Answers.Body: <p>White is a piece up and has a completely winning position. Black could try to create some counterplay profitting from the fact that White's pieces are a bit uncoordinated right now.</p>
  <p>But realistically, any decently skilled player should be able to convert this position into a win for White.</p>
  <p>Finally, note that there's no threshold for which positions can be won or drawn (otherwise the engine would just output &quot;White wins&quot;, &quot;Black wins&quot; or &quot;draw&quot;). There are some won positions that will be evaluated as +0.5, and some drawn ones that the engine will think they're +1.</p>
  
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Answers.Text: Good answer, though after Ne3, White's pieces don't look all that uncoordinated. I don't see much possibility for any counterplay.
Answers.UserDisplayName: John Coleman
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Answers.Text: @JohnColeman you're absolutely right. For some reason I thought it was Black to move!
Answers.UserDisplayName: David
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Answers.LastEditDate: 2021-06-09T00:19:30.820Z
Answers.UserDisplayName: David
Answers.Body: <p>It's hard to prove with 100% certainty, but White will very likely win with optimal play. An advantage over +5 is way too much. There are some theoretically drawn endgames where Stockfish claims one side has a very large advantage, but this position isn't one of them. There are too many pieces and pawns still on the board, and they are able to move around quite a bit. The game isn't constrained enough to fall in the category of a theoretically drawn endgame that Stockfish cannot assess properly. And even if the game was more simplified, a +5 evaluation should still be assumed as completely winning unless you have strong reasons to think otherwise.</p>
  <p>Generally, once you reach an evaluation of roughly +1.5, that's when there are good chances of the game being won with optimal play.</p>
  
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Answers.Text: +1 for Stockfish to show +5.6 and fail to convert, the best bet is there's either 1) a fortress or 2) OCBs. This position is neither.
Answers.UserDisplayName: Allure
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Answers.Text: @Allure Yep, basically any position where SF doesn't learn anything extra from searching deeper, and has to rely only on the quality its evaluation function. Although with the new neural net in SF 13, the situation seems to be improving even in these types of endgames. E.g., compare the SF 13 and SF 11 evaluations of 8/8/5k2/3B1PbP/6P1/5K2/8/8 w - - 0 1.
Answers.UserDisplayName: Inertial Ignorance
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Answers.LastActivityDate: 2021-06-08T23:42:06.180Z
Answers.LastEditDate: 2021-06-08T23:42:06.180Z
Answers.UserDisplayName: Inertial Ignorance
Answers.Body: <p>If black has perfect play and white doesn't, black can draw or even win. But if white has perfect play, chanses are low a draw will occur and white will probably win.</p>
  <p>Conclusion, probably no draw and white will probably win</p>
  
