Highest Depth search in modern computers?

[Leo]

Initial position - depth 70 Stockfish 130118 64 POPCNT

Hardware:
Intel i3-2130 @ 3.4 GHz 2 threads

Code: Select all

depth     time ms     DD:hh:mm:ss          nodes          bf    cp      nps       hf
-------------------------------------------------------------------------------------
 20           2.961   00:00:00:03            7.809.122   1.46   32   2.637.325    24
 21           4.007   00:00:00:04           10.399.247   1.33   30   2.595.270    34
 22           8.118   00:00:00:08           20.773.844   2.00   26   2.558.985    73
 23          11.769   00:00:00:12           29.580.482   1.42   22   2.513.423   110
 24          18.206   00:00:00:18           45.477.435   1.54   32   2.497.936   155
 25          21.969   00:00:00:22           55.381.467   1.22   38   2.520.891   203
 26          27.229   00:00:00:27           69.549.803   1.26   28   2.554.254   249
 27          34.406   00:00:00:34           88.341.585   1.27   32   2.567.621   312
 28          44.319   00:00:00:44          114.308.137   1.29   22   2.579.212   401
 29          51.010   00:00:00:51          131.493.550   1.15   22   2.577.799   454
 30          67.166   00:00:01:07          172.669.782   1.31   25   2.570.791   550
 31          95.972   00:00:01:36          245.796.848   1.42   27   2.561.130   706
 32         121.732   00:00:02:02          312.584.774   1.27   30   2.567.811   831
 33         195.528   00:00:03:16          504.220.842   1.61   25   2.578.765   947
 34         270.284   00:00:04:30          701.974.776   1.39   10   2.597.174   994
 35         542.696   00:00:09:03        1.423.172.418   2.03    8   2.622.411   999
 36         852.233   00:00:14:12        2.248.334.831   1.58    7   2.638.169   999
 37       1.025.618   00:00:17:06        2.704.202.685   1.20    9   2.636.656   999
 38       1.269.916   00:00:21:10        3.352.076.991   1.24    6   2.639.605   999
 39       1.821.664   00:00:30:22        4.843.938.257   1.45    9   2.659.073   999
 40       2.422.055   00:00:40:22        6.432.149.569   1.33   13   2.655.657   999
 41       2.687.778   00:00:44:48        7.139.720.058   1.11   25   2.656.365   999
 42       3.379.961   00:00:56:20        8.999.060.694   1.26    8   2.662.474   999
 43       6.255.902   00:01:44:16       16.685.266.411   1.85   19   2.667.124   999
 44      11.966.099   00:03:19:26       31.935.614.594   1.91   18   2.668.840   999
 45      13.996.185   00:03:53:16       37.305.243.123   1.17   18   2.665.386   999
 46      18.986.926   00:05:16:27       50.476.904.815   1.35   15   2.658.508   999
 47      29.555.211   00:08:12:35       78.749.855.020   1.56   16   2.664.499   999
 48      32.379.375   00:08:59:39       86.258.487.995   1.10   22   2.663.994   999
 49      38.171.214   00:10:36:11      102.087.328.823   1.18   18   2.674.458   999
 50      59.954.177   00:16:39:14      162.433.347.175   1.59   13   2.709.291   999
 51      68.229.137   00:18:57:09      184.638.998.399   1.14   13   2.706.160   999
 52     147.657.664   01:17:00:58      401.226.073.057   2.17   24   2.717.272   999
 53     176.568.889   02:01:02:49      481.184.993.983   1.20    9   2.725.196   999
 54     183.776.030   02:03:02:56      500.828.026.388   1.04   12   2.725.208   999
 55     612.348.337   07:02:05:48    1.683.626.096.810   3.36    8   2.749.458   999
 56     691.324.582   08:00:02:05    1.902.007.602.700   1.13    8   2.751.251   999
 57     942.416.277   10:21:46:56    2.600.369.228.395   1.37   12   2.759.257   999
 58   1.108.243.196   12:19:50:43    3.065.487.180.680   1.18   14   2.766.078   999
 59   1.133.362.443   13:02:49:22    3.136.008.925.222   1.02   15   2.766.995   999
 60   1.539.239.134   17:19:33:59    4.277.389.258.149   1.36    8   2.778.898   999
 61   2.017.290.614   23:08:21:31    5.614.261.530.698   1.31   12   2.783.070   999
 62   2.587.485.027   29:22:44:45    7.198.730.538.139   1.28    9   2.782.134   999
 63   2.785.825.750   32:05:50:26    7.749.378.651.635   1.08   15   2.781.717   999
 64   3.639.352.274   42:02:55:52   10.149.662.885.237   1.31    8   2.788.865   999
 65   6.125.138.474   70:21:25:38   17.288.598.093.977   1.70    8   2.822.564   999
 66   6.510.453.751   75:08:27:34   18.387.727.244.730   1.08    8   2.824.339   999
 67   7.462.845.087   86:09:00:45   21.068.240.925.795   1.15   16   2.823.084   999
 68   9.549.220.198  109:12:33:40   27.111.553.587.762   1.29   11   2.839.138   999
 69  12.613.582.864  144:23:46:23   35.925.549.032.091   1.33    8   2.848.164   999
 70  14.474.647.554  165:12:44:08   41.192.897.168.184   1.15    8   2.845.865   999

