user23297: In the following endgame position, from Dautov vs Heinemann, from the book FUNDAMENTAL CHESS ENDING, what happens with perfect play?
[FEN "R7/5pkp/4b1p1/3p4/8/5P2/5KPP/8 b - - 0 1"]

The book says black has some difficult problems to solve (but does not clarify whether they win), while a Stockfish 11 analysis at a depth of 54 plies returns +2.52, which is promising for white. What's going on?

user13012: This position is typical of those that give computers great difficulty because they must be analysed backwards. White will try (somehow) to  gain space and penetrate mostly on the dark squares, while placing his Pawns "to maximum advantage" and looking for an opportunity to sacrifice the exchange. In twenty to thirty moves time. If he is lucky (!) there will be some combinational play that increases his advantage.
The problem is that you cannot arrive at this by analysing to 54 ply. At move 1 you have to conceptualize what the winning idea will be, and play toward it. Otherwise, an evaluation based on general principles (as it must be because there are no immediate tactics) may be optimistic but will not get you there. The situation can be summed up with fair accuracy by saying that the computer does not analyse to depth 54, but instead to depth 1, 54 times and this is not at all the same thing.
A strong human player would deal with this by making moves that "look good" while avoiding for as long as possible decisions that cannot be reversed. They would hope that while doing this, any final play that exists might slowly come into focus. If this position had arisen in a world championship match, I think that decades might be spent trying to arrive at a verdict.

23297: <p>In the following endgame position, from Dautov vs Heinemann, from the book FUNDAMENTAL CHESS ENDING, what happens with perfect play?</p>
<pre><code>[FEN &quot;R7/5pkp/4b1p1/3p4/8/5P2/5KPP/8 b - - 0 1&quot;]
</code></pre>
<p>The book says black has some difficult problems to solve (but does not clarify whether they win), while a Stockfish 11 analysis at a depth of 54 plies returns +2.52, which is promising for white. What's going on?</p>
 13012: <p>This position is typical of those that give computers great difficulty because they must be analysed backwards. White will try (somehow) to  gain space and penetrate mostly on the dark squares, while placing his Pawns &quot;to maximum advantage&quot; and looking for an opportunity to sacrifice the exchange. In twenty to thirty moves time. If he is lucky (!) there will be some combinational play that increases his advantage.</p>
<p>The problem is that you cannot arrive at this by analysing to 54 ply. At move 1 you have to conceptualize what the winning idea will be, and play toward it. Otherwise, an evaluation based on general principles (as it must be because there are no immediate tactics) may be optimistic but will not get you there. The situation can be summed up with fair accuracy by saying that the computer does not analyse to depth 54, but instead to depth 1, 54 times and this is not at all the same thing.</p>
<p>A strong human player would deal with this by making moves that &quot;look good&quot; while avoiding for as long as possible decisions that cannot be reversed. They would hope that while doing this, any final play that exists might slowly come into focus. If this position had arisen in a world championship match, I think that decades might be spent trying to arrive at a verdict.</p>
