Is e4 significantly better than d4?

[Ozymandias]

It'd be ridiculous only against perfect play, because then 1.e4 and 1.d4 draw and they're objectively equal, but we don't have perfect play around. Some people disagree with me on this, and say draw death hit us years ago, but those people also claim they can draw a game against all possible moves, including technology from the future, and that's hard to believe.

Let me try to make it easier by asking: would you need an engine from the future to draw this position against any opponent?:

[d]4k3/4n2Q/2p5/6p1/3P2P1/8/4K3/2b5 b - - 0 74

[supersharp77]

Lc0 is very strong about positional openings. The best net to LTC and strong RTX hardware in games and performing the best in my opening test-suite is JHorthos 320x24b bignet J13B.2-136 (built upon late T40 nets). It practically understands in 1 million nodes search all human opening theory built in 100 years when only the positional things are considered. So, I decided to see what it thinks about the starting position of chess in very long searches, well surpassing the 16GB capacity of my RAM, using 128GB SSD cache. And well surpassing the known opening knowledge (presumably).

GPU: RTX 2070
The batch file can look like this:

Code: Select all

setoption name Backend value cudnn-fp16
setoption name MinibatchSize value 400 
setoption name NNCacheSize value 10000000
setoption name WeightsFile value .\J13B.2-136
setoption name ScoreType value win_percentage
setoption name MultiPV value 20
setoption name VerboseMoveStats value true
go nodes 250000000 searchmoves d2d4 g1f3 c2c4

First, a fast 1 million search from the starting position. This is already enough to see practically all human 1-ply theory of the position (there is no tactics). The quantity to look at is "Q", the performance from White POW here is (1+Q) / 2.

Code: Select all

info string g2g4  (378 ) N:     286 (+ 0) (P:  1.43%) (Q: -0.40008) (D:  0.282)
(U: 0.60112) (Q+U:  0.20104) (V: -0.4436)
info string f2f3  (346 ) N:     524 (+ 0) (P:  1.72%) (Q: -0.22862) (D:  0.364)
(U: 0.39472) (Q+U:  0.16610) (V: -0.2382)
info string g1h3  (161 ) N:     802 (+ 0) (P:  2.05%) (Q: -0.15754) (D:  0.414)
(U: 0.30835) (Q+U:  0.15081) (V: -0.1577)
info string h2h4  (403 ) N:     876 (+ 0) (P:  2.07%) (Q: -0.13819) (D:  0.408)
(U: 0.28454) (Q+U:  0.14635) (V: -0.1346)
info string b1a3  (34  ) N:     959 (+ 0) (P:  2.17%) (Q: -0.12870) (D:  0.410)
(U: 0.27319) (Q+U:  0.14449) (V: -0.1111)
info string b2b4  (234 ) N:    1080 (+ 0) (P:  2.29%) (Q: -0.11460) (D:  0.413)
(U: 0.25634) (Q+U:  0.14174) (V: -0.0917)
info string f2f4  (351 ) N:    1244 (+ 0) (P:  2.30%) (Q: -0.08744) (D:  0.407)
(U: 0.22316) (Q+U:  0.13572) (V: -0.1041)
info string a2a4  (207 ) N:    1693 (+ 0) (P:  2.57%) (Q: -0.05450) (D:  0.450)
(U: 0.18322) (Q+U:  0.12872) (V: -0.0337)
info string a2a3  (204 ) N:    2642 (+ 0) (P:  2.85%) (Q: -0.01052) (D:  0.450)
(U: 0.13013) (Q+U:  0.11961) (V: -0.0056)
info string d2d3  (288 ) N:    2737 (+ 0) (P:  2.77%) (Q: -0.00428) (D:  0.449)
(U: 0.12238) (Q+U:  0.11810) (V: -0.0129)
info string h2h3  (400 ) N:    2750 (+ 0) (P:  2.91%) (Q: -0.00897) (D:  0.464)
(U: 0.12797) (Q+U:  0.11900) (V: -0.0022)
info string b2b3  (230 ) N:    2991 (+ 0) (P:  2.95%) (Q: -0.00178) (D:  0.422)
(U: 0.11923) (Q+U:  0.11745) (V: -0.0061)
info string b1c3  (36  ) N:    4315 (+ 0) (P:  3.09%) (Q:  0.02509) (D:  0.437)
(U: 0.08652) (Q+U:  0.11161) (V:  0.0120)
info string c2c3  (259 ) N:    5604 (+ 0) (P:  3.62%) (Q:  0.03195) (D:  0.459)
(U: 0.07806) (Q+U:  0.11001) (V:  0.0444)
info string g2g3  (374 ) N:   10261 (+ 0) (P:  5.75%) (Q:  0.04036) (D:  0.464)
(U: 0.06775) (Q+U:  0.10811) (V:  0.0553)
info string e2e3  (317 ) N:   14263 (+ 0) (P:  5.98%) (Q:  0.05455) (D:  0.468)
(U: 0.05062) (Q+U:  0.10517) (V:  0.0571)
info string c2c4  (264 ) N:   28066 (+ 0) (P:  7.63%) (Q:  0.06911) (D:  0.451)
(U: 0.03283) (Q+U:  0.10194) (V:  0.0737)
info string g1f3  (159 ) N:   64502 (+ 0) (P: 10.01%) (Q:  0.08059) (D:  0.481)
(U: 0.01874) (Q+U:  0.09933) (V:  0.0848)
info string d2d4  (293 ) N:  439604 (+ 0) (P: 16.58%) (Q:  0.09024) (D:  0.490)
(U: 0.00456) (Q+U:  0.09480) (V:  0.0909)
info string e2e4  (322 ) N:  578066 (+850) (P: 19.27%) (Q:  0.09088) (D:  0.497)
 (U: 0.00402) (Q+U:  0.09490) (V:  0.1079)
bestmove e2e4 ponder e7e5

