Answers.Body: <p>The game tree branch 1.f3 appears to be the smallest of the 20 opening moves, so maybe it would be computationally easier to try there. Also it looks like after 1.f3 White already has some disadvantage, so maybe it would be easier to find a provable loss for White after a strong Black move. Maybe 1.f3 e5 could be provable solved.</p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2024-06-19T13:48:06.590Z
Answers.LastActivityDate: 2024-06-19T16:09:51.610Z
Answers.LastEditDate: 2024-06-19T16:09:51.610Z
Answers.UserDisplayName: Fools Mate
Answers.Body: <p>I am assuming proving such a thing is impossible with today's technology, so I will give a close one.</p>
  <pre><code>[FEN &quot;rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1&quot;]
  [StartPly &quot;2&quot;]
  
  1. d4 g5 2. Bxg5
  </code></pre>
  <p>In this position after <code>2.Bxg5</code>, 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.</p>
  <p>Note: The reason I analyzed 3rd ply even though the question was asking 2nd ply is because after <code>1.d4 g5</code>, the advantage is for white and the best move for white is <code>Bxg5</code>. This way we get a better engine analysis.</p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2021-12-05T11:38:12.390Z
Answers.Text: Agreed. Maybe 1.h4 g5 is even closer to being provably winning for White?
Answers.UserDisplayName: Arne
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2021-12-05T12:04:58.417Z
Answers.Text: @Arne: Lichess Stockfish Standard speaking, yes, by 0.2 pawn units or so. I tend to agree.
Answers.UserDisplayName: Hauke Reddmann
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2021-12-05T07:22:20.893Z
Answers.LastActivityDate: 2021-12-05T07:51:13.977Z
Answers.LastEditDate: 2021-12-05T07:51:13.977Z
Answers.UserDisplayName: Minot
Body: <p>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.</p>
  <p>On the other hand, there <em><strong>trivially</strong></em> (1. f3 e6 2. g4) exist boards reachable in 3 plies which have proven outcomes.</p>
  <p>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?</p>
  <p>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.</p>
  
Tags: <opening><theory><computer-chess><solving>
Title: Is it computationally feasible to find a board with proven outcome, reachable in 2 plies?
ThreadText: # Is it computationally feasible to find a board with proven outcome, reachable in 2 plies?
  
  (Asked by: username_0 on 2021-12-05)
  
  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.
  
  **Tags:** opening, theory, computer-chess, solving
  
  
  ---
  
  ## 2 answers
  
  ### Answer by username_2 on 2021-12-05. Score: 4 | Accepted answer
  
  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.
  
  > **Comments:**
  > **username_3**: Agreed. Maybe 1.h4 g5 is even closer to being provably winning for White?  
  > **username_4**: @username_3: Lichess Stockfish Standard speaking, yes, by 0.2 pawn units or so. I tend to agree.  
  
  ---
  
  ### Answer by username_1 on 2024-06-19. Score: 0
  
  The game tree branch 1.f3 appears to be the smallest of the 20 opening moves, so maybe it would be computationally easier to try there. Also it looks like after 1.f3 White already has some disadvantage, so maybe it would be easier to find a provable loss for White after a strong Black move. Maybe 1.f3 e5 could be provable solved.
  
  
  ---
  
  