Lucena Position

The other thing to keep in mind is that it's not about how many times it happens.  It's about knowing patterns and how many times it CAN happen.  I might make one move over another in a R+4P vs R+3P ending, where I'm down the pawn, because going with Option A leads to a drawn position, but Option B gives my opponent Lucena's position.

So Lucena's position doesn't have to happen for it to be important.  Just knowing it helps you prevent it happening when you are down a pawn, or may drive you to what you need to do to simply your R+4P vs R+3P down to a winning R+P vs R position!

It's not faulty. It's done on purpose to show that the king alone can't win that position.

Then maybe you should learn what the bridge technique is before you identify it as such and imply that 1.Rd2+ is bad.

The line you list works, but that's not the Bridge technique.  The Bridge, from your starting position, would be 1.Rd2+ Kc7 2.Rd4! Rf2 3.Ke7 Re2+ 4.Kf6 Rf2+ 5.Ke6 Re2+ 6.Kf5 Rf2+ 7.Rf4!, which explains why the King must be 3 files away from the pawn for the Bridge to work.

Then you should learn to be a bit more humble. Or do we have to call the positions the way you want? There is no such "brigde" position actually. There's the Lucena position, there's the position I've shown above, and there's hundred more, some have name, some have not. Focus on the moves I've shown, and stop trying to teach people what to write. It's the second post I've seen of yours where people complaint about your arrogant replies.

"Or do we have to call the positions the way you want?"

What a freaking joke! 

Do we call China "China" because that's what I want to call it?

If we put lipstick on a pig, we still have a pig, no matter what we do with it!

Lucena's Position involves building a Bridge.  The act of building the "Bridge" (I didn't give it its name) is to force the opposing King three squares away from the pawn, then move the Rook to the 4th rank, then move the King in a zigzag fashion, and block with the pawn once the King is on the 5th rank.

To say that you are building a bridge with 1.Rh2 is incorrect!

The concept of building a bridge is quite simple:

The K is in a safe place in front of the pawn on the eighth rank (using White as the side with the extra pawn). It needs a second safe place to hide from the defender's checks, relatively close to the pawn. And then, it needs a bridge from one safe place to the other. 

In the Lucena position, the second safe place is created  by playing the R to the 4th rank, allowing the K to go to the 5th rank and block the ensuing checks with the Rook. It's possible to create a safe square closer to the pawn in less critical positions, but it's necessary to learn the Lucena maneuver because that, along with the Philidor position, is the most critical position for evaluating the endgame.

Thrillerfan is right that the opposing K needs to be pushed away from the pawn, because if the defender is too close, when rooks are traded the P/Q may be taken if the K is too close. But that's not actually part of the bridge building process, it's protecting the pawn for AFTER the bridge has served its purpose.

Riurik's position in post 16 gives 1.Rh2 an exclamation mark. It's not White's best move. Thrillerfan is completely correct to state that 1.Rd2! is even better. It leads to a faster mate, and it's conceptually easier to play without going wrong. 

The point is to learn the Lucena technique first, and if there are times when there are quicker methods, good. But at least you know what to do in the most difficult positions.

In fact, Riurik demonstrates that he doesn't understand the Lucena position in his sideline analyzing Rd2:

Are you guys reading the whole thread, or just the last post? I said that I used that variation to show that the king alone without the rook cannot win (note the underline). Rh2 is the quickest way in the position I've shown.

And now comes the most embarrasing part for you two: the example I showed is from GM Chris Ward's book "Starting Out: Rook Endgames". Now you can keep on talking.

What did I say that was materially wrong? 

I don't have GM Ward's Rook endgame book, but I do know him. I sincerely doubt he gave the line 1.Rh2 an exclam, and I also doubt he showed the line with 2.Ke7? as White's main line. Of course, I can ask him about it. 

Plug the following into the Nalimov tablebase: 5K2/3k1P2/8/8/8/8/R7/6r1 w - - 0 1

Here's the link: http://www.k4it.de/index.php?lang=en&topic=egtb

That's the position where you say 1.Rh2 is fastest. You're wrong there. 

I know, you never admit you're wrong. But this one is clear as day.

Yes, please, go ask him. In the meantime I'll copy here the full example with his comments and his evaluations, from his chapter called "Building bridge".

(All copyrights to Mr. Chris Ward)

1. Rook checking the defender's king then going to the fourth rank. 2. King goes to the fifth rank. 3. Blocking the check by the rook.

Thanks for the details.

                                                             Lucena's Classical technique

As I said, I don't have this particular book by GM Ward, but in example #32, he hints that he deals with the Lucena position in example #33. On move nine of example #32, he writes, 

"There is a crafty solution to this outlined in the next example, but for now observe the simplicity of the text."

Please show us his example #33.

In #33 I believe he deals actually with the Lucena position. I'll post the entire example here tomorrow, no problem.

Power Of Mighty Bishop In The End Game

https://www.youtube.com/watch?v=Y2BWx2cPBUU

I think the Lucena position is overrated. I have played 15,000 blitz games on chess.com and I have used the classical lucena position with the moving of the rook to the fourth rank to interpose against blacks checks exactly once. 

My opponents have never never once used it against me. 

This is very easy

Actually, although this position doesn't occur too frequently, it is the position everyone strives to attain in a typical rook pawn endgame. I would recommend that you try / learn it because it may come in handy and increase your likelihood of a win in a rook pawn endgame.