Even when a position seems hopeless, sometimes a strategic avenue of escape is a draw by repetition. With this hint in mind, please try to find white’s best move and strategy.
Black has a winning material advantage. Nevertheless, white compels black to accept a draw by repetition by having its rook take black’s g6 pawn, which checks black. Black’s best reply is capture the rook and accept the perpetual check by the white queen, as she slides back and forth from g6 to h6.
Black, however, may be tempted to decline the draw by perpetual check because of its material advantage. One option after the rook check is to retreat the black king to h8. White strikes now with bishop to c3, check. Black’s best reply is to block the check with its d4 rook. White’s rook then steps onto d6, overwhelming the black d4 rook, and black is lost (see next diagram).
The remaining option after the rook check from g6 is for the black king to flee to f7. This position is complicated, and, on balance, white is better. White’s best response to king to c7 is for white’s rook on g6 to check from g7. If the black king escapes to e8, white plays queen to e4, which wins.
Another choice after Rg7+ is for black's king to move to e6. White’s queen next checks from e4, as black’s d4 rook intercedes on e5 on his liege’s behalf. The next move for white is a little tricky. The trick is now is for white to check black with its rook from e7 (see next diagram).
This leads an indirect rook exchange as black’s king is forced to take white’s rook, leaving black’s e4 rook open for capture with a queen check. From here, white’s active queen and bishop versus black inert rook and queen compensate for black’s technical, material edge. Specifically, if the black king steps on a dark square, it’s like a land mine and white’s dark squared bishop gets a check and white’s queen and bishop blown up black’s rook.
For example, if the black king retreats to d8, white does not immediately check black from h4 with its bishop. First, white’s queen maneuvers to a better position by checking from d6. Because this forks the black king and rook, black’s king moves to e8. White checks from e6, forcing the black king back to d8.
Now white checks from h4 with its bishop. The black king must move to c7, and white strikes from e7 with its queen, which forks the black king and rook (see next diagram).
After the indirect rook exchange, black’s other options lead to draws by perpetual queen checks, as black’s king is tethered to its rook and white’s bishop “preys” for black’s king to step on a dark square.
The lesson this week that should not need repeating is that a draw is sometimes the better part of valor.