perft(11)

[sje]

A figure for perft(11) was given some years ago, but was not (at least to my knowledge) ever confirmed.

As a side effect of current testing, here's Symbolic's confirmation (2,097,651,003,696,806) and the ply one subtotals:

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Na3 70080800068168
Nc3 91451554526572
Nf3 89933046388964
Nh3 71046267678634
a3 60403292887824
a4 85054341127064
b3 79510326025357
b4 80419308561211
c3 92235553734553
c4 103605670223681
d3 151857971385067
d4 211583204457112
e3 241074613621302
e4 245841494675197
f3 51614296095395
f4 68372448303691
g3 82762826570051
g4 73966186324024
h3 60097879424719
h4 86739921618220

Depth: 11   Count: 2097651003696806   Elapsed: 464766

The test took a little over 129 hours running on a 2 GHz Intel C2D.

[Dann Corbit]

Interesting that when you sort by move count, the most popular openings tend to be also the most played (though e3 seems to be a striking anomaly):

Code: Select all

f3   51614296095395
h3   60097879424719
a3   60403292887824
f4   68372448303691
Na3  70080800068168
Nh3  71046267678634
g4   73966186324024
b3   79510326025357
b4   80419308561211
g3   82762826570051
a4   85054341127064
h4   86739921618220
Nf3  89933046388964
Nc3  91451554526572
c3   92235553734553
c4  103605670223681
d3  151857971385067
d4  211583204457112
e3  241074613621302
e4  245841494675197

[Dann Corbit]

Interesting that when you sort by move count, the most popular openings tend to be also the most played (though e3 seems to be a striking anomaly):

Code: Select all

f3   51614296095395
h3   60097879424719
a3   60403292887824
f4   68372448303691
Na3  70080800068168
Nh3  71046267678634
g4   73966186324024
b3   79510326025357
b4   80419308561211
g3   82762826570051
a4   85054341127064
h4   86739921618220
Nf3  89933046388964
Nc3  91451554526572
c3   92235553734553
c4  103605670223681
d3  151857971385067
d4  211583204457112
e3  241074613621302
e4  245841494675197

For comparison/contrast, here is the openings report from my SCID database:

Code: Select all

    Move   ECO       Frequency    Score  AvElo Perf AvYear %Draws
 1: e4     B00a  3057844: 44.2%   53.6%  2387  2419   589   25%
 2: d4     A40a  2425808: 35.1%   54.5%  2444  2485   210   28%
 3: Nf3    A04    604083:  8.7%   54.2%  2478  2503  1999   30%
 4: c4     A10    581544:  8.4%   54.0%  2477  2502  1998   29%
 5: g3     A00t    60421:  0.8%   52.8%  2426  2439  1999   28%
 6: f4     A02     47059:  0.6%   48.1%  2247  2296  1996   21%
 7: b3     A01     41349:  0.5%   51.6%  2501  2516  2000   22%
 8: Nc3    A00l    29138:  0.4%   49.5%  2236  2264  2000   19%
 9: b4     A00p    19350:  0.2%   49.1%  2134  2154  1995   20%
10: e3     A00k    12615:  0.1%   38.7%  2255  2249  1999   12%
11: g4     A00n     9271:  0.1%   44.7%  2430  2403  1999   14%
12: d3     A00j     5443:  0.0%   43.6%  2268  2257  2000   18%
13: c3     A00i     2206:  0.0%   46.7%  2454  2467  2001   16%
14: a3     A00f     2131:  0.0%   47.8%  2344  2333  2000   16%
15: h4     A00c     1653:  0.0%   38.0%  2523  2442  2001    9%
16: h3     A00d     1543:  0.0%   36.7%  2455  2454  2001   14%
17: a4     A00e     1487:  0.0%   39.5%  2593  2525  2002   13%
18: f3     A00b     1013:  0.0%   40.4%  2373  2335  2000    8%
19: Nh3    A00g      238:  0.0%   38.2%  2256  2267  2002   16%
20: Na3    A00h      110:  0.0%   26.8%  2079  1939  2004    6%
_______________________________________________________________
TOTAL:           6904306:100.0%   53.8%  1049  1055   117   27%

[sje]

There is of course some positive correlation between mobility and opening popularity, and having the ply one splay helps show this.

