The Philidor Position, 1777. (!) 

I first became interested in this ending, (King & Queen vs. King & Rook); over 30 years ago. Sometime in the late 60's, when I was about nine years old, I went to a tournament in another state. Two players were struggling mightily with this ending, and seemingly making no progress. We had to leave before the game was finished, so I will never know how that game turned out. 
 (A good player told me it was, "An easy win," and not to worry about it. 
  Of course, my experience is that it is NOT all that easy!!)  

Then a few years later, (in the early 70's); I went to New York for a chess tournament. We got there a few days early, so we did the obligatory sight-seeing. One night a local  relative suggested we go to one of the local chess clubs. 
(The Manhattan club, I think; but I am NOT completely sure.)

At the club, they were setting up the position for an ADJOURNED game, (they don't do this anymore); and we of course decided to watch. Two players were duking it out, it may have been a game for the club championship. One player was an IM, (White) who was famous for his book knowledge. The other was a fairly young player, (A highly rated Master); who eventually became a GM. 
(I shall refer to them hereafter only as 'Player A' and 'Player B.')

The two players had obviously analyzed the adjourned position very deeply, a casual glance at the adjourned position revealed that Black had a sizeable advantage. After quite some play, 'Player B' had won 'Player A's' Queen, I think everyone expected a quick resignation. But crafty, old 'Player A' had other ideas. 

Eventually Black won all of White's Pawns, leaving 'Player A' ONLY with his King and a lone Rook vs. Black's King and Queen. Surely now White would throw in the towel? ('Player B' looked very confident, I am sure he had already looked up the  Philidor Position   in some endgame book, and knew it was, ... 
 "An easy win." !!)

But play continued. 'Player B' centralized his King and then began driving his opponent's King backwards. But ... surprisingly, rather than keeping his King and Rook together - as it said you had to in all the books - 'Player A's' (White) Rook dove to the opposite side of the board and began checking the Black King from behind. This whole procedure repeated itself more than once. All the while, 'Player B' has his head buried in his hands, and is falling further and further behind on the clock. 
(I think at one point an club officer came over and asked them if they wanted to adjourn again, or if they would play it out. It was agreed by both parties that they would finish the game that night, perhaps at a faster time control.) 

I got bored at one point and wandered off to play a 5-minute game of blitz (or two); when I returned Black seemed lost in thought. White's King was one square away from his right-hand side edge of the edge of the board, the White Rook was zooming back and forth one file away, all the while keeping the Black King at bay. (A new defensive position??!?!?)  

Eventually 'Player B' broke 'Player A's' defensive position, but once again 'Player A' separated his King and Rook and 'Player B' was tied in knots trying to deal with it. 

Then suddenly 'Player B' seemingly had it all figured out. Now he was slowly backing the White King into the corner, but it was obvious that Black had lost a lot of time. 'Player A' began counting on his score-sheet. He whispered something to his opponent. 'Player B' seemed to check his score-sheet ... he looked down a pretty long time. Suddenly they shook hands and then disappeared ... maybe into another room to analyze the game. Meanwhile the room was in something of an uproar. What had happened in the game? Eventually a club officer was kind enough to find out, the game was drawn!
(Apparently 'Player A' had figured out that the 50-move limit would kick in before 'Player B' would be able to win his Rook. So they agreed to a draw.) 

 *** 

The above game really got me very interested in the ending of King and Queen vs. King and Rook. I made it something of a specialty of mine.

I {later} got the book by GM Paul Keres, "Practical Chess Endings." (What a lot of people do not know is that this book may have grown out of a series of articles that Keres did for a Soviet magazine many years before on the endings.) At first I was very impressed with his analysis of this ending, but the more I closely looked at his analysis, the less impressed I was. Eventually, it began to look more like both players were COOPERATING, rather than two different players both working to achieve a different goal. (I eventually found several errors in Keres's analysis. The most ludicrous was the fact that the sixth move, (Q-K6+) which he once gave an exclam to when writing for a German magazine,  {This article was probably nothing more than a translation and re-print of an earlier article.};  is completely unnecessary. He also gives himself an exclam for his tenth move (Q-KB4) and says: "This is probably the simplest of several winning tries." The really funny thing is that White can play 6. Qf4!  ... and reach the same position that is reached after move 10 - - -  except we have eliminated FOUR completely  unnecessary and extraneous moves!!!   This is almost an unbelievable error from a player of Paul Keres class - he was a world class GM when he first wrote these words. The editor of this book also totally failed to catch this mistake.)