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Answers.Text: It says both players play optimally
Answers.UserDisplayName: Fatso Boo
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Answers.Text: Chanses are high white can make a win out if that position
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Answers.UserDisplayName: Irsu85
Answers.Body: <p>When a chess engine shows an evaluation of a position, there are typically 3 possible values, all of which are based on the engine's attempt to simulate perfect play for both sides:</p>
  <p>(1) <strong>If the engine sees a forced checkmate</strong> [meaning, when one side plays perfectly, no matter what the other side does, the winning side can checkmate], <strong>it will indicate how many moves are needed to complete this</strong>. Something like &quot;#3&quot; to indicate checkmate in 3 moves has been calculated. I would expect in all modern engines that this number is 'perfect' - ie: I would tend to assume that if the engine has actually calculated mate like this, then it is not 'missing' any possible tactics or moves that the losing side could do to ultimately prevent checkmate.</p>
  <p>(2) <strong>If the engine detects a checkmate or strong advantage on one side, but also finds a forced-stalemate that the 'losing' side could activate, then it will typically indicate as '+0' or similar</strong>, basically saying &quot;there is a draw here, available to the person who should want to use it&quot;.</p>
  <p>(3) <strong>If the engine cannot explicitly find mate, it will attempt to assign a numerical value to the position</strong>, where a '+1' assigns a slight advantage to white [about as much as a human would evaluate a 1 pawn advantage], or where '-5' assigns a large advantage to black [about as much as a human would evaluate a 1 rook advantage, although you should be aware that far more goes into these numbers than just 'counting pieces', the analogy is given as a frame of reference, only].</p>
  <p>Note that this value provided is only as good as the engine that gives it; an engine that only looks 2 moves ahead might miss that there is a 3-move tactic that loses a queen. More likely, the engine may miss broad-stroke concepts that limit or enhance one side of the board. Notoriously, the most common 'missed elements' that a chess engine has difficulty evaluating is typically where there is something like a 'fortress'; that is, a position where a human might quickly see that no progress is possible due to a locked-in pawn chain [or similar concept].</p>
  <p>Generally speaking, modern engines are quite good at evaluating positions, and may also be more conservative when projecting high-value numbers. So for a modern engine, I would expect that any '+5' evaluation is quite likely to be a confident number. <strong>Now remember - If the engine could calculate enough moves to find mate, it would tell you - so it doesn't yet know how mate would come, just that there is an incredible strength to one side</strong>.</p>
  <p>Of course there are cases where +5.6 additional 'material' wouldn't lead to mate; for example, you can't checkmate a king with only 2 knights on the board, so even if someone were &quot;2 knights up&quot;, that would still end in a draw. Depending on what other material is on the board at the endgame, 1 extra pawn might be able to promote and win, whereas 2 minor pieces have no effect.</p>
  <p><strong>So let's try to figure out &quot;how likely&quot; it is that a +5.6 position leads to mate.</strong> Going back to a simplistic assumption that a +5 evaluation means more or less &quot;a rook up&quot;, let's consider whether you could win a game if you were a rook down, with no immediately compensating tactics or position. We can consider this by looking at the idea of giving 'piece odds' as a handicap method when players of different strengths play. Based on this answer, it looks like a difference of a knight would be about the same as a 700 ELO rating difference. <a href="https://chess.stackexchange.com/questions/2747/what-is-the-required-elo-to-beat-a-grandmaster-with-queen-odds">What is the required Elo to beat a Grandmaster with queen odds?</a></p>
  <p>So if you consider that a 700 ELO rating differential implies that the weaker player has something like a 1% chance to win (per here: <a href="https://www.318chess.com/elo.html" rel="noreferrer">https://www.318chess.com/elo.html</a>), if you are a rook's-worth of material worse than your opponent, what is your chance of winning? In this estimation - less than 1%. I offer this merely as a thought-experiment, to again provide a frame of reference for how good a &quot;+5.6&quot; evaluated position would actually be.</p>
  <p><strong>In conclusion, the engine hasn't 100% confirmed that mate exists, but the odds of escaping mate as the losing side are vanishingly small</strong>. The odds of stalemate are perhaps stronger, but that's hard to say. If the computer detected the chance of stalemate it would indicate it as such per 2) above, so this would have to be a stalemate that only becomes visible after many further moves of perfect play, beyond the engine's line of site.</p>
  
