Is e4 significantly better than d4?

[OneTrickPony]

The Berlin endgame is a pretty reasonable 1. e4 mainline, though.

I don't know. Imo white gets absolutely nothing in the Berlin endgame and in otb chess I actually prefer to be black there.
One easy equalizing plan is Be7, Nh4 but black can play something more ambitious as well.

[Jouni]

All opening moves draw (0,00 score) except g4 loses! Can You prove that with super hardware soon?

[Raphexon]

I don't know, I still seem to trust more Leela than even Larry. I have zero opening theory knowledge, but I am a bit skeptical when people come with some esoteric to me knowledge, while in the openings Leela already at 1 node is positionally probably GM level. Sorry, I think I will stick with my simplistic approach using Leela with the best available net at long analyses.

I went through proposed by Leela line ply by ply to 100 million nodes each ply, and remarkably e4 line was followed all the way to the 8 moves I showed in the diagram in the first post. The same thing, remarkably, happened with the d4 line, this time to 6 moves.

The positions in diagrams do occur in many recent games of top GMs. I let analyze these e4 and d4 lines at the endposition for more than 100 million nodes each. The net is the best JHorthos bignet. Crucially, these trends are hardly visible at say 10 million nodes, the scores stabilize after more than 50-100 million nodes.

Here is the e4 line analyzed after 8 moves, previously checked ply by ply 8-mover, now analyzed to 100+ million nodes:

[d]r1bk1b1r/ppp2ppp/2p5/4Pn2/8/5N2/PPP2PPP/RNB2RK1 w - - 0 9


info depth 27 seldepth 72 time 6867298 nodes 123995548 score cp 5471 hashfull 10
00 nps 18055 tbhits 0 multipv 1 pv b1c3 d8e8 h2h3 h7h5 c1f4 f8b4 c3e2 c8e6 e2d4
f5d4 f3d4 e6d5 a1c1 a8d8 f1d1 b4e7 c2c4 d5e4 f2f3 e7c5 f4e3 e4g6 g2g4 h5g4 h3g4
f7f6 e5f6 g7f6 g1g2 e8f7 d4f5 d8d1 c1d1 g6f5 e3c5 f5e6 g2g3 h8g8 g3f4 a7a5 a2a4
g8e8 d1h1 f7g6 h1e1 e6f7 e1e8 f7e8 c5e7 e8f7 b2b3 b7b5 b3b4 a5b4 a4a5 b4b3 e7a3
f7c4 a5a6 c6c5



Here is the d4 line analyzed after 6 moves, previously checked ply by ply 6-mover, now analyzed to 100+ million nodes:

[d]rnbq1rk1/ppp1bppp/4pn2/3p4/2PP4/5NP1/PP1BPPBP/RN1QK2R w KQ d6 0 7


info depth 25 seldepth 73 time 12398405 nodes 140132643 score cp 5306 hashfull 1
000 nps 11302 tbhits 0 multipv 1 pv d1c2 b8d7 e1g1 c7c6 d2f4 b7b6 b1d2 f6h5 e2e3
c8a6 f1c1 a6b7 c4d5 e6d5 h2h4 c6c5 d2b1 h5f4 e3f4 c5d4 f3d4 a8c8 b1c3 d7f6 c1d1
f8e8 a2a3 g7g6 d1d2 e7c5 a1d1 d8e7 c2b3 f6e4 d2e2 e7f6 c3d5 b7d5 b3d5


=========================================

e4 best line performs 50% better than d4 best line. These are not weird openings.

With e4 line, if it so bad an opening for Black, why very recently it was played as Black by super GMs from Nakamura to Carlsen, Topalov, Karjakin, Anand, etc.? It is a pretty common opening for top GMs, both as White and Black.

With d4 line, if it so bad an opening for White, why very recently it was played as White by super GMs from Nakamura to Carlsen, Kramnik, Gelfand, Aronian, etc.? It is not an uncommon opening for top GMs, both as White and Black.

========================

I know nothing of opening theory, and sorry, I sort of love Leela in the openings, I am very biased trusting it .

Oof that E4 PV, trading that queen early is a nice way for Leela to cut down the branching factor for A/B engines.
If the game for her PV up to that point I think Leela would generally perform better with D4 than with E4 (against SF.) With the knowledge she's better at positional play.

[Ovyron]

All opening moves draw (0,00 score) except g4 loses! Can You prove that with super hardware soon?

I can defend 1.g4 against anyone in the world. Fancy a corr game to see where your winning line is refuted?

1.g4 has some hard limit evaluation of about -0.95, so it's defensible, and if black manages an advantage of -0.96, it's because white has done something wrong afterwards.

Just because a position is 99% in favor of some side, it doesn't mean that it's not trivial for someone to find that 1% every move within 48 hours and play it.

...

A more interesting question would be... how bad can white play and still save the game? Like, 1.g4 d5 2.f4 Bxg4 doesn't seem defensible, so there should be positions at the edge where it's not clear if they're defensible or not.

[Laskos]

I am still into silly things. An I still think Lc0 bignet on my RTX 2070 is stronger positionally than any human. I understand the arguments against, and they are very solid, but I will stick to silly approaches.

I took the KingBase, selected the games of FIDE Elo 2700+ both players, and played games from their d4 and e4 openings to 8 moves. The opponents are Lc0 Terminator Bignet at 100 nodes against SF_dev at 70,000 nodes. 4,000 games each match.