I 'met' a player (playing correspondence chess) who worked at a Soviet Consulate's Office in the U.S. When I mentioned, via a letter, (during the 1970's); I was interested in these endings ... but there was nothing in the English language on this subject - they were kind (& magnanimous) enough to send me a whole box of endgame books! I studied these intently. I thought I found many ideas that were new or unknown at that time.

***

The above story almost sounds like fiction ... unless you know the facts. Later in the 1970's, (December, 1978) the [then]   current    U.S. Champion,   GM Walter S. Browne, could  NOT  win the ending of Q+K vs. K+R when playing the mini-(super)-computer, Belle. This, despite the fact that the position was played at the time limit of 40 moves in 2.5 hours!!!  (Belle had analyzed practically every conceivable position of this endgame, and was allowed to access this information/database during play.)  The position was a win for the stronger side in like 31 moves with perfect play. Browne did NOT win in over 50 moves, and even exceeded both the move, and the time limit allowed for him in this position. (!!) 
(This event was later reported in the magazine, 'Chess Life.'  Although I no longer have this particular issue of this magazine, I remember the issue well. It had GM Browne on the cover - he had won a chess tournament in Las Vegas and he was standing next to a Vegas roulette wheel. This story is also given at the beginning of Chapter Three {#3} in Nunn's book.)  

I remained VERY interested in the ending of K+Q vs. K+R - it almost became a hobby of mine. I developed several notebooks filled with analysis of this ending, I wrote letters - and many people replied, sending me a lot of material to analyze. At one time, I may have had EVERY SINGLE MASTER EXAMPLE of this ending in my little collection of notebooks on this subject! Friends would come over to the house and wanted to play or analyze chess, I often asked them to look at this ending with me - until nearly all of my friends completely tired of this subject!! I also continued to gather every book and scrap of paper I could find on this ending. 

  Several times I sent various magazine editors copies of over 200 pages of analysis. I tried sending  
  it to editors of chess magazines all over the world, but no one seemed interested in it - at least for   
  a very long time. 

I continued to analyze this ending and wrote dozens of GM's and magazines about my research and analysis. Eventually my hard work paid off. GM Pal Benko, in his column,  "The End-Game Laboratory"  in  'Chess Life'  (April and May issues, 1988);  recognized and acknowledged my work. There is now a    "Goldsby Position,"    in the endgame of  King and Queen versus King and Rook.  I am VERY honored by this recognition, many World Champions do NOT have a position in the end-game named after them. It certainly was the result of many YEARS (maybe decades!) of hard work! 

I remain very interested in this subject. (I have a database on my computer that has over 200 positions in this endgame alone, but they are not all analyzed in great detail.) GM John Nunn has written a fantastic book on the subject of "Pawn-less endings."  ("The Secrets of Pawnless Endings.")  I am not satisfied with the section of the book (Chapter Three) on this ending, (Q+K vs. K+R); however. Many times his positions looked contrived. Specifically, many of the key positions are not covered. The Queen is many times on its strongest square, the Rook is many times on the 'weaker' side of the board. 
 (The weaker side being the shorter side of the chess board, where the  
  Rook is NOT nearly as effective as it would otherwise be.)  

There are several mistakes in his analysis. (For example, Diagram # 78, on page # 57: There are close to half a dozen different errors in his analysis of this one position alone. In particular, he missed one line - transposing to the fairly well-known "Philidor Position" - that would have shaved like 5-7 moves OFF his solution!! {This is a VERY significant reduction.} This, despite the fact that tells us in the introduction to his book that his analysis should be mistake-free ... ALL lines were checked and verified by computer analysis!!!)  He also misses several opportunities to construct, "The Goldsby Position," (in this endgame); and shorten the length of his printed analysis. In addition to all this, he does NOT acknowledge my work, even though my ideas have been published in magazines all around the world!! This is a big over-sight by a writer of his stature. This entire Chapter could be completely re-written. 

I hope this is accomplished in the next version of this book. 
(IF there is a next version.)