The engine defied Dvoretsky, who wrote, "Black's rook must remain passive, staying on the eighth rank" (Dvoretsky's Endgame Manual. 5th ed. [2020], 161). I explained to the students what I recalled of Dvoretsky's explanation, and drew the arrows visible in the diagram.
White to move
From my lead, the students chose the first move well.1.Rb7 Rd8 2.Rh7
Only after struggling against the engine's surprising response did we come to understand that 2.Rg7+ is better.
2...Rd6!
3.f7 is not possible. We tried 3.Rg7+ Kf8 4.Rh7 Kg8 and realized something else was needed.
3.Re7 Kf8 confused us, although it should not have.
After 3.Rb7 Rd8, we felt that our progress was still missing something.
After several trials and error, we found the correct idea.
3.Rg7+ Kf8 4.Ra7 Rd8 5.Rh7
Black to move
Now Black must allow either the skewer or f7+ followed by the skewer.Playing several Lucena positions against Stockfish over the past few years, I've learned that the engine often diverges from the line given in the textbook. Often this complicates the solution and the human must solve a problem.
These curve balls are why computer training is valuable.
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