[Leo]

Initial position - depth 70 Stockfish 130118 64 POPCNT

Hardware:
Intel i3-2130 @ 3.4 GHz 2 threads

Code: Select all

depth     time ms     DD:hh:mm:ss          nodes          bf    cp      nps       hf
-------------------------------------------------------------------------------------
 20           2.961   00:00:00:03            7.809.122   1.46   32   2.637.325    24
 21           4.007   00:00:00:04           10.399.247   1.33   30   2.595.270    34
 22           8.118   00:00:00:08           20.773.844   2.00   26   2.558.985    73
 23          11.769   00:00:00:12           29.580.482   1.42   22   2.513.423   110
 24          18.206   00:00:00:18           45.477.435   1.54   32   2.497.936   155
 25          21.969   00:00:00:22           55.381.467   1.22   38   2.520.891   203
 26          27.229   00:00:00:27           69.549.803   1.26   28   2.554.254   249
 27          34.406   00:00:00:34           88.341.585   1.27   32   2.567.621   312
 28          44.319   00:00:00:44          114.308.137   1.29   22   2.579.212   401
 29          51.010   00:00:00:51          131.493.550   1.15   22   2.577.799   454
 30          67.166   00:00:01:07          172.669.782   1.31   25   2.570.791   550
 31          95.972   00:00:01:36          245.796.848   1.42   27   2.561.130   706
 32         121.732   00:00:02:02          312.584.774   1.27   30   2.567.811   831
 33         195.528   00:00:03:16          504.220.842   1.61   25   2.578.765   947
 34         270.284   00:00:04:30          701.974.776   1.39   10   2.597.174   994
 35         542.696   00:00:09:03        1.423.172.418   2.03    8   2.622.411   999
 36         852.233   00:00:14:12        2.248.334.831   1.58    7   2.638.169   999
 37       1.025.618   00:00:17:06        2.704.202.685   1.20    9   2.636.656   999
 38       1.269.916   00:00:21:10        3.352.076.991   1.24    6   2.639.605   999
 39       1.821.664   00:00:30:22        4.843.938.257   1.45    9   2.659.073   999
 40       2.422.055   00:00:40:22        6.432.149.569   1.33   13   2.655.657   999
 41       2.687.778   00:00:44:48        7.139.720.058   1.11   25   2.656.365   999
 42       3.379.961   00:00:56:20        8.999.060.694   1.26    8   2.662.474   999
 43       6.255.902   00:01:44:16       16.685.266.411   1.85   19   2.667.124   999
 44      11.966.099   00:03:19:26       31.935.614.594   1.91   18   2.668.840   999
 45      13.996.185   00:03:53:16       37.305.243.123   1.17   18   2.665.386   999
 46      18.986.926   00:05:16:27       50.476.904.815   1.35   15   2.658.508   999
 47      29.555.211   00:08:12:35       78.749.855.020   1.56   16   2.664.499   999
 48      32.379.375   00:08:59:39       86.258.487.995   1.10   22   2.663.994   999
 49      38.171.214   00:10:36:11      102.087.328.823   1.18   18   2.674.458   999
 50      59.954.177   00:16:39:14      162.433.347.175   1.59   13   2.709.291   999
 51      68.229.137   00:18:57:09      184.638.998.399   1.14   13   2.706.160   999
 52     147.657.664   01:17:00:58      401.226.073.057   2.17   24   2.717.272   999
 53     176.568.889   02:01:02:49      481.184.993.983   1.20    9   2.725.196   999
 54     183.776.030   02:03:02:56      500.828.026.388   1.04   12   2.725.208   999
 55     612.348.337   07:02:05:48    1.683.626.096.810   3.36    8   2.749.458   999
 56     691.324.582   08:00:02:05    1.902.007.602.700   1.13    8   2.751.251   999
 57     942.416.277   10:21:46:56    2.600.369.228.395   1.37   12   2.759.257   999
 58   1.108.243.196   12:19:50:43    3.065.487.180.680   1.18   14   2.766.078   999
 59   1.133.362.443   13:02:49:22    3.136.008.925.222   1.02   15   2.766.995   999
 60   1.539.239.134   17:19:33:59    4.277.389.258.149   1.36    8   2.778.898   999
 61   2.017.290.614   23:08:21:31    5.614.261.530.698   1.31   12   2.783.070   999
 62   2.587.485.027   29:22:44:45    7.198.730.538.139   1.28    9   2.782.134   999
 63   2.785.825.750   32:05:50:26    7.749.378.651.635   1.08   15   2.781.717   999
 64   3.639.352.274   42:02:55:52   10.149.662.885.237   1.31    8   2.788.865   999
 65   6.125.138.474   70:21:25:38   17.288.598.093.977   1.70    8   2.822.564   999
 66   6.510.453.751   75:08:27:34   18.387.727.244.730   1.08    8   2.824.339   999
 67   7.462.845.087   86:09:00:45   21.068.240.925.795   1.15   16   2.823.084   999
 68   9.549.220.198  109:12:33:40   27.111.553.587.762   1.29   11   2.839.138   999
 69  12.613.582.864  144:23:46:23   35.925.549.032.091   1.33    8   2.848.164   999
 70  14.474.647.554  165:12:44:08   41.192.897.168.184   1.15    8   2.845.865   999

