I think I figured out how to solve this quickly and without errors after all. I make moves so that I occupy the opposition until the opponent's king is on a7, while my king is on b5. After that I make an outflanking.
Opposition and outflanking
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I've tried to solve this problem several times (without making a move rollback after a wrong move), but I still can't solve it with 100% accuracy.
Is there a strictly defined algorithm that helps to solve this type of problem? How to clearly define the moment when to make a move that loses the opposition?