So, the lead candidates are e2e4 with 54.54% performance and d2d4 with 54.51% performance, an insignificant difference. And it confirms the human opening theory.


But now the things become serious. Longish (many hours) 250+ million nodes search with this bignet. The difference widens dramatically, so much that d2d4 is hardly explored anymore:

Code: Select all

info string g2g4  (378 ) N:    9986 (+ 0) (P:  1.43%) (Q: -0.39817) (D:  0.275)
(U: 0.50416) (Q+U:  0.10599) (V:  -.----)
info string f2f3  (346 ) N:   17137 (+ 0) (P:  1.72%) (Q: -0.24788) (D:  0.349)
(U: 0.35290) (Q+U:  0.10502) (V:  -.----)
info string g1h3  (161 ) N:   26407 (+ 0) (P:  2.05%) (Q: -0.16915) (D:  0.403)
(U: 0.27364) (Q+U:  0.10449) (V:  -.----)
info string h2h4  (403 ) N:   31379 (+ 0) (P:  2.07%) (Q: -0.12788) (D:  0.409)
(U: 0.23209) (Q+U:  0.10421) (V:  -.----)
info string b1a3  (34  ) N:   31863 (+ 0) (P:  2.17%) (Q: -0.13594) (D:  0.390)
(U: 0.24021) (Q+U:  0.10428) (V:  -.----)
info string b2b4  (234 ) N:   39780 (+ 0) (P:  2.29%) (Q: -0.09927) (D:  0.433)
(U: 0.20329) (Q+U:  0.10402) (V:  -.----)
info string f2f4  (351 ) N:   41298 (+ 0) (P:  2.30%) (Q: -0.09236) (D:  0.413)
(U: 0.19634) (Q+U:  0.10398) (V:  -.----)
info string a2a4  (207 ) N:   58013 (+ 0) (P:  2.57%) (Q: -0.05243) (D:  0.457)
(U: 0.15614) (Q+U:  0.10372) (V:  -.----)
info string d2d3  (288 ) N:   83276 (+ 0) (P:  2.77%) (Q: -0.01397) (D:  0.455)
(U: 0.11743) (Q+U:  0.10347) (V:  -.----)
info string a2a3  (204 ) N:   85754 (+ 0) (P:  2.85%) (Q: -0.01359) (D:  0.447)
(U: 0.11705) (Q+U:  0.10346) (V:  -.----)
info string h2h3  (400 ) N:   97278 (+ 0) (P:  2.91%) (Q: -0.00223) (D:  0.454)
(U: 0.10562) (Q+U:  0.10339) (V:  -.----)
info string b2b3  (230 ) N:   98455 (+ 0) (P:  2.95%) (Q: -0.00236) (D:  0.442)
(U: 0.10575) (Q+U:  0.10339) (V:  -.----)
info string b1c3  (36  ) N:  122110 (+ 0) (P:  3.09%) (Q:  0.01402) (D:  0.437)
(U: 0.08925) (Q+U:  0.10328) (V:  -.----)
info string c2c3  (259 ) N:  201218 (+ 0) (P:  3.62%) (Q:  0.03965) (D:  0.463)
(U: 0.06346) (Q+U:  0.10310) (V:  -.----)
info string g2g3  (374 ) N:  348785 (+ 0) (P:  5.75%) (Q:  0.04488) (D:  0.467)
(U: 0.05818) (Q+U:  0.10305) (V:  -.----)
info string e2e3  (317 ) N:  413542 (+ 0) (P:  5.98%) (Q:  0.05205) (D:  0.475)
(U: 0.05095) (Q+U:  0.10300) (V:  -.----)
info string c2c4  (264 ) N:  688398 (+ 0) (P:  7.63%) (Q:  0.06384) (D:  0.464)
(U: 0.03907) (Q+U:  0.10291) (V:  -.----)
info string g1f3  (159 ) N: 1576963 (+ 0) (P: 10.01%) (Q:  0.08036) (D:  0.500)
(U: 0.02238) (Q+U:  0.10274) (V:  -.----)
info string d2d4  (293 ) N: 5674011 (+ 0) (P: 16.58%) (Q:  0.08522) (D:  0.510)
(U: 0.01030) (Q+U:  0.09552) (V:  -.----)
info string e2e4  (322 ) N: 248014778 (+121) (P: 19.27%) (Q:  0.10216) (D:  0.51
8) (U: 0.00027) (Q+U:  0.10243) (V:  -.----)
bestmove e2e4 ponder e7e5

