# Is it computationally feasible to find a board with proven outcome, reachable in 2 plies?

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.

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.

• 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