user2785: This question relates to a game I played on LiChess (link), from which we have the following position:
[FEN "8/2rn4/2pN2k1/r1Pp2p1/p2P4/3KPP2/R7/7R w - - 4 42"]

In this position with white to move, I played 48. Rha1, eventually winning the a pawn.  LiChess's version of Stockfish declared this a blunder and gives 48. Rah2 a score of +5.6.  Playing it through, it even looks like white forces mate after giving many checks, although Stockfish doesn't claim this.
Question: In this two-rook and knight position, does 48. Rah2 lead to mate after a gajillion checks?
Ideally, it'd be nice if there was some way to understand the mate, as a human, if it exists.

user14202: This is trivial calculation, though I can see it tempting to just target a weak pawn -- it's the King we are after!
Phonon is correct in that you need to practice concrete calculation.  But I disagree that the lines are too deep. 
First:
1.Rah2 threatens Rh7 when R1h6 will be mate. Let's try to defend this straight forward threat:
Black moves his knight to allow his rook to defend h7:
--Phonon's line of 1...Nf6 just loses a piece to 2.Rh6+ Kg7 3.Rxf6 followed by the fork on e8 (of course playing for more as in Phonon's line is better you don't need to calculate more when you already see a win), so how else can Black defend?
-- 1...Nf8? 2.Rh6 and now the knight forks the King again! 
It becomes easy to see that Black can't avoid these forks and mate at the same time.
-- 1...g4 2.f4 doesn't change anything
Supplemental:  To finish answering the direct question "Does it lead to mate":  I will say it does not directly force mate.  Black can jettison material to avert immediate mate.  

user3594: This is really a concrete-calculation question, to which you should find an answer yourself by either going through the obvious candidate lines or playing it out with the help of an engine. Your calculation techniques will benefit far more from that process, even if you don't find the answer, than asking for the direct answer.
In any case, clearly black is doing terribly poorly: there's no initiative, the rooks are completely out of play and stand defensively, and the king is quite isolated on g6, and even in the worst case scenario the passed a pawn is not hard to defend against. On the other hand, white's able to easily coordinate all 3 pieces for an attack on the king, either forcing material loss or checkmate. 
So the game's really lost even if you fail to find the mate, simplest being to mount an attack on the defense-free king on g6 well caged thanks to the monster knight on d6. Focus on winning material first and then convert if the mate does not appear to be a trivial one. That said, the only way black can delay the imminent mate threat is to bring the knight into the defense, namely, Nf6 which at least stops a rook landing on h7 and secures some space for the king. As far as I see, even if black ignored the threat and just pushed the a pawn after Rah2, the cage around the king may be enough to force mate but it may easily be a case of mate in 12-15 moves1, which means, it's far simpler to grab material first and simplify the task before calculating for such forced lines. 
Here's one line (among the various ways this can unfold) where black attempts a defense by bringing the knight, to which white can reply with a e3-e4 pawn push in order to advance a pawn to e5 forcing the knight away from its "ideal" defensive post on f6.
 [FEN "8/2rn4/2pN2k1/r1Pp2p1/p2P4/3KPP2/R7/7R w - - 4 42"]

 1.Rah2 Nf6 2.Rh6+ {The immediate e4 may allow Rh7 for black, forcing the trade of a pair of rooks} Kg7 3.e4 {e5 is unavoidable, best black can do is to take once to at least free up the g4 square for the knight.} a3 {ignoring white's threat just to see what the mating net looks like} 4.e5 Ng8 5.Rh7+ Kf8 6.Rxc7  {Mate on f7 next} Ne7 7.Rxe7 Kxe7  {at this point, even if you don't see the mating pattern, you can simply win the a pawn first and then convert the game.} 8.Rh8 a2 9.Re8+ Kd7 10.e6+ Kc7 11.Rc8# 


1: This is far too deep to calculate mentally, what players (at any level really) do in such a case, they simply go with the first few obvious moves (checks), moves they know cannot be possibly wrong, and after a while if it appears to have simplified then you can sit down and calculate a forced mate (assuming there's time) else you just have to be practical and go with the first best line you see, specially in such case where the position is trivially winning for white anyway.  