e2e4 performs at an increasing 55.11%, while d2d4 performs at a decreasing 54.26%. Observe that d2d4 is not that well explored, and things get even worse for d2d4 when it is further explored. I restricted the moves to be explored to d2d4 g1f3 and c2c4, the following candidates after e2e4. The most explored, as expected, was d2d4:

About 130 million nodes (hours of search again):

Code: Select all

info string c2c4  (264 ) N: 1444102 (+ 0) (P:  7.63%) (Q:  0.05985) (D:  0.477)
(U: 0.01254) (Q+U:  0.07239) (V:  -.----)
info string g1f3  (159 ) N: 6657797 (+ 0) (P: 10.01%) (Q:  0.06870) (D:  0.520)
(U: 0.00357) (Q+U:  0.07227) (V:  -.----)
info string d2d4  (293 ) N: 124278559 (+117) (P: 16.58%) (Q:  0.07200) (D:  0.48
8) (U: 0.00032) (Q+U:  0.07231) (V:  -.----)
bestmove d2d4 ponder g8f6

The performance of d2d4 decreases further to 53.60% (while that previous of e2e4 increased to 55.11% in the previous very long search). To observe that all these values are VERY slowly moving, there are no any jumps like those with regular AB engines. So, e4 performs about 40% better than d4, taking the draw as the baseline. All other opening moves are worse than both. The difference IS significant.


To have a glimpse of what Leela sees ahead, a speculative one following the PV:

• e4 line:

info depth 36 seldepth 99 time 31466907 nodes 257660432 score cp 5510 hashfull 1
000 nps 8188 tbhits 0 multipv 1 pv e2e4 e7e5 g1f3 b8c6 f1b5 g8f6 e1g1 f6e4 d2d4
e4d6 b5c6 d7c6 d4e5 d6f5 d1d8 e8d8 b1c3 f8e7 h2h3 f5h4 f3h4 e7h4 f1d1 d8e8 g2g4
h7h5 f2f3 c8e6 c3e2 e6d5 g1g2 f7f6 e2f4 h5g4 h3g4 a8d8 c1e3 e8f7 e5e6 d5e6 f4e6
f7e6 f3f4 b7b6 g2f3 c6c5 a2a4 h8e8 a4a5 g7g6 c2c4 d8d6 d1d6 e6d6 e3d2 e8d8 d2c3
d6e6 a1h1 g6g5 f4f5 e6e7 f3e2 b6a5 b2b3 d8b8 h1h3 e7f7 c3a5 b8e8 h3e3 h4g3 a5c3
e8e3 e2e3 c7c6 e3d3 f7e7 d3c2 g3f2 c2d3 f2g3 c3d2

