6 
[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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    Well, technically... black can surrender. :D
    – Vilx-
    Commented Aug 24, 2019 at 21:16

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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.

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    Interesting position - move the Queen to g7 and ANY move by white draws!
    – Ian Bush
    Commented Aug 25, 2019 at 9:57
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    This answer is meaningless without an explanation of what is going on in the endgame. For instance. Ka8 looks like the most natural move. Why doesn't it work? And I don't mean "why" as in "the charts says so" but in "what's the reason behind?"
    – David
    Commented Aug 26, 2019 at 14:51
  • Could add that in the Ka8 line black is pinning the white pawn on b7 (with Qd5 and later Qd7, if white plays Ka7)
    – user1583209
    Commented Mar 18, 2020 at 7:13

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