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As is well known, neither the 0-ply game, the starting state, nor 1-ply games, all of white's first moves, have rigorously proven outcomes. Not even first moves for white considered very bad (1. g4) can be rigorously shown to be a draw or a win for black given perfect play.

On the other hand, there trivially (1. f3 e6 2. g4) exist boards reachable in 3 plies which have proven outcomes.

But: Is it feasible to push this one ply lower? That is, can it currently be shown that there exists at least one combination of first moves by white and black resulting in a state where the result of perfect play is known?

My gut feeling would be that lowering from 3 to 2 plies changes the problem from trivial to impossible within current physical constraints of computers, but I would be very happy to hear if one of the 400 2-ply possibilities can be theorized to be within grasp.

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I am assuming proving such a thing is impossible with today's technology, so I will give a close one.

[FEN "rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1"]
[StartPly "2"]

1. d4 g5 2. Bxg5

In this position after 2.Bxg5, Stockfish 14+ NNUE gives +3.0 with depth 32. Of course I am saying neither +3.0 is a proof of a decisive game nor the depth is good, but I think it is one of the closest ones.

Note: The reason I analyzed 3rd ply even though the question was asking 2nd ply is because after 1.d4 g5, the advantage is for white and the best move for white is Bxg5. This way we get a better engine analysis.

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  • Agreed. Maybe 1.h4 g5 is even closer to being provably winning for White?
    – Arne
    Dec 5, 2021 at 11:38
  • @Arne: Lichess Stockfish Standard speaking, yes, by 0.2 pawn units or so. I tend to agree. Dec 5, 2021 at 12:04

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