Highest Depth search in modern computers?

[h1a8]

How deep (in plys) and on average can a top modern computer for general consumers (i9-14900k for example) search with brute force (no pruning) in like a few hours or a day?

Assume a top supercomputer can calculate 1e18 positions per second.
Then how deep can they search on average (in ply) using only brute force in like a few hours or a day?

Let's assume the starting position of the chessboard.

I know reasonable answers may be off. But I'm curious to you guys expert opinions.

[Jouni]

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

[smatovic]

Brute force w/o pruning -> perft?

Fast perft on GPU (upto 20 Billion nps w/o hashing)
https://www.talkchess.com/forum3/viewtopic.php?t=48387

What is a good perft speed?
https://www.talkchess.com/forum3/viewtopic.php?t=83043

Perft Results
https://www.chessprogramming.org/Perft_Results

--
Srdja

[Ajedrecista]

Hello:

I am not an expert at all, but here are my two cents: I would like to have a computer that can count (not saying calculate lines with evals) 1e18 positions from the start position! Perft(13) would be computed in less than two seconds, Perft(15) in less than 34 minutes and Perft(16) (still unknown) in less than 19 hours. I see that Srdja also talks about perft.

The question remains open because a search without pruning still has the eval function, and there are light, faster evals like only material, others like material + PST and so on, up to heavy, slow evals like neural networks.

It sounds familiar to me that Jouni's example is taken from an old experiment of a German user called Andreas, who wanted to share some branching factors with us. That search used SF engine, which prunes moves during the search, not being exactly what you asked for.

Regards from Spain.

Ajedrecista.

[chrisw]

PERFT is without the beta algorithm. The OP would presumably allow AB

[smatovic]

PERFT is without the beta algorithm. The OP would presumably allow AB

You could take perft nps w/o tricks like bulk counting, half speed for some simple eval, then take 6th root of searched nodes for AB with perfect move ordering, something like that, depends on evaluation function I guess.

--
Srdja

[chrisw]

PERFT is without the beta algorithm. The OP would presumably allow AB

You could take perft nps w/o tricks like bulk counting, half speed for some simple eval, then take 6th root of searched nodes for AB with perfect move ordering, something like that, depends on evaluation function I guess.

--
Srdja

no need to disallow hash either, although any hash table would pale into insignificance vis a vis total nodes

[hgm]

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.

[smatovic]

You could take perft nps w/o tricks like bulk counting, half speed for some simple eval, then take 6th root of searched nodes for AB with perfect move ordering, something like that, depends on evaluation function I guess.

--
Srdja

Ah, as HGM mentioned, it is the square-root.

--
Srdja

[Leo]

How deep (in plys) and on average can a top modern computer for general consumers (i9-14900k for example) search with brute force (no pruning) in like a few hours or a day?

Assume a top supercomputer can calculate 1e18 positions per second.
Then how deep can they search on average (in ply) using only brute force in like a few hours or a day?

Let's assume the starting position of the chessboard.

I know reasonable answers may be off. But I'm curious to you guys expert opinions.

I like the question. I remember 55 ply or something. 5 years ago.