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Answers.CreationDate: 2021-06-08T20:01:14.263Z
Answers.Text: "700 ELO rating being something like `7 standard deviations greater chance of winning' would mean probably something like 1/10,000 chance of winning." - That's way off (and that's not what the standard deviation is.) You'd need about a 1600 point difference for a supposed 1/10000 chance (although the theoretical odds are known to be not so accurate at that much of a ratings difference.) 700 points would be more like 1/57 if my math is correct.
Answers.UserDisplayName: D M
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Answers.Text: @DM Thanks, I have edited to fix this misunderstanding.
Answers.UserDisplayName: Grade 'Eh' Bacon
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Answers.Text: The engines are notoriously poor at seeing conclusions from end games. You can be up a lot of material and still be able to set up a fortress. This particular example could end up as a knight and pawn endgame, something the engine would score highly but is drawn.
Answers.UserDisplayName: Stian
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Answers.Text: An important further point is that the probability of a turnaround is actually much smaller still than your estimate, because giving material odds from the starting position (1) is known to cost more elo as you rise in elo, and we are talking about perfect play here, and (2) because Stockfish evaluates us as a Rook up **in an early endgame** not opening. That's a much more decisive position to be in.
Answers.UserDisplayName: Mobeus Zoom
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Answers.Text: "for example, you can't checkmate a king with only 2 knights on the board, so even if someone were "2 knights up", that would still end in a draw." Although 2N vs 1P can have forced checkmates, due to the ability to use the opponent's pawn to lose a tempo. So if you find yourself in 2N+P vs P, you may have a forced mate even though you're only two knights up, as long as you don't capture your opponent's pawn.
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Answers.Text: @Acccumulation Absolutely agree - just trying to illustrate that a significant material advantage came come to nothing if the endgame allows for it.
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Answers.UserDisplayName: Grade 'Eh' Bacon
Body: <p>This shows a +5.6 winning for white at depth 33 (Stockfish 13+). White does have a bit of material advantage (knight) and black has more pawn islands. Can black convert this into a draw (assuming both players play optimally) or will this necessarily lead to white winning the game?</p>
  <pre><code>[Title &quot;Game: White to play&quot;]
  [FEN &quot;8/2p3pk/2p4p/p2r4/4p1P1/1Pr5/P1PRK1N1/7R w - - 0 1&quot;]
  </code></pre>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-06-08T05:49:01.617Z
Comments.Text: No, the eval shows the score with perfect play, so the position after 7 moves would be greatly in white's favor.
Comments.UserDisplayName: Mike Jones
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-06-08T06:01:58.093Z
Comments.Text: @MikeJones Right, that's essentially why I asked if with perfect play, black will necessarily lose or be able to draw the game?
Comments.UserDisplayName: dictatemetokcus
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Comments.CreationDate: 2021-06-08T08:31:43.890Z
Comments.Text: An interesting question. Espacially it would be to nice to know where the threshold is for a forced lost game. I did not find something on this on the internet. I think in your example it is relatively clear that it is a forced loss for white because white is a knight up, blacks pawn structure is horrible and black can as far as I can see it not take advantage of his passed pawn.
Comments.UserDisplayName: maxmitz
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Comments.CreationDate: 2021-06-08T18:51:36.490Z
Comments.Text: I don't think this question deserves the downvotes; I think it is quite interesting and cogently asked.
Comments.UserDisplayName: Grade 'Eh' Bacon
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-06-09T12:41:02.167Z
Comments.Text: I suggest the following conversion factors. My current ELO is ~2100, but I'm still a 2300 in an endgame. Thus: +6, I win against a computer, +4, I win against a grandmaster, +2, I win against myself. :-) After Ne3, everything is under control, too many pawns are left on the queenside, I win against a computer even if blitzing. Fits.
Comments.UserDisplayName: Hauke Reddmann
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Comments.CreationDate: 2021-06-09T18:46:30.473Z
Comments.Text: @Grade'Eh'Bacon just because you provided a good answer doesn't make it a great question - you answered the question 'what is the relationship between eval and winning probability', an altogether different and deeper question than what the user is asking, 'can Black hold *this position* with perfect play'.
Comments.UserDisplayName: Mobeus Zoom
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-06-09T18:47:20.497Z
Comments.Text: @MobeusZoom The question in the title is good, though the question in the body could be edited back a bit to remain more on-topic - and I have now proposed such an edit.
Comments.UserDisplayName: Grade 'Eh' Bacon
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Comments.CreationDate: 2021-06-10T01:24:13.087Z
Comments.Text: @Grade'Eh'Bacon I downvoted because this seems like a rather trivial question from my point of view - when an engine shows +5 eval, it is usually expected to win. That makes the default answer to this question "no". I grant that I follow engine chess a lot more than most people, so this being obvious to me might not be obvious to anyone else, but I would still expect the question to give some explanation as to why Black might not be busted. Even if one knows nothing about engine chess, +5 is (superficially) being a rook up, and anyone with chess experience knows that's a winning advantage.
Comments.UserDisplayName: Allure
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-06-10T13:52:04.617Z
Comments.Text: @Allure 'Trivial' is a relative concept, and in something like chess, this question is not at all 'known' to someone say, 1200 or below, where I would guess that a majority of their games involve at least 1 piece blunder. At a novice level of play, being a rook down is not at all 'game over', and it can be hard to even imagine what 'perfect play' might look like, from that vantage point.
Comments.UserDisplayName: Grade 'Eh' Bacon
Tags: <problems><puzzles>
Title: Can black convert a +5.6 game into a draw (assuming both players play optimally)?
ThreadText: # Can black convert a +5.6 game into a draw (assuming both players play optimally)?
  
