user31663: In the board below, I'm not entirely sure who is winning, black's rook looks dangerous at the moment.
Its white to move
How does white have an advantage?
4rk2/5p1p/2p3pP/8/p7/PqP1Q3/1P1R1P2/1K6 w - - 12 39


user26052: In the position given, White, when plugged into Stockfish, has a +8 advantage. Seeing that white is to move, the first move should be Qc5+, followed by Kg8. Notice Re7 is not possible because of mate in 1 (Rd8#). Following Kg8 should be Qe5, and if Rxe5 it is mate in 2 with Rd8+, Re8, Rxe8#. Kf8 is the only move for black. Following this should be Qh8+, Ke7,Re2+, Kd6(any other king move results in mate in 8.), Qd4,and now black has to trade queens, or else it is mate in 10. Qd5, Qxd5+, Kxd5, can be possible, but Rxe8, Qxd4, cxd4 results in a better position, and from here Stockfish rates this +13.3. Kc2 or Rh8 for white results in a win.
In a more interactive manner:
[fen "4rk2/5p1p/2p3pP/8/p7/PqP1Q3/1P1R1P2/1K6 w - - 0 1"]

1. Qc5+ Kg8 (1... Re7 2. Rd8#) 2. Qe5 Kf8 (2... Rxe5 3. Rd8+ Re8 4. Rxe8#) 3. Qh8+ Ke7 4. Re2+ Kd6 5. Qd4+ {As Scounged in the comments, Qd4 is to stop perpetual check, as Qxe8 would be a blunder} Qd5 6. Rxe8 Qxd4 (6. Qxd5 Kxd5) 7. cxd4 Kd5


user15223: (Human thought process below)
White's h6-pawn gives him a decisive advantage. Note how it restricts Black's king. If the king is on g8 or h8, then Qg7 is checkmate, and so is Rd8 if Black's rook leaves the back rank. If the king is on f8, then Qg7+ still forces the king into the open, not to mention threatens Qxh7 followed by promotion. This immediately suggests the move 1. Qc5+. Black can't interpose with 1...Re7 because 2. Rd8 is checkmate, so the king is forced to g8. Then 2. Qe5 (exploiting the fact that the black rook can't leave the back rank) threatens 3. Qg7#, forcing 3...Kf8.
At this point a 2-move tactic suggests itself: 4. Qh8+ Ke7 5. Re2+ wins the rook on e8. An extra rook is more than enough material to win, so Black's only recourse is a perpetual check. ...Qd1+-Qb3+ is a perpetual, so White must stop it, and conveniently 6. Qd4+ does this. White then collects the e8-rook and wins.
Stockfish does suggest moves like 4...Qe6, but I don't think many humans would analyze that, because that is equivalent to resigns after 5. Rxe6+.

31663: <p>In the board below, I'm not entirely sure who is winning, black's rook looks dangerous at the moment.</p>
<p>Its white to move</p>
<p>How does white have an advantage?</p>
<pre><code>4rk2/5p1p/2p3pP/8/p7/PqP1Q3/1P1R1P2/1K6 w - - 12 39
</code></pre>
 26052: <p>In the position given, White, when plugged into Stockfish, has a +8 advantage. Seeing that white is to move, the first move should be Qc5+, followed by Kg8. Notice Re7 is not possible because of mate in 1 (Rd8#). Following Kg8 should be Qe5, and if Rxe5 it is mate in 2 with Rd8+, Re8, Rxe8#. Kf8 is the only move for black. Following this should be Qh8+, Ke7,Re2+, Kd6(any other king move results in mate in 8.), Qd4,and now black has to trade queens, or else it is mate in 10. Qd5, Qxd5+, Kxd5, can be possible, but Rxe8, Qxd4, cxd4 results in a better position, and from here Stockfish rates this +13.3. Kc2 or Rh8 for white results in a win.</p>
<p>In a more interactive manner:</p>
<pre><code>[fen &quot;4rk2/5p1p/2p3pP/8/p7/PqP1Q3/1P1R1P2/1K6 w - - 0 1&quot;]

1. Qc5+ Kg8 (1... Re7 2. Rd8#) 2. Qe5 Kf8 (2... Rxe5 3. Rd8+ Re8 4. Rxe8#) 3. Qh8+ Ke7 4. Re2+ Kd6 5. Qd4+ {As Scounged in the comments, Qd4 is to stop perpetual check, as Qxe8 would be a blunder} Qd5 6. Rxe8 Qxd4 (6. Qxd5 Kxd5) 7. cxd4 Kd5
</code></pre>
 15223: <p>(Human thought process below)</p>
<p>White's h6-pawn gives him a decisive advantage. Note how it restricts Black's king. If the king is on g8 or h8, then Qg7 is checkmate, and so is Rd8 if Black's rook leaves the back rank. If the king is on f8, then Qg7+ still forces the king into the open, not to mention threatens Qxh7 followed by promotion. This immediately suggests the move 1. Qc5+. Black can't interpose with 1...Re7 because 2. Rd8 is checkmate, so the king is forced to g8. Then 2. Qe5 (exploiting the fact that the black rook can't leave the back rank) threatens 3. Qg7#, forcing 3...Kf8.</p>
<p>At this point a 2-move tactic suggests itself: 4. Qh8+ Ke7 5. Re2+ wins the rook on e8. An extra rook is more than enough material to win, so Black's only recourse is a perpetual check. ...Qd1+-Qb3+ is a perpetual, so White must stop it, and conveniently 6. Qd4+ does this. White then collects the e8-rook and wins.</p>
<p>Stockfish does suggest moves like 4...Qe6, but I don't think many humans would analyze that, because that is equivalent to resigns after 5. Rxe6+.</p>