After 8 moves, it's still in main theory:
C67
Spanish Game, Berlin Defense, l'Hermet Variation, Berlin Wall Defense

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

It is played by many top players today. Its performance among 2700+ players from my database is:

Players average: 2761
Performance: 2815

White Win: 22.1%
Draw: 66.2%
Black Win: 11.7%
========================
Overall performance: 55.2%

Although the draw rate is very high (66.2% compared to 52.4% from the starting position), White Win/Loss ratio is among the highest (almost 2) of the opening repertoire. According to Lc0, Black cannot defend better against e2e4.

• d4 line:

info depth 28 seldepth 75 time 38173609 nodes 132380459 score cp 5359 hashfull 1
000 nps 3467 tbhits 0 multipv 1 pv d2d4 g8f6 c2c4 e7e6 g2g3 f8b4 c1d2 b4e7 g1f3
e8g8 f1g2 d7d5 e1g1 c7c6 d1c2 b8d7 d2f4 b7b6 f1d1 c8a6 f3e5 a8c8 b1c3 a6c4 e5c4
d5c4 e2e4 b6b5 a2a4 a7a6 a4b5 a6b5 d4d5 c6d5 e4d5 e6e5 f4g5 e7c5 g2h3 h7h6 h3d7
h6g5 d7b5 c5d4 b5c6 f6e8 c3b5 e8d6 b5d4 e5d4 b2b3 c4b3 c2b3 c8b8 b3d3 b8b4 a1a4
b4a4 c6a4 d8f6 d3d4 f6d4 d1d4 f8b8 d4g4 f7f6 a4d7 g8f7 g4a4 f6f5 a4a6 f7e7 d7e6

It is soon out of general theory (Catalan Opening, General), but after 6 moves it's still played by many top players today, and it seems not that rare among top players (maybe a new trend?)

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

Its performance among 2700+ players from my database is:

Players average: 2752
Performance: 2775

White Win: 22.2%
Draw: 60.4%
Black Win: 17.4%
========================
Overall performance: 52.4%

The draw rate is somewhat lower here (still pretty high), but the White performance is not that good, too many Black wins. According to Lc0, White cannot do better with d2d4.

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


Is it all due to some simple or stupid peculiarities of Lc0, this net, some tactics or something like that?

Interesting thoughts and concept but if you have bad data going in: The type of net/nets you are using..you will get inaccurate results /answers on the back end. My thought on this important issue play out like this. Best opening moves

1. e4
2. d4
3a. c4
3b. Nf3
3c. g3
4a. b3
4b. f4
4c. b4

e4 is by far the most popular of the first move choices and gives good to excellent results for white with modern players only shying away from e4 because of the extra time and preparation needed to stay up on defenses like the sicilian
the caro kann,the french, the pirc, lasker pelikan, hedgehog, classical e5, Ruy Lopez, Philidor, Gambits etc...Takes a lot of time and perhaps they just don't want to put the study time in hence they play more d4 or c4 lines...also they avoid all the 'cooks' and prepared variations. Whites edge can vanish more quickly in e4 with incorrect play.
d4 lines are still much less analyzed (but are slowly catching up..ex Volga Gambit or Benoni or Slav sac lines or queens indian..Kings Indian Grunfeld) so the results of playing d4 over a long period are much lesser known. From the thousands and thousands of chessgames I've played in or watched (both human and engine games)
many of the d4 lines end in some type of complex endgame with a higher percentage of draws (many e4 games give some sort of 'result'.)...I would totally disregard those berlin defense games as the top GM's have steered themselves into that variation because they are deliberately looking to "play draws" and avoid prep.. overall d4 with best play should give white as very slight pull += lasting for around 10-20 moves.
c4 and Nf3 are much less played and analyzed than e4 or d4 and The current World Champ has used c4 quite a bit probably because you don't need to prep nearly as much as e4 or d4. White edge mostly evaporates before move 10 and white is equal (and sometimes slightly worse) with best play =
Of the other lines....b4 is wholly unexplored and Nc3 is seen often in my engine tourneys with a type of simple queenpawn
opening reached and mostly equal positions with black sometimes having a edge due to pinning the Nc3 with Bb4 early
With LC0's tactics as BAD as it is currently it's probably best to not take anything it says on the openings too seriously.
It seems that Alpha Zero and LC0 (Leela) focused on d4 and c4 a bit more than e4 do get the type of positions that those programs find best.