  (Asked by: username_0 on 2021-06-08)
  
  This shows a +5.6 winning for white at depth 33 (Stockfish 13+). White does have a bit of material advantage (knight) and black has more pawn islands. Can black convert this into a draw (assuming both players play optimally) or will this necessarily lead to white winning the game?
  [Title "Game: White to play"]
  [FEN "8/2p3pk/2p4p/p2r4/4p1P1/1Pr5/P1PRK1N1/7R w - - 0 1"]
  
  **Tags:** problems, puzzles
  
  > **Comments:**
  > **username_1**: No, the eval shows the score with perfect play, so the position after 7 moves would be greatly in white's favor.  
  > **username_0**: @MikeJones Right, that's essentially why I asked if with perfect play, black will necessarily lose or be able to draw the game?  
  > **username_2**: An interesting question. Espacially it would be to nice to know where the threshold is for a forced lost game. I did not find something on this on the internet. I think in your example it is relatively clear that it is a forced loss for white because white is a knight up, blacks pawn structure is horrible and black can as far as I can see it not take advantage of his passed pawn.  
  > **username_3**: I don't think this question deserves the downvotes; I think it is quite interesting and cogently asked.  
  > **username_4**: I suggest the following conversion factors. My current ELO is ~2100, but I'm still a 2300 in an endgame. Thus: +6, I win against a computer, +4, I win against a grandmaster, +2, I win against myself. :-) After Ne3, everything is under control, too many pawns are left on the queenside, I win against a computer even if blitzing. Fits.  
  > **username_5**: @Grade'Eh'Bacon just because you provided a good answer doesn't make it a great question - you answered the question 'what is the relationship between eval and winning probability', an altogether different and deeper question than what the user is asking, 'can Black hold *this position* with perfect play'.  
  > **username_3**: @MobeusZoom The question in the title is good, though the question in the body could be edited back a bit to remain more on-topic - and I have now proposed such an edit.  
  > **username_6**: @Grade'Eh'Bacon I downvoted because this seems like a rather trivial question from my point of view - when an engine shows +5 eval, it is usually expected to win. That makes the default answer to this question "no". I grant that I follow engine chess a lot more than most people, so this being obvious to me might not be obvious to anyone else, but I would still expect the question to give some explanation as to why Black might not be busted. Even if one knows nothing about engine chess, +5 is (superficially) being a rook up, and anyone with chess experience knows that's a winning advantage.  
  > **username_3**: @username_6 'Trivial' is a relative concept, and in something like chess, this question is not at all 'known' to someone say, 1200 or below, where I would guess that a majority of their games involve at least 1 piece blunder. At a novice level of play, being a rook down is not at all 'game over', and it can be hard to even imagine what 'perfect play' might look like, from that vantage point.  
  