The ply one splay is also useful for verification although I hadn't seen one for perft(11) until I made one myself.

There is a report that perft(12) is 62,854,969,236,701,747. That might take some hundred days or so on my C2D as there isn't much memory on that box for local transposition tables.

On a side note, the run adds confidence that a 64 bit hash length is more than sufficient for use in chess transposition tables.

On another side note, it was back in 1987 that my old program Spector calculated perft(7) = 3,195,901,860. With neither bulk counting nor transposition assistance, the run took about 36 hours on a 16 MHz Motorola 68020. That's a node rate of about 25 KHz, and that was pretty good back then. There was no 64 bit arithmetic support available, so I had to add the ply one sums by hand to get the total.

[diep]

Interesting that when you sort by move count, the most popular openings tend to be also the most played (though e3 seems to be a striking anomaly):

Code: Select all

f3   51614296095395
h3   60097879424719
a3   60403292887824
f4   68372448303691
Na3  70080800068168
Nh3  71046267678634
g4   73966186324024
b3   79510326025357
b4   80419308561211
g3   82762826570051
a4   85054341127064
h4   86739921618220
Nf3  89933046388964
Nc3  91451554526572
c3   92235553734553
c4  103605670223681
d3  151857971385067
d4  211583204457112
e3  241074613621302
e4  245841494675197

Maximizing mobility is important
Yet in this manner it is a heuristic.

Note that e3 as an openingsmove is a beginnersmove.

The big problem of playing e3 first move is that you shut in c1 bishop.
It's a kind of French opening with reversed colors without any reason to directly make a bishop on c1 bad, so your openings advantage immediately has gone.

I remember a game when i was young against someone who is many times GM now: 1.b4,e5 2.a3,d5 3.e3

And my c1 bishop was buried forever and black got a huge attack on whites kingside and won with that handsdown.

that was also the last game i played in a serious tournament with 1.b4

Note that a year or 2 ago i played a game against Van Geet, though it was a rapid game, he started with b3 and followed with e3 soon. It was 0-1 very quickly, as i took instantly the center with e5 and d5.

Van Geet, as some might remember some openingslines have been named after him, always tries weirdo openings.

I remember a game against the young Erwin l'Ami in the competition of my club. Erwin l'Ami - Van Geet: 1.e4,Nh6 soon with a huge attack kingside after a quick h4 from white and 1-0 within 20 moves.

The center is really important in chess. Mobility is of course a heuristic, yet an important one.

Vincent

[Dann Corbit]

I wouldn't play e3 because it looks so timid.
Here is overnight Rybka analysis (with multi-pv=3) of:

[d]rnbqkbnr/pppppppp/8/8/8/4P3/PPPP1PPP/RNBQKBNR b KQkq -

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     25	15:26:13	6.270.654,244	178.665	-0.09	g7g6 Ng1f3 Ng8f6 d2d4 Bf8g7 c2c4 OO Nb1c3 c7c5 d4d5 d7d6 Bf1e2 e7e6 OO e6xd5 c4xd5 Nb8a6 e3e4 Rf8e8 Nf3d2 Bc8d7
     25	15:26:13	9.960.831,401	183.542	-0.07	c7c5 Ng1f3 Ng8f6 d2d4 e7e6 c2c4 d7d5 Nb1c3 Nb8c6 Bf1d3 d5xc4 Bd3xc4 c5xd4 e3xd4 Bf8d6 OO OO Bc1e3 Bc8d7 Ra1c1
     25	15:26:13	5.653.292,012	178.745	-0.07	Ng8f6 Ng1f3 e7e6 c2c4 d7d5 Nb1c3 c7c5 d2d4 Nb8c6 Bf1d3 d5xc4 Bd3xc4 c5xd4 e3xd4 Bf8d6 OO OO Bc1e3 Bc8d7 Ra1c1