Is rook & king v. rook & king always a draw?

If there is no direkt way to mate or winning the rook by a skewer or a dicovered check,

there is no way to win this against a well playing opponent. It's still possible to win this game against an opponent who blunders (maybe the opponent is very low on time) or just on time. With enough playing strength and some time on the clock there will be a threefold repetition, a draw by 50 moves rule, the exchange into a king vs. king draw or just a draw agreement in most cases.

Winning K+R against K is the easy part. Everyone should know a safe method to do. Even if this method takes 20 instead of 5 moves.

Post 20 is a simple mate or skewer, Post 40 is transposing into K+R vs. K at move 1, i see no value in that example. And there of course the common termination is +- (white wins) or -+ (black wins).

Post 25 is something very very special. I doubt that this position occured in any real game ever. But of course there are legal ways to reach this. Its more a kind of a simplified version of the same tactic on a full board.

When teaching K+R against K to beginners, there are two methods:

1. "the box", making the box in which the king can move smaller and smaller

2. "the opposition", bringing the kings into the opposition and give check with the rook to take line after line.

Sometimes a player is happy with the first teached method, sometimes he is more happy with the second. Important is that he has any idea what to do and plays for the known method move after move.

Something like

is of course much faster than any other moves of the rook along the 7th rank. I would show that every beginner, but don't except that they see this themself when getting into such positions first time.

For me No. 44 is a simple three move tactic. Every 1000 rated beginner should find the solution.

Sometimes it is also useful to think. Here is an example of the variant of your method 2 that I was taught immediately after learning the rules, played exactly move after move...

Perfectly agree.

My question was not, "would you call it difficult", but, "would you say that there is a direkt way to mate or winning the rook by a skewer or a dicovered check" (particularly since 2...Rc1+ would be almost as good a defence as any).

I think your original post might have been better phrased, "there is no way to win this against a well playing opponent unless there obviously is".

#48 So the beginner learns about the 50moves rule and that something like 1. Rf8 Kg4 2. Kg1 Kg5 3. Kf2 and so on would be the same method on the h-file. Perfect!

When thinking about this absurd sequence: I showed the mate on the 1st and 8th rank and on a- and h-file. It takes some trys until most pupils understand how to. Then i also gave the task to choose the nearest of the four possibilties. Last teached that two years ago...

#49 That's a desperate sacrifice, to life some moves more. It's directy connected to the mate threat. So for inch pinchers thats a motiv more.

But you prove my point. He probably thinks of that for himself. There was nothing about it in the rules I was taught. The first step was to place the rook on a row between the kings nearest the enemy king provided it couldn't be captured.

(And perfect but not perfectly accurate. I would chase the king up the g and h files after Rf8 - after 2.Kg1 Black can play 2...Kg3.)

What seems to be most important in this and other pawnless endgames is that the board continues to have four edges throughout. In many of the examples posted on this site the poster appears to have decided which edge to use at the outset and sticks to it come hell or high water.

Hmmm, even IM Silman only shows mates on the 8th rank on his 5 1/2 pages on that endgame. Just a small "He must move black to the corner (every corner!) of the chessbord". (translated back into english from the german translation of his endgame book...) And the king is somtimes nearer to other edges. But he uses the somewhat faster box metod, where he takes rank after rank + file after file. So 50 moves with that method is nearly impossible.

I could check what the step method (step 1) offers.

Maybe some people really try to follow such advices too excactly and producing such absurd 50 moves. Or there is bad training material around. Everyone can write a forum or a blog post. I don't know. Most kids in my club don't have problems with this mate after one or two hours training. The others often quit chess very fast, it's nothing for them.

There is certainly bad training material around. I've seen tutorials on this endgame that take double the number of moves they should and this site is full of explanations that take two or three times what they should even against wildly inaccurate defence.

I don't know why Silman would be talking about corners - there are mates anywhere around the edge. E.g. here is @TripleXDooM's example with accurate play from move 3 onwards:

I was serious when I gave in post #46 what I regard as the best method (4 obviously being optional if you're only interested in winning in practical games, but then 3 is also optional because your opponent will resign). I think it applies in any endgame. Even if you don't get a complete solution then after the effort it's easier to fill in the gaps by looking it up (preferably from an EGTB if available).

Note, for example, in the second diagram in post #41 @TripleXDooM is obviously fixated on mating on the a file and fails to notice he can restrict the king to three squares on the 8th. rank instead. This is no doubt following a method he has learnt in the distant past (apparently very similar to the one I learnt and failed to mate with in post #48) without looking at the position. (OK, it works in his case.)

As you concede, the problem lies with sticking too closely to the script. The mating method itself, while inefficient, is not too absurd. It works fine against accurate defence. Here is exactly the same method from the same position against the Nalimov tablebase for example (perfectly accurate defence).

The fastest that can be guaranteed is 11 moves, but the method is well within the 50 move rule this time. The problem in #48 is actually that the defence is absurd but the method has not been adapted to take advantage of the fact. This is a general problem with any fixed but inaccurate method of attack  in any endgame if the defender can divine the method in use.  
 

MelloMarshmell0 vs PeeledOrange - https://www.chess.com/live/game/65569285997

just won a king-rook vs king-rook end game. Starts move 52. Im a little sloppy cause im trying to work it out. Basically you have to get your rook to the outer edge and keep pinning the enemy king back, then give an extra row between your rook and enemy king - then you let the opponent keep checking your king until you enter your rook’s row (you must time it so your king is directly across from the enemy king) - if you keep the enemy rook on the same side of your king as your own rook (you might have to bully the enemy rook with your king to get it into position), then the rook will have reposition to start a fresh round of attacks which gives you a free tempo. While the enemy rook repositions you check the enemy king, knocking it back a row. Lather rinse, repeat till the king runs out of space. It’s not a forcible mate, but if the opponent doesnt catch on and thinks he’s playing for a draw, opponent might get sloppy enough to make it work. Just have to be sure to never let opponent x-ray your rook through your king (why you have to keep opponent’s rook on same side as your own.)

wait a minute

More accurately, your opponent just lost a king-rook vs king-rook end game.

Probably nodded off.

Full marks for perseverance though.