  ---
  
  ## 4 answers
  
  ### Answer by username_3 on 2021-06-08. Score: 13 | Accepted answer
  
  When a chess engine shows an evaluation of a position, there are typically 3 possible values, all of which are based on the engine's attempt to simulate perfect play for both sides:
  
  (1) **If the engine sees a forced checkmate** [meaning, when one side plays perfectly, no matter what the other side does, the winning side can checkmate], **it will indicate how many moves are needed to complete this**. Something like "#3" to indicate checkmate in 3 moves has been calculated. I would expect in all modern engines that this number is 'perfect' - ie: I would tend to assume that if the engine has actually calculated mate like this, then it is not 'missing' any possible tactics or moves that the losing side could do to ultimately prevent checkmate.
  
  (2) **If the engine detects a checkmate or strong advantage on one side, but also finds a forced-stalemate that the 'losing' side could activate, then it will typically indicate as '+0' or similar**, basically saying "there is a draw here, available to the person who should want to use it".
  
  (3) **If the engine cannot explicitly find mate, it will attempt to assign a numerical value to the position**, where a '+1' assigns a slight advantage to white [about as much as a human would evaluate a 1 pawn advantage], or where '-5' assigns a large advantage to black [about as much as a human would evaluate a 1 rook advantage, although you should be aware that far more goes into these numbers than just 'counting pieces', the analogy is given as a frame of reference, only].
  
  Note that this value provided is only as good as the engine that gives it; an engine that only looks 2 moves ahead might miss that there is a 3-move tactic that loses a queen. More likely, the engine may miss broad-stroke concepts that limit or enhance one side of the board. Notoriously, the most common 'missed elements' that a chess engine has difficulty evaluating is typically where there is something like a 'fortress'; that is, a position where a human might quickly see that no progress is possible due to a locked-in pawn chain [or similar concept].
  
  Generally speaking, modern engines are quite good at evaluating positions, and may also be more conservative when projecting high-value numbers. So for a modern engine, I would expect that any '+5' evaluation is quite likely to be a confident number. **Now remember - If the engine could calculate enough moves to find mate, it would tell you - so it doesn't yet know how mate would come, just that there is an incredible strength to one side**.
  
  Of course there are cases where +5.6 additional 'material' wouldn't lead to mate; for example, you can't checkmate a king with only 2 knights on the board, so even if someone were "2 knights up", that would still end in a draw. Depending on what other material is on the board at the endgame, 1 extra pawn might be able to promote and win, whereas 2 minor pieces have no effect.
  
  **So let's try to figure out "how likely" it is that a +5.6 position leads to mate.** Going back to a simplistic assumption that a +5 evaluation means more or less "a rook up", let's consider whether you could win a game if you were a rook down, with no immediately compensating tactics or position. We can consider this by looking at the idea of giving 'piece odds' as a handicap method when players of different strengths play. Based on this answer, it looks like a difference of a knight would be about the same as a 700 ELO rating difference. [What is the required Elo to beat a Grandmaster with queen odds?](https://chess.stackexchange.com/questions/2747/what-is-the-required-elo-to-beat-a-grandmaster-with-queen-odds)
  
  So if you consider that a 700 ELO rating differential implies that the weaker player has something like a 1% chance to win (per here: <https://www.318chess.com/elo.html>), if you are a rook's-worth of material worse than your opponent, what is your chance of winning? In this estimation - less than 1%. I offer this merely as a thought-experiment, to again provide a frame of reference for how good a "+5.6" evaluated position would actually be.
  
  **In conclusion, the engine hasn't 100% confirmed that mate exists, but the odds of escaping mate as the losing side are vanishingly small**. The odds of stalemate are perhaps stronger, but that's hard to say. If the computer detected the chance of stalemate it would indicate it as such per 2) above, so this would have to be a stalemate that only becomes visible after many further moves of perfect play, beyond the engine's line of site.
  
