8 days, is 25.2% complete and the estimated total calculation time is 39 days.

[Ajedrecista]

Hello Peter:

I can confirm this too. The number of unique positions up to ply 7 are 1 38 1405 29256 598246 8815285 128870228 1511172255 and perft(10) is 5029284456467481.

JetChess confirms unique positions from ply 1 up to ply 6. Here is the calculation done by JetChess 1.0.0.0 using 1.25 GB of hash and four steps in an Intel Pentium D930 (3 GHz) of year 2006. Please remember that JetChess is single core and 32-bit:

Code: Select all

rnbqkbnr/ppp2ppp/8/3pp3/3PP3/8/PPP2PPP/RNBQKBNR w KQkq - 0 3

Count  0:      32209250
Count  1:      32216253
Count  2:      32222820
Count  3:      32221905

Positions:    128870228

128,870,228 (positions after 6 half moves).

Time: 382.613 s (0:06:22.613).

I will try unique positions at ply 7 tomorrow in an Intel i5-760 (2.8 GHz) if I do not forget it and if I have spare time to do this... but I think that it will take too much time and it might be impossible. I do it simply as a sanity check because both Steven and you already agree in unique positions at ply 7.

As a first estimate of the result of JetChess: the settings are 1.25 GB of hash and 32 steps; after the first step:

Code: Select all

Count  0:      47224493

Then 32*47224493 = 1511183776 unique positions, which has a relative error of around 7.62 ppm. The approximated elapsed time in my Intel Pentium D930 was around 11 minutes for doing 1/32 of this calculation.

By the way, the perft 14 calculation has now been running for 9.8 days, is 25.2% complete and the estimated total calculation time is 39 days.

Thank you very much again for your interest and for the updates. I stay tuned!

Regards from Spain.

Ajedrecista.

[Ajedrecista]

Hello:

I will try unique positions at ply 7 tomorrow in an Intel i5-760 (2.8 GHz) if I do not forget it and if I have spare time to do this... but I think that it will take too much time and it might be impossible. I do it simply as a sanity check because both Steven and you already agree in unique positions at ply 7.

It is impossible: there is a hash overflow in JetChess (it only shows the first step out of 32). Anyway, if Steven and you agree in more than 1.51e+9 unique positions, it looks like your results are good. Please keep up your good work!

Regards from Spain.

Ajedrecista.

[sje]

Smallest perft(10) sub-result (?)
[d]rnbqkbnr/pp1pp1pp/2p2p2/8/8/2P2P2/PP1PP1PP/RNBQKBNR w KQkq - 0 3[/d]
The perft(10) for the above ply 4 position is 81,692,479,086,364.

Code: Select all

[] df
rnbqkbnr/pp1pp1pp/2p2p2/8/8/2P2P2/PP1PP1PP/RNBQKBNR w KQkq - 0 3
[] emptran 10
Kf2 3,215,090,878,895
Na3 3,593,436,310,853
Nh3 3,658,641,050,163
a3 2,439,504,803,807
Qc2 4,955,357,249,257
Qb3 5,512,695,972,184
Qa4 8,061,006,177,573
a4 2,710,494,109,452
b3 2,238,517,741,449
c4 3,030,952,386,877
b4 3,025,897,186,416
e3 5,724,552,039,159
d3 5,557,819,595,799
e4 5,840,805,760,224
d4 6,633,974,813,106
h3 2,469,309,286,734
g3 3,228,036,825,167
g4 3,181,867,089,979
f4 3,268,720,914,603
h4 3,345,798,894,667
Depth: 10   Count: 81,692,479,086,364   Elapsed: 5090.6  (1.60477e+10 Hz / 6.23142e-11 s)

[Ajedrecista]

Hello Steven:

Smallest perft(10) sub-result (?)
[d]rnbqkbnr/pp1pp1pp/2p2p2/8/8/2P2P2/PP1PP1PP/RNBQKBNR w KQkq - 0 3[/d]
The perft(10) for the above ply 4 position is 81,692,479,086,364.

Code: Select all

[] df
rnbqkbnr/pp1pp1pp/2p2p2/8/8/2P2P2/PP1PP1PP/RNBQKBNR w KQkq - 0 3
[] emptran 10
Kf2 3,215,090,878,895
Na3 3,593,436,310,853
Nh3 3,658,641,050,163
a3 2,439,504,803,807
Qc2 4,955,357,249,257
Qb3 5,512,695,972,184
Qa4 8,061,006,177,573
a4 2,710,494,109,452
b3 2,238,517,741,449
c4 3,030,952,386,877
b4 3,025,897,186,416
e3 5,724,552,039,159
d3 5,557,819,595,799
e4 5,840,805,760,224
d4 6,633,974,813,106
h3 2,469,309,286,734
g3 3,228,036,825,167
g4 3,181,867,089,979
f4 3,268,720,914,603
h4 3,345,798,894,667
Depth: 10   Count: 81,692,479,086,364   Elapsed: 5090.6  (1.60477e+10 Hz / 6.23142e-11 s)

I computed unique positions with JetChess 1.0.0.0 in an Intel i5-760 (2.8 GHz):

Code: Select all

Unique positions:

Ply 1:          20
Ply 2:         399
Ply 3:       5,595
Ply 4:      78,397
Ply 5:     886,971
Ply 6:  10,006,578
Ply 7:  97,776,976
Ply 8: 952,596,526

I hope the results are correct. Here is the count for ply 8, using 1.25 GB of hash and 32 steps:

Code: Select all

rnbqkbnr/pp1pp1pp/2p2p2/8/8/2P2P2/PP1PP1PP/RNBQKBNR w KQkq - 0 3

Count  0:      29781254
Count  1:      29756666
Count  2:      29762056
Count  3:      29780686
Count  4:      29760615
Count  5:      29780324
Count  6:      29781779
Count  7:      29759174
Count  8:      29774212
Count  9:      29754635
Count 10:      29761936
Count 11:      29774428
Count 12:      29756466
Count 13:      29780358
Count 14:      29784759
Count 15:      29758250
Count 16:      29780370
Count 17:      29758352
Count 18:      29750488
Count 19:      29777633
Count 20:      29752113
Count 21:      29783705
Count 22:      29779035
Count 23:      29752804
Count 24:      29773686
Count 25:      29761633
Count 26:      29759685
Count 27:      29775114
Count 28:      29762983
Count 29:      29781336
Count 30:      29778107
Count 31:      29761884

Positions:    952596526

952,596,526 (positions after 8 half moves).

Time: 6059.972 s (1:40:59.972).

Regards from Spain.

Ajedrecista.

[petero2]

Smallest perft(10) sub-result (?)
[d]rnbqkbnr/pp1pp1pp/2p2p2/8/8/2P2P2/PP1PP1PP/RNBQKBNR w KQkq - 0 3[/d]

That is not the smallest. This is smaller:
[d]rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 4 3[/d]

[petero2]

Hello:

I will try unique positions at ply 7 tomorrow in an Intel i5-760 (2.8 GHz) if I do not forget it and if I have spare time to do this... but I think that it will take too much time and it might be impossible. I do it simply as a sanity check because both Steven and you already agree in unique positions at ply 7.

It is impossible: there is a hash overflow in JetChess (it only shows the first step out of 32). Anyway, if Steven and you agree in more than 1.51e+9 unique positions, it looks like your results are good. :)

Actually it is Paul and I that agree on the unique count. Steven's algorithm gives sub-totals but not number of unique positions, while Paul's algorithm (which I use) gives number of unique positions but no sub-totals.