[fen "1K6/1P3q2/1P6/P7/3k4/8/8/8 w - - 0 1"]
Is there any way that white can win or draw in the above game?
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This position has six pieces on the board, and is hence present in a number of chess endgame tablebases.
For example, the Syzygy tablebases show that this position is a theoretical draw, but that there is only one move which guarantees the draw:
Kc8. All other moves allow black to force a win.
[FEN "1K6/1P3q2/1P6/P7/3k4/8/8/8 w - - 0 1"] 1. Kc8 Qe8+ 2. Kc7 Qe7+ 3. Kc8
This position is a draw because White is constantly threatening to promote and win, which leaves Black with no choice but to perpetually check White. The problem with Ka8 and is that Black can pin the White pawn and gain tempo through constant checking, gaining time to advance their king and win.
If this position were to occur in an actual game, the result would likely be unclear as it would be incredibly easy for either blunder, and end up losing.