[Ovyron]

That would be subjective not objective.

Are we arguing semantics now? By its definition it's like "not influenced by personal feelings or opinions in considering and representing facts", so objectivity is all about facts.

There fact is that against a fallible opponent there's a best move in the opening position, and if 1.e4 and 1.d4 were the only playable moves, one of them would be better than the other.

This is the same line of reasoning that would prove that against opponents of an enough high level that want to beat you in a game, where you are white and 1. f3 e5 has been played, playing 2.g4 will lose you the game against them.

Against a fallible opponent, there's an arbitrarily high number of chess lines (which I'll call "strings") that would defeat this opponent. If you had a time machine that would allow you to play the game over and over, eventually you would find such a string, and defeat this opponent. Either 1.e4 or 1.d4 have more strings in them, so the one with the most strings is the better move. The strongest possible fallible opponent is like this, so the best move of the two against her would be the better move objectively.

There can be facts that you can't prove. (And now I'll be recycling arguments I've been using since 2007) suppose we play a game where I have 4 cards, I have them in some order, and one of them is red, and if you choose the red one, you win. From your perspective, there's 25% that you pick the red one. You don't know which one is it, and you have no method to figure it out, so picking any of them is the same. You conclude that all the cards are the same and choosing one isn't better than choosing the others.

But I decided on their order, so I know the top card is the red one. I know for a fact that the objectively best card to pick is the top one. This is the underlying truth, and it has nothing to do with "personal feelings or opinions".

I can't tell you what move is best between 1.e4 or 1.d4, but it can be logically inducted that there's an underlying truth about the fact that one of them is objectively better than the other.

[Ovyron]

The cool kids now double post when answering to multiple people in the same thread.

Let me try to make it easier by asking: would you need an engine from the future to draw this position against any opponent?:

[d]4k3/4n2Q/2p5/6p1/3P2P1/8/4K3/2b5 b - - 0 74

No (I can do it with today's engines. We could build some tablebases from this position that output a drawing line against any opponent).

But if humanity put all their time and resources into producing a string of chess moves that would beat you (from the opening position), they could do it.

Heck, if Google put all their time and resources into a correspondence game with you, or were given a year to use all their time and resources to prepare for a game against you and pretty much did nothing but prepare for the game or make more money to prepare for the game (they'd probably hire all the strongest correspondence chess players to make an ultimate team or something, or train an artificial intelligence to simulate how the game against you would go, etc.) they'd beat you.

There's currently just not enough incentive for someone in the world to try to beat you this badly, but there's probably people out there that if they were on a "beat Ozymandias or die" situation, they could pull it out. If nobody can, no matter what, and you're infallible, then I'm wrong, but I'm not saying you're not infallible, I'm saying that's hard to believe.

[Ozymandias]

No (I can do it with today's engines. We could build some tablebases from this position that output a drawing line against any opponent).

But...

Ok, so you can do it with current engine support. There may still be some positions out there, not covered by opening theory, that are complex enough and far away from TBs, as to be winnable by superior technology, I just doubt it. Notice how that position was held by far inferior HW. In a similar fashion, a stronger engine from today could likewise hold it against future opposition. The question is, how complex and favourable, can a position not yet covered by opening theory be? The way I see it, for current technology to still be "vulnerable", the best position to meet the question's parameters, would need to bee way more complex and have an enforceable advantage (*). Again, I don't see those kind of positions being played. The few wins still happening are due to mistakes on the losing side. If you think otherwise, show me one.

* The position posted is a +4, but is also a fortress.

[Ovyron]

* The position posted is a +4, but is also a fortress.

I hadn't see it before, but it took me less than 2 minutes to realize it was a draw, and to realize I could easily hold it with today's technology (how easy is it? can someone beat Stockfish Depth 22 from there?). So if I was white on this game, I'd have seen it was a draw from a much earlier position, tagged it as 0.00 (the "true score") and avoided it as such (software like Chess Openings Wizard allows one to give arbitrary scores to leaf nodes and backsolve). For what it's worth.

The few wins still happening are due to mistakes on the losing side.

This is the crux of the issue, while we agree on this, if there was a string of chess moves that could beat you, and someone played it against you, after the game was over, it'd just look like one of those few wins due to a mistake by the losing side. By saying that you're infallible, you're saying that for any chess position that exists, no matter how complex it is, you're able to find a move that doesn't lose.

So let's talk about complexity, I think that if there's a position complex enough so that all engines from today claim it's 0.00 at very high depths, but the position was actually lost, you might miss it, so a player luring you into it could defeat you. The position you showed was just the opposite, if you claim such a reverse situation couldn't happen I'll have to think of something else.

This is the most complex position I've ever seen, "SSS Tier" I think they call it:

[d]8/3P3k/n2K3p/2p3n1/1b4N1/2p1p1P1/8/3B4 w - -

This is a white win I could never find. Figures that someone as white could have lured me into this position (because engines think black has an advantage), and I couldn't have avoided it, because I don't see the white win even on my face. My claim would be that fallible people would still be prone into playing into these traps (and, huh, back to the thread, that it's easier to build these traps for one of 1.e4 or 1.d4.)

[Laskos]

The performance of d2d4 decreases further to 53.60% (while that previous of e2e4 increased to 55.11% in the previous very long search). To observe that all these values are VERY slowly moving, there are no any jumps like those with regular AB engines. So, e4 performs about 40% better than d4, taking the draw as the baseline. All other opening moves are worse than both. The difference IS significant.

Daniel pointed to the statistic of outcomes being more useful than an eval from the root with hundreds of millions of nodes, as shown above in the opening post. I performed this statistic of outcomes of Lc0 net 42850 at 440 nodes versus Lc0 net 42850 at 400 nodes, to have some engine "diversity". The games were from the 5 most promising White 1-ply openings. The noise in the opening was the following:

Code: Select all

      {                                 
        "name" : "Temperature",          
        "value" : "1.00"          
      },
      {                                 
        "name" : "TempDecayMoves",          
        "value" : "20"          
      },
      {                                 
        "name" : "TempCutoffMove",  
        "value" : 10          
      }                                   

The outcomes do not depend much on the shape of the noise, but this decreasing temperature seemed the best option.

2*16,000 + 3*8,000 = 56,000 games were played. The level of play is somewhere GM level at tournament time control. The statistic of outcomes for these 5 openings is the following:

Openings_5.jpg

The results for d4 and e4 for the statistic of outcomes is remarkably similar to the analysis to hundreds of millions of nodes using a different net quoted above. Not that stretched and only a 30% difference between d4 and e4, but within error margins of the long analysis result.

I consider this statistic of outcomes more relevant than that of human games outcomes, where preparation counts a lot, as well as psychological factors as "surprise" and such (for example, "left-handedness", as explained in another post). And the results come somehow naturally, unlike the results in databases of human games, which look a bit weird.

I am agnostic of the opening theory, but I am not entirely sure it's very relevant. What I see here, or it seems to me, is that in GM level play, aside subjective factors (preparation, psychology, tricks), objectively and "inhumanely", e4 is the best opening for White.

[Ozymandias]

Daniel pointed to the statistic of outcomes being more useful than an eval from the root

The root may not be the best place to show that usefulness. I posted in this page a position, where even SF gives +4, but the result is a draw. Lc0 may even give a higher evaluation.

In light of this shortcoming, my question is, could a PGN be scanned for results and the % score be stored for every move, as if it were an evaluation? Due to RAM limitations, when dealing with big PGNs, it may not be possible to scan the entirety of the games' length, but still.

[Vinvin]

You can already split 1.e4 in 3 clear different openings : 1...e5 , 1...c5 and 1...e6.

[Ovyron]

You can already split 1.e4 in 3 clear different openings : 1...e5 , 1...c5 and 1...e6.

I hold that 1...e6 can be taken off the equations. To decide on that move is best, do everything that you already do, but pretend 1...e6 is an illegal move by black. Because black has no reason to play it, and it'd only skew the results in favor of 1.e4.

The same thing can be done for most moves, so you only need to check about the square root of the positions you're currently checking.

(so, if in the GM level you can expect your opponent to play 1...e6 against your 1.e4, that's a good reason to agree with Laskos)