2785: <p>This question relates to a game I played on LiChess (<a href="https://lichess.org/Gu6PCLRj" rel="nofollow noreferrer">link</a>), from which we have the following position:</p>

<pre><code>[FEN "8/2rn4/2pN2k1/r1Pp2p1/p2P4/3KPP2/R7/7R w - - 4 42"]
</code></pre>

<p>In this position with white to move, I played 48. Rha1, eventually winning the a pawn.  LiChess's version of Stockfish declared this a blunder and gives 48. Rah2 a score of +5.6.  Playing it through, it even looks like white forces mate after giving many checks, although Stockfish doesn't claim this.</p>

<p><em>Question</em>: In this two-rook and knight position, does 48. Rah2 lead to mate after a gajillion checks?</p>

<p>Ideally, it'd be nice if there was some way to understand the mate, as a human, if it exists.</p>
 14202: <p><strong>This is trivial calculation</strong>, though I can see it tempting to just target a weak pawn -- it's the King we are after!</p>

<p>Phonon is correct in that you need to practice concrete calculation.  But I disagree that the lines are too deep. </p>

<p>First:
1.Rah2 threatens Rh7 when R1h6 will be mate. Let's try to defend this straight forward threat:</p>

<p>Black moves his knight to allow his rook to defend h7:
--Phonon's line of 1...Nf6 just loses a piece to 2.Rh6+ Kg7 3.Rxf6 followed by the fork on e8 (of course playing for more as in Phonon's line is better you don't need to calculate more when you already see a win), so how else can Black defend?
-- 1...Nf8? 2.Rh6 and now the knight forks the King again! </p>

<p>It becomes easy to see that Black can't avoid these forks and mate at the same time.
-- 1...g4 2.f4 doesn't change anything</p>

<p><strong>Supplemental:</strong>  To finish answering the direct question "Does it lead to mate":  I will say it does not directly force mate.  Black can jettison material to avert immediate mate.  </p>
 3594: <p>This is really a concrete-calculation question, to which you should find an answer yourself by either going through the obvious candidate lines or playing it out with the help of an engine. Your calculation techniques will benefit far more from that process, even if you don't find the answer, than asking for the direct answer.</p>

<p>In any case, clearly black is doing terribly poorly: there's no initiative, the rooks are completely out of play and stand defensively, and the king is quite isolated on <code>g6,</code> and even in the worst case scenario the passed <code>a</code> pawn is not hard to defend against. On the other hand, white's able to easily coordinate all 3 pieces for an attack on the king, either forcing material loss or checkmate. 
So the game's really lost even if you fail to find the mate, simplest being to mount an attack on the defense-free king on <code>g6</code> well caged thanks to the monster knight on <code>d6</code>. Focus on winning material first and then convert if the mate does not appear to be a trivial one. That said, the only way black can delay the imminent mate threat is to bring the knight into the defense, namely, <code>Nf6</code> which at least stops a rook landing on <code>h7</code> and secures some space for the king. As far as I see, even if black ignored the threat and just pushed the <code>a</code> pawn after <code>Rah2,</code> the cage around the king may be enough to force mate but it may easily be a case of mate in 12-15 moves<sup>1</sup>, which means, it's far simpler to grab material first and simplify the task before calculating for such forced lines. </p>

<p>Here's one line (among the various ways this can unfold) where black attempts a defense by bringing the knight, to which white can reply with a e3-e4 pawn push in order to advance a pawn to <code>e5</code> forcing the knight away from its "ideal" defensive post on <code>f6.</code></p>

<pre><code> [FEN "8/2rn4/2pN2k1/r1Pp2p1/p2P4/3KPP2/R7/7R w - - 4 42"]

 1.Rah2 Nf6 2.Rh6+ {The immediate e4 may allow Rh7 for black, forcing the trade of a pair of rooks} Kg7 3.e4 {e5 is unavoidable, best black can do is to take once to at least free up the g4 square for the knight.} a3 {ignoring white's threat just to see what the mating net looks like} 4.e5 Ng8 5.Rh7+ Kf8 6.Rxc7  {Mate on f7 next} Ne7 7.Rxe7 Kxe7  {at this point, even if you don't see the mating pattern, you can simply win the a pawn first and then convert the game.} 8.Rh8 a2 9.Re8+ Kd7 10.e6+ Kc7 11.Rc8# 
</code></pre>

<hr>

<p><sup><sup>1</sup>: This is far too deep to calculate mentally, what players (at any level really) do in such a case, they simply go with the first few obvious moves (checks), moves they know cannot be possibly wrong, and after a while if it appears to have simplified then you can sit down and calculate a forced mate (assuming there's time) else you just have to be practical and go with the first best line you see, specially in such case where the position is trivially winning for white anyway.  </sup></p>
