user28034: 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"]


user12873: 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.

user18809: 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.

user14340: 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?
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.

28034: <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>
 12873: <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>
 18809: <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>
 14340: <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>