Thanks. If I run my computer like that the wire melts as it enters the circuit breaker

[towforce]

Branching ratio of alpha-beta for Chess should be about 6 (the square-root of the average number of moves) = 10^0.78. A day is about 1e5 sec, so at 1e18 nps that would be 1e23 nodes. That would give a depth of 23/0.78 = 29.5 ply.

That doesn't take account of the speedup by a hash table. But it also doesn't take account of the fact that for the results to have any meaning you would need to do a Quiescence search, which drives up the number of leaves by a factor 7 or so. These effects might cancel each other.

Very good answer - thank you!

In Europe, and especially in the USA, I think that most "well off" people could afford a computer system that would have been in the Top500 supercomputer list (link) 10-15 years ago (obviously it would be more sensible to buy a house and a car, as most people choose to do). Alternatively, one can rent high powered computer systems on Google Compute - but if you use them all the time, this will also be expensive for most people.

[mgaortega]

https://en.wikipedia.org/wiki/Shannon_number

[ehenkes]

Little tests on my Personal Computer:

Intel i9-10900X @ 3.7 GHz
Stockfish 18
startpos
Hash 6000, Threads 10
...
info depth 46 seldepth 67 multipv 1 score cp 23 nodes 865127108 nps 4993115 hashfull 706 tbhits 0 time 173264
...
info depth 48 seldepth 81 multipv 1 score cp 20 nodes 2247123862 nps 4991778 hashfull 985 tbhits 0 time 450165 pv g1f3 d7d5 ...

From now on it is too slow.
------------------------------------------------------------

Intel i9-10900X @ 3.7 GHz
Stockfish 18
startpos
Hash 20000, Threads 15
...
info depth 42 seldepth 65 multipv 1 score cp 19 nodes 1081457230 nps 6208812 hashfull 295 tbhits 0 time 174181 pv e2e4 e7e5 ...
...
info depth 44 seldepth 71 multipv 1 score cp 26 nodes 1609305492 nps 6184878 hashfull 442 tbhits 0 time 260200 pv e2e4 e7e5 ...
...
info depth 48 seldepth 62 multipv 1 score cp 21 nodes 2480487030 nps 6122029 hashfull 642 tbhits 0 time 405174 pv e2e4 e7e5 ...
...
info depth 49 seldepth 75 multipv 1 score cp 23 nodes 2858575335 nps 6095992 hashfull 711 tbhits 0 time 468927 pv e2e4 e7e5 ...
...
info depth 51 seldepth 74 multipv 1 score cp 23 nodes 3184984786 nps 6085555 hashfull 758 tbhits 0 time 523368 pv e2e4 e7e5 ...
...
info depth 52 seldepth 71 multipv 1 score cp 18 nodes 5513587613 nps 5904994 hashfull 949 tbhits 0 time 933716 pv d2d4 g8f6
...

