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Remembering the topic "h-pawn vs. hostile world"

I decided to show in one training a not-very-known position by young people. Rook and h-pawn seems to be enough to achieve the full point versus a simple bishop, but sometimes reality go beyond than fiction:
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White probably was very relaxed

, thinking that victory was trivial, but the lack of space to advance h-pawn is a key factor to defend this position.
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An easy win might be the team pawn in h7 and king in h6, but if pawn cross 3th row things will get complicated...

because white king needs to leave free-pass to the pawn. And is for it that best option is:
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1) force to black king get out the corner, to f-file: Kh6, a check in last row, etc.
2) move our white king out the h-column, with the rook in front of him in the g-column. For example Kg4 and Rg5, with black king on f7. After it h-pawn is free to make the race.
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The fight continued:
1.h4? and result was a draw

in a winning, but difficult position:
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Now, to win is vital make
a coup d'oeil (in insight) to bishop's position, before treating to leave h-column. This is the process with any comments (revealing that easy was if pawn was rested in h3...)

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Past week, seeing any Youtube videos about blitz games in Moscow, I saw any impressive games. It's not a normal
modus operandi in my style, but I considered appropiated to comment - yes, it was a blitz!

- two interesting games between Vallejo and Andreikin. To feel the games videos can be found here:
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This is the first game (really the second in the match):
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After a serious mistake by white in the opening black got the advantage, but with few time on the clock - Andreikin was really fast!

- and facing practical problems, game got confused. When all results seems possible, Vallejo play the strongest move
37...f4! 38.Bxf4 Rf2+ 39.Ke1 Rxf4 40.a6
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Andreikin had seen all these moves too, but seeing their faces

, none of them knows what occurs now! With clock saying 'tic-tac' Vallejo thought that
40...Rb4 was enough, but wasn't. Normally is said "rooks behind opposite passed pawns". Ok, really it is, but two pawns are a lot to stay behind peacefully

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Correct was stop the pawns in a 'normal' way (with more time, it's clear!):
1) king goes to pawn which is near him (c5) and
2) rook touch more far-far away pawn (a6).
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The concret way: 40...Ke5! 41.a7 Rf8 42.Bc6 Kd4!, draw.
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After 41...Rb4 Andreikin thought any seconds and found 42.c6!, but position is yet a draw with 41...Rb1+ 42.Ke2 Rb2+, when white king cannot take on e3 because Rxb5, Re5+ and Re8, stopping all the pawns at the door.
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Instead of it Paco took the bishop, but it is not possible to make a fortress because black pawn is h-pawn and not g-pawn!

With g-pawn, the game is draw: g7, Kg8-h7, Rf6-h6 (two important support points!)
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Game continued 52...Kf8 53.Kd6 Rg7 54.Qf6+ Kg8 55.Qd8+, and white win by time, but ending is winning (see the comments). Rook will move out of g6 and it will be food for white's queen.
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The other game was very complicated, strategically speaking. With white Vallejo faced a difficult middlegame but after a 'mortal combat' on the queenside, many pawns have been changed, and the lack of one pawn is less important. Anyway the diagram shows a very promising situation - winning, really - for black...
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Now strong was 37...Kf5 or even 37...Kd5, saving pawns, and it's a matter of technique the victory.
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With time pressure - but with a lot of time more than Vallejo! - Dimitry gone semi-wronged with
37...Kd7? 38.fxe5! Ne4 39.exf6! gxf6 40.Nf7 Nxg3 41.Nxh6. Black has now only a little survivor, but Ng4-e3-d1-f2-h3 will pursue it. Anyway, as a recent game - Ivanchuk, maybe? - two knights (only, with one opponent pawn) can secure the full point if pawn is not very advanced!

The game reached it:
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From here in advance Andreikin plays for time, allowing white's king migrate from the corner. Seeing that Vallejo saw his opponent with annoying gesture

, and soon they agreed a draw. Victory is near, blocking g2 pawn and resctricting white's king until the spider's web is spinned

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52...Nh4! 53.Kh2 Nf1+ 54.Kg1 Ne3! Whether pawn advances black's king goes to h3 or g3 (against g2-g4) with a fast checkmate with Nf2-h3+ and Ng4-f2++. 55.Kh2 Ng5 Now white's king must return to the corner. 56.Kh1 Kg3 57.Kg1 Ne4 58.Kh1
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Now the final act:
58...Nd2 59.Kg1 Nef1!? 60.Kh1 Kf2! 61.g4 Ne4! and on next move Neg3 will be checkmate. If you have interest, the analysis - maybe sometimes wronged!

- is here:
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One 'complicated' endings are queen's endgames. When I was young, a beginner in chess, I became very surprised seeing any of them in tournament GM's games. Why on the hell they advanced their kings to bizarre positions - far away from opponent pawns -?

Why the defender was not giving more checks?

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Time gone fast

but any answers came to me, but I need to say that I haven't so much ideas clear!:
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1) It is very important to strong side make the most of opponent king's position. You are on the same row or column (or diagonal), you can cover with the queen and achieve the change at the same time. It is for it that versus f or c pawn, secure squares for weak side could be a5-a6, or h5-h6.
For weak side --> Far away=security for our queen! 
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2) Prevention is a basic matter for a team conformed only by a queen... So, instead of be arrested by a burst of checks

, the key mission is that opposite king can not find a shield between his pawn and his queen, to advance the pawn with careful.
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The game continued 56...Qa2?! and white's king gone at precise moment to c2. It is the best moment because black's king is enough far to a change of queens, drawing the pawn ending. So, at this time get closer the pawn is good for black's monarch.
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I think that a centralization was good:
56...Qe4!, trying first Kf6-g5, getting fifth row (important to cover lateral checks). Believing I know a lot of these endings

I will propose
57.Qg4! as best move to prevent it.
57...Kf6 is a semizugzwang because queen must move (checks on f5 or e6!)
58.Qh4+ Ke6 and now
59.Ka6! seems to me an interesting answer (analysis inside):
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It is wining for black? Maybe yes, maybe not, I don't know. Anyone can help me? Thanks!
