Please explain the engine's analysis here??

This was a position I reached in a game recently. 

I put this position into the engine, and to my surprise, the engine said the best move was one that I didn't even consider - please explain this, and details would be preferable. 

In this position, I wanted to play 1.a4! and attack black's weak pawns and activating my rook at the same time. This idea is *thematic* in the Ruy Lopez and many other openings. 

But the engine wants me to play 1.Rh1, which I don't understand. 

 Yeah, you guessed it. A satirical post of the troll USCFtigerprowl. Who should have been muted far before 2Q1C was.

Probably because the idea is to keep as many of your pawns on the board as possible. Was a4 that much different of an evaluation when left to think than Rh1?

Doesn't Rh1 win an immediate pawn (the h pawn; if h5 then gxh5)? On the other hand, a4 followed by c6 may be stronger but it is less obviously winning material. Just a thought.

It probably calculated a faster mate or likely faster mate against best play. Maybe it saw you could get the Rook to the 7th rank without the King getting there first and then you could bring your K up to the 6th rank, achieve opposition and play the Rook to the 8th rank for mate.

I played this winning move, Kg7: a standard move you see in all the endgame books, in a game here on 2-8-17 and, as you can see, Stockfish 8 liked f6+ better even though it would have resulted in the Black King being able to get to f8 and achieve a stalemate-like position where I'd have to Queen a different Pawn while making sure his pawns had at least one legal move among them.  My guess is, with best play, f6+ somehow leads to a faster mate:

rh1 is getting a strong rook file and putting pressure on the h pawn, a4 is opening up an inferior file and giving black some time to activate his rook that you forgot to place, while trading pawns in these kinds of positions actually helps black anyway. and if there was no rook you forgot to place, then I don't see why you are bothering with this position at all

The engine may be right (they usually are), but does it really matter in that clearly won position ?

All that matters imho is that you found the way to a decisively winning advantage - it should not matter that much anymore how exactly you realize your win.

After all, winning is binary - you get the full point if you win no matter if you lost a pawn or two more then you strictly needed to in the endgame.

So I suggest in a situation like this, to always go with the plan that seems most clear to you . this will save time on the clock which probably is the only thing at this point that can still take victory away from you.

Simplify the position fast, and get a sure win and never mind counting material or positional evaluation too much - just win.

LOL are people blind or something? Cant they see you are a rook up?. I am calling 2Q1C, he must fight off your trolling.

You're accusing me of trolling!?

That's like calling a coworker "careless" for forgetting something when you were the one who forgot your car keys on the way to work that morning.

*Insert massive tirade here*

This is clearly legitimate discussion about how best to convert an advantage, get out, troll.

lol youre a rook up it's hard to play a losing move- everything is winning as long as you take their pawns with your rook, doesn't really matter how you do it. The engines just are thinking about the fastest way to do it, not the only way. (in a overly winning endgame like this, there are many ways to win, but in some situations, there is only one move that doesnt immediately lose. that is where you really should listen to the engine)

I like your trolling Cherub, it is kind of semi-annoying, not as good as 2Q1C´s one, he was better at sounding naive... Maybe because we all associated you to dull analysis. 

But I like it, specially when you brag about wins LOL.

SORRY SIR, NOT MY INTENTION TO DISRPUT THIS INTERESTING CHESS DISCUSSION.

the hook is well baited

@kinglysack true.

Thank you. Now we may get discourse in peace.

the tension is overwhelming

Excuse me, the purpose of this thread is to address my question, not trolling, and not your chess game...

Now, I'd love for someone to answer my question. 

youre a rook up it's hard to play a losing move- everything is winning as long as you take their pawns with your rook, doesn't really matter how you do it. The engines just are thinking about the fastest way to do it, not the only way. (in a overly winning endgame like this, there are many ways to win, but in some situations, there is only one move that doesnt immediately lose. that is where you really should listen to the engine)