  > **Comments:**
  > **username_12**: "700 ELO rating being something like `7 standard deviations greater chance of winning' would mean probably something like 1/10,000 chance of winning." - That's way off (and that's not what the standard deviation is.) You'd need about a 1600 point difference for a supposed 1/10000 chance (although the theoretical odds are known to be not so accurate at that much of a ratings difference.) 700 points would be more like 1/57 if my math is correct.  
  > **username_3**: @DM Thanks, I have edited to fix this misunderstanding.  
  > **username_13**: The engines are notoriously poor at seeing conclusions from end games. You can be up a lot of material and still be able to set up a fortress. This particular example could end up as a knight and pawn endgame, something the engine would score highly but is drawn.  
  > **username_5**: An important further point is that the probability of a turnaround is actually much smaller still than your estimate, because giving material odds from the starting position (1) is known to cost more elo as you rise in elo, and we are talking about perfect play here, and (2) because Stockfish evaluates us as a Rook up **in an early endgame** not opening. That's a much more decisive position to be in.  
  > **username_14**: "for example, you can't checkmate a king with only 2 knights on the board, so even if someone were "2 knights up", that would still end in a draw." Although 2N vs 1P can have forced checkmates, due to the ability to use the opponent's pawn to lose a tempo. So if you find yourself in 2N+P vs P, you may have a forced mate even though you're only two knights up, as long as you don't capture your opponent's pawn.  
  > **username_3**: @username_14 Absolutely agree - just trying to illustrate that a significant material advantage came come to nothing if the endgame allows for it.  
  
  ---
  
  ### Answer by username_7 on 2021-06-08. Score: 12
  
  White is a piece up and has a completely winning position. Black could try to create some counterplay profitting from the fact that White's pieces are a bit uncoordinated right now.
  
  But realistically, any decently skilled player should be able to convert this position into a win for White.
  
  Finally, note that there's no threshold for which positions can be won or drawn (otherwise the engine would just output "White wins", "Black wins" or "draw"). There are some won positions that will be evaluated as +0.5, and some drawn ones that the engine will think they're +1.
  
  > **Comments:**
  > **username_8**: Good answer, though after Ne3, White's pieces don't look all that uncoordinated. I don't see much possibility for any counterplay.  
  > **username_7**: @JohnColeman you're absolutely right. For some reason I thought it was Black to move!  
  
  ---
  
  ### Answer by username_9 on 2021-06-08. Score: 5
  
  It's hard to prove with 100% certainty, but White will very likely win with optimal play. An advantage over +5 is way too much. There are some theoretically drawn endgames where Stockfish claims one side has a very large advantage, but this position isn't one of them. There are too many pieces and pawns still on the board, and they are able to move around quite a bit. The game isn't constrained enough to fall in the category of a theoretically drawn endgame that Stockfish cannot assess properly. And even if the game was more simplified, a +5 evaluation should still be assumed as completely winning unless you have strong reasons to think otherwise.
  
  Generally, once you reach an evaluation of roughly +1.5, that's when there are good chances of the game being won with optimal play.
  
  > **Comments:**
  > **username_6**: +1 for Stockfish to show +5.6 and fail to convert, the best bet is there's either 1) a fortress or 2) OCBs. This position is neither.  
  > **username_9**: @username_6 Yep, basically any position where SF doesn't learn anything extra from searching deeper, and has to rely only on the quality its evaluation function. Although with the new neural net in SF 13, the situation seems to be improving even in these types of endgames. E.g., compare the SF 13 and SF 11 evaluations of 8/8/5k2/3B1PbP/6P1/5K2/8/8 w - - 0 1.  
  
  ---
  
  ### Answer by username_10 on 2021-06-08. Score: -3
  
  If black has perfect play and white doesn't, black can draw or even win. But if white has perfect play, chanses are low a draw will occur and white will probably win.
  
  Conclusion, probably no draw and white will probably win
  
  > **Comments:**
  > **username_11**: It says both players play optimally  
  > **username_10**: Chanses are high white can make a win out if that position  
  
  ---
  
  