Elo 2700+
16 plies human GM openings


d4:
Score of lc0_320x24_178 vs SF_dev: 1283 - 1552 - 1165 [0.466] 4000
Elo difference: -23.40 +/- 9.07
Finished match

White performance:
+1547 =1165 -1288
53.2%


e4:
Score of lc0_320x24_178 vs SF_dev: 1294 - 1646 - 1060 [0.456] 4000
Elo difference: -30.65 +/- 9.24
Finished match

White performance:
+1656 =1060 -1284
54.7%


Almost outside the error margins that e4 performs better than d4 with engine play (very different engines, for consistency). The same about 40% better. To note that human performance in this Elo 2700+ database for e4 and d4 openings is within error margins, close to 54.4% both.

So, by now I have both the eval and the statistic of outcomes. It's silly, but good to know anyway.

[dragontamer5788]

I am still into silly things. An I still think Lc0 bignet on my RTX 2070 is stronger positionally than any human. I understand the arguments against, and they are very solid, but I will stick to silly approaches.

I took the KingBase, selected the games of FIDE Elo 2700+ both players, and played games from their d4 and e4 openings to 8 moves. The opponents are Lc0 Terminator Bignet at 100 nodes against SF_dev at 70,000 nodes. 4,000 games each match.

Elo 2700+
16 plies human GM openings


d4:
Score of lc0_320x24_178 vs SF_dev: 1283 - 1552 - 1165 [0.466] 4000
Elo difference: -23.40 +/- 9.07
Finished match

White performance:
+1547 =1165 -1288
53.2%


e4:
Score of lc0_320x24_178 vs SF_dev: 1294 - 1646 - 1060 [0.456] 4000
Elo difference: -30.65 +/- 9.24
Finished match

White performance:
+1656 =1060 -1284
54.7%


Almost outside the error margins that e4 performs better than d4 with engine play (very different engines, for consistency). The same about 40% better. To note that human performance in this Elo 2700+ database for e4 and d4 openings is within error margins, close to 54.4% both.

So, by now I have both the eval and the statistic of outcomes. It's silly, but good to know anyway.

Hmmm... technically speaking... shouldn't you perform a Minimax evaluation over the ply?

Hypothetically, if 1.d4 d5 2. c4 ... ended up being a 60% chance of win for White (hypothetically), but 2.e5 ended up being a 40% chance of win (I'm making up numbers here), it could be that 2.e5 would "bring down the average score".

In effect, maybe you've refuted 2 or 3 openings in the 1.d4 tree, but maybe not the entire 1.d4 tree.

[Laskos]

I am still into silly things. An I still think Lc0 bignet on my RTX 2070 is stronger positionally than any human. I understand the arguments against, and they are very solid, but I will stick to silly approaches.

I took the KingBase, selected the games of FIDE Elo 2700+ both players, and played games from their d4 and e4 openings to 8 moves. The opponents are Lc0 Terminator Bignet at 100 nodes against SF_dev at 70,000 nodes. 4,000 games each match.

Elo 2700+
16 plies human GM openings


d4:
Score of lc0_320x24_178 vs SF_dev: 1283 - 1552 - 1165 [0.466] 4000
Elo difference: -23.40 +/- 9.07
Finished match

White performance:
+1547 =1165 -1288
53.2%


e4:
Score of lc0_320x24_178 vs SF_dev: 1294 - 1646 - 1060 [0.456] 4000
Elo difference: -30.65 +/- 9.24
Finished match

White performance:
+1656 =1060 -1284
54.7%


Almost outside the error margins that e4 performs better than d4 with engine play (very different engines, for consistency). The same about 40% better. To note that human performance in this Elo 2700+ database for e4 and d4 openings is within error margins, close to 54.4% both.

So, by now I have both the eval and the statistic of outcomes. It's silly, but good to know anyway.

Hmmm... technically speaking... shouldn't you perform a Minimax evaluation over the ply?

Hypothetically, if 1.d4 d5 2. c4 ... ended up being a 60% chance of win for White (hypothetically), but 2.e5 ended up being a 40% chance of win (I'm making up numbers here), it could be that 2.e5 would "bring down the average score".

In effect, maybe you've refuted 2 or 3 openings in the 1.d4 tree, but maybe not the entire 1.d4 tree.

How can one refute the entire d4 tree? I think that when we will be able to do that, we will be close to be able to show weakly that Chess is a draw.

[dragontamer5788]

How can one refute the entire d4 tree? I think that when we will be able to do that, we will be close to be able to show weakly that Chess is a draw.

Fair point. I need to work on the precision of my words a bit...

I think that what I'm trying to say is that a degree of minimax should be applied to your results. I haven't thought about it too deeply, but you have 4000-sample games across 4000-different starting positions on d4. We don't want the "average performance" of those 4000 moves, we want to know which of those 4000 moves is "best for white".

I want to see best-move(d4) vs best-move(e4). What you seem to have calculated is average-move(d4) vs average-move(e4). Does that make sense?

[OneTrickPony]

Looking at ChessTempo database which conveniently shows performance rating for all the moves and filtering for 2700+ vs 2700+ games I can see:

1.e4 - 2792
1.d4 - 2791
1.Nf3 - 2793
1.c4 - 2794

Looks pretty even to me. It's likely more useful to look at 2600+ games from last 10 years instead because sensible opening theory was established by then. Here we get:

1.e4 - 2623
1.d4 - 2627
1.Nf3 - 2629
1.c4 - 2640

Having this and evidence from Leela evals I conclude there is very little difference between 1.e4 and 1.d4 but if anything the evidence we have today suggests 1.d4 is marginally better.
On serious note: it depends if you prefer to grind d3 or Re1 Berlin or Bf4 QGD or Ragozin endgames. d3 Berlin is likely the most complicated (but also produces the lowest evals) while Bf4 positions are the safest for white.

[Graham Banks]

Chessbase online database gives: