Winning position after move one?

Question

Question: There are 400 possible two-ply openings; that is, positions that can arise after each player has made one move. Which of these positions, if any, are winning (either for white or for black) with perfect play?

Context: It's very likely that chess is a draw with perfect play, which would mean that there is no one-ply opening that gives white a winning position. This question asks about the worst first move for white; if there is any first move so bad that black is winning with correct play, then that move (combined with black's best response) would of course be an answer to this question.

On the other hand, there definitely are some three-ply openings where black is winning; for example, black has mate in one after 1. f3 e5 2. g4.

My attempts: I ran Stockfish 15 on a handful of two-ply openings that seemed most likely to be winning for white, along with the two one-ply openings that seem worst for white. The most promising lines I found were as follows (along with the depth and number of meganodes in my searches, plus the best continuation and comments on transpositions):

• 1. d4 g5: +2.95 (depth 55/68, 55298 MN; 2. Bxg5)
• 1. h4 g5: +2.87 (depth 52/72, 4894 MN; 2. hxg5)
• 1. e4 g5: +2.14 (depth 38/44, 301 MN; 2. d4, transposes to sideline of 1. d4 g5)
• 1. Nc3 g5: +2.12 (depth 39/47, 314 MN; 2. d4, transposes to sideline of 1. d4 g5)
• 1. d3 g5: +2.07 (depth 36/39, 173 MN; 2. Bxg5)
• 1. e4 f5: +2.07 (depth 41/53, 267 MN; 2. exf5)
• 1. e4 b5: +1.94 (depth 37/49, 135 MN; 2. Bxb5)
• 1. Nf3 g5: +1.80 (depth 44/59, 1020 MN; 2. Nxg5, transposes with 1. Nh3 g5 2. Nxg5)
• 1. Nf3 e5: +1.76 (depth 37/46, 177 MN; 2. Nxe5)
• 1. e3 b5: +1.76 (depth 34/41, 59 MN; 2. Bxb5)
• 1. e4 f6: +1.69 (depth 39/47, 302 MN, 2. d4, transposes with 1. d4 f6 2. e4)
• 1. d4 e5: +1.67 (depth 38/52, 200 MN; 2. dxe5)
• 1. g4: -1.55 (depth 35/48, 165 MN; 1... d5)
• 1. d4 Nh6: +1.53 (depth 35/45, 119 MN; 2. e4, transposes with 1. e4 Nh6 2. d4)
• 1. Nf3 f6: +1.52 (depth 33/40, 31 MN; 2. e4, transposes to sideline of 1. e4 f6)
• 1. Nc3 f6: +1.51 (depth 30/38, 62 MN; 2. e4, transposes to sideline of 1. e4 f6)
• 1. a4 b5: +1.50 (depth 44/61, 268 MN; 2. axb5)
• 1. c4 g5: +1.50 (depth 32/43, 34 MN; 2. d4, transposes to sideline of 1. d4 g5)
• 1. e4 Na6: +1.38 (depth 45/62, 2541 MN; 2. Nc3, transposes with 1. Nc3 Na6 2. e4)
• 1. Nf3 Nh6: +1.33 (depth 36/47, 110 MN; 2. d4, transposes to sideline of 1. d4 Nh6)
• 1. Nc3 Nh6: +1.19 (depth=41/51, 440 MN; 2. e4, transposes to sideline of 1. e4 Nh6)
• 1. Nf3 Na6: +1.16 (depth=38/49, 208 MN; 2. e4, transposes to sideline of 1. e4 Na6)
• 1. Nc3 b5: +1.14 (depth 44/57, 367 MN; 2. Nxb5, transposes with 1. Na3 b5 2. Nxb5)
• 1. d4 Na6: +1.10 (depth=37/44, 133 MN; 2. e4, transposes to sideline of 1. e4 Na6)
• 1. f3: -0.74 (depth 36/47, 114 MN; 1... e5)

I realize that all of these positions are way too complicated to expect a definitive answer in either direction (forced win or forced draw)--see this closely related question. Instead, what I'm looking for is reasonable evidence one way or the other, for all of the most unequal two-ply openings. For example, if white wins 90 times out of 100 when a strong engine plays itself (or when multiple strong engines play each other) from a given position, then I would regard that as strong evidence that the position is a win for white with perfect play.

PS since I know someone will say it otherwise: this is a theoretical question, and I'm not interested in "loophole" answers like resigning or letting your clock run out.

Answer 1

1.g4 d5: -1.5 (depth 38, Nc3 next)

Answer 2

You've actually already done most of the "hard work" by getting the opening evals. The rest is just looking at the statistics for how often the engine wins against itself. Here is the data for Stockfish.

Given an eval of +2.5, Stockfish wins against itself about 95% of the time, so 1. d4 g5 is very likely winning for White.