From now on it is too slow.
-----------------------------------

For tests it is important that hashfull is below 1000 (=100%).
Thus, practical values on modern personal computers seem to be in the range 50 to 60 plies depth.

[Eelco de Groot]

Branching ratio of alpha-beta for Chess should be about 6 (the square-root of the average number of moves) = 10^0.78. A day is about 1e5 sec, so at 1e18 nps that would be 1e23 nodes. That would give a depth of 23/0.78 = 29.5 ply.

That doesn't take account of the speedup by a hash table. But it also doesn't take account of the fact that for the results to have any meaning you would need to do a Quiescence search, which drives up the number of leaves by a factor 7 or so. These effects might cancel each other.

Very good answer - thank you!

In Europe, and especially in the USA, I think that most "well off" people could afford a computer system that would have been in the Top500 supercomputer list (link) 10-15 years ago (obviously it would be more sensible to buy a house and a car, as most people choose to do). Alternatively, one can rent high powered computer systems on Google Compute - but if you use them all the time, this will also be expensive for most people.

All you really need is Jim Ablett and his version of Kaissa ca. 1974. It can calculate 7 ply full width on an ICL 4/70. Run enough 7 ply deep self play games and Ed can turn that in a NNUE version. With the modern search of CSTal it easily becomes a 3500 Elo program, on todays hardware .


I still fondly remember reading a very small news article, with no pictures or even games or a chess diagram but fascinating nevertheless about those matches between Kaissa and Chess 4.5 I think it was for the world championship, in weekly or perhaps monthly now by 1974, scientific magazine for kids, 'Kijk". Modern, international, computerchess competition for the world title was born then!

Kaissa ran on a mainframe (British ICL System 4/70 computer) equipped with a 64-bit processor. 64 is also the
number of squares on a chessboard, so it was possible to use a single memory word to represent a yes-or-no or
true-or-false predicate for the whole board. This was called the bit board. The ICL 4/70 computer had 24,000
bytes of memory. It enabled the program to evaluate 200 positions per second. It could store 10,000 opening
positions in its memory. The program was written in Assembly language. The Assembly code occupied 384K bytes
(8-bit words). The Russians would have had a more powerful chess program if it had used an IBM machine, but they
were not allowed to buy or use one. The speed of the ICL 4/70 was 900,000 instructions per second.

[Eelco de Groot]

Vladimir Arlazarov, picture by Monty Newborn https://www.computerhistory.org/chess/s ... 9bbd7ee98/


Ken Thompson visits the Kaissa team in Moscow, picture by Monroe Newborn, computerhistory.org

Earlier visit to Moscow with Frederic Friedel

[syzygy]

I still fondly remember reading a very small news article, with no pictures or even games or a chess diagram but fascinating nevertheless about those matches between Kaissa and Chess 4.5 I think it was for the world championship, in weekly or perhaps monthly now by 1974, scientific magazine for kids, 'Kijk". Modern, international, computerchess competition for the world title was born then!

I missed that one, but I remember very well the article by Max Pam of May 1985 testing several chess computers.

I learned about Kaissa and Chess 4.5 from David Levy's Computer Chess Compendium.

[Alexander Schmidt]

All you really need is Jim Ablett and his version of Kaissa ca. 1974. It can calculate 7 ply full width on an ICL 4/70. Run enough 7 ply deep self play games and Ed can turn that in a NNUE version. With the modern search of CSTal it easily becomes a 3500 Elo program, on todays hardware .

It would take several years to make a 7 ply full search up to depth 7 with 200 nodes per second. Also Kaissa doesn't do a full search. You can see this in the number of calculated nodes, it calculates 500 nodes during a 3 ply search at starting position, full search would be around 8000 nodes.