Deep Shredder and Hiarcs both insist that the drawing lines are:

19. Qg4 Kh7 20. Qh5+ Kg7 21. Qg4 Kh7 22. Qh5+ etc (draw by repetition).

19. Qg4 Kh7 20. Rf5 Be3+ 21. Kh1 Qe6 <NOT Qd6> 22. Qh4+ Kg7 23. Raf1 Qh6 24. Qe7 Qe6 25. Qh4 Qh6 etc (draw by repetition)

19. Qg4 Kh7 20. Rf5 Be3+ 21. Kh1 Qe6 22. Qh4+ Kg7 23. Raf1 f6 24. Qg4+ Kf7 25. Qf3 Kg8 26. Qg4+ Kf7 27. Qf3 Kg8 (ditto)

<malaya2006: <Alphastar:> Here's what could occur: 19. Qg4 Kh7 20. Rf5 Be3+ 21. Kh1 Qd6 (I calculated this far and concluded that there isn't much for white here) 22. Raf1! Qg6 23. Qh4+ Kg7 (23. ..Bh6 24. Qxd4 unclear) 24. R1f3 f6 25. h3! Rh8 26. Qe4 Rhg8 27. Qxb7+ Kh8 28. g4 pretty much unclear. i think you missed 22.Rh5+ Bh6 23.Qh4 which leaves White 2 pawns up.>

No, the bishop is still there:

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But this last statement (no promise) holds only within the limited horizon of maybe 20 plies that the program can explore. So yes, it is possible that both 19.Rf4 and 19.Qh4 win (and Rf4 definitely puts more pressure on the black).

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<MostlyAverageJoe> <How is white to proceed to win from this position? It might be very well "a matter of technique", but it is way beyond my chess abilities to find it, so if someone can explain it to me, I would be grateful.>

I see white to move with a queenside pawn majority that should allow for the creation of a passed pawn. Whether this leads to a win I do not know, but I like my chances and would play white every time.

In this position it’s reasonable to say that the worst white should do is draw. Black’s only hope is to draw. I think that that’s the best we can say about it.

In taking up <MostlyAverageJoe>'s challenge, you proposed 30. b4. I think Black replies with 30. ... f5 to start attempting to dissolve the Kingside, so he only has to defend on on side of the board. I think what happens next is 31. a4, Kf6. I don't see any way for White to make progress.

Show us that simple win, then.

Initially, f5 was indeed showing as the best response for black, but some deeper analysis refuted it with Rf1. I ended up looking into the line resulting from 30.b4 Kg6

Good news for white: after another 29 moves, he got two passed pawns. Here's the position (black to move):

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No, no, definitely not Rae8? - bad move.

You need to find an improvement for white in one of these lines:

19. Rf4 Rfe8 20.h4 Rac8 21.Rg4 Re5 22.Rc1 Kg7

or

19. Rf4 Rfe8 20. h4 Rac8 21. Rg4 Re5 22. Rc1 Rc6 23. Rxg5+ Rxg5 24. Qxg5+ Qxg5 25. hxg5 Rb6 26. b3 Kg7 27. a4 Rc6 28. Kf2 Rc5 29. Kf3 Rxg5 30.Re1 Kf6 31. g4 Rc5 32. Re2 b6 33. Kf4 Rd5 34. b4 Rd7 35. g5+ Kg6 36. b5 Rc7 37. Rg2 +−

The rook endings that result are not very clear, overall because Black have some compensations for the material superiority of White (2 pawns but one of them in g5 is lost).

<zb2cr> & <jimfromprovidence> <Indeed, 30.b4 seems to be the best for white from the position derived from Rybka's line. I did some quick forward analysis from there with some backtracking. Initially, f5 was indeed showing as the best response for black, but some deeper analysis refuted it with Rf1. I ended up looking into the line resulting from 30.b4 Kg6 Good news for white: after another 29 moves, he got two passed pawns. Here's the position (black to move):

Good news for black: it is a tablebase draw :-)>

<maj> You are trying to have it both ways. You first say that a position is unknowable since a computer can’t determine it if it’s more than 10 moves out (20 ply), yet you demonstrate a position after 29 moves (58 ply??) that supports your contention that a draw is possible.

That’s one position of a probably incalculable amount of permutations. <zb2cr> fell into that argument with you.

The position is unknowable until it's played out. That’s it.

I'll still go with white, thanks.

Indeed Rf4!! wins! Did you look at my line?

The pawn ending is lost for Black.

Not really; most of the time I've spent on this puzzle was in trying to find a convincing way for the white to win, and I failed each and every time. The line I mentioned was not meant to prove anything; I should've made it clear that it was just an example of several drawn results that resulted from my attempts. Yes, white can create a passed pawn, but in this particular line it was still not enough.

BTW, I 100% agree with your assessment <...that the worst white should do is draw. Black’s only hope is to draw>.

I am still wondering how to formulate a sound strategy for the white to win. Creating a passed pawn on Q side is required, of course. Dissolving the K side and moving the fight to Q side, as suggested by <zb2cr> is probably not a good idea. Elementary rule of exchanging pieces when ahead in material seems hold here; white should try to exchange rooks while black should keep his. Both sides should try to advance their respective K-side pawns.

33...Rc7 improves the score to (+1.61)

32...Rc7 improves the score to (+1.52)

27...Re6 improves the score to (+1.25)

and this brings the valuation down enough to admit a substantial possibility of a draw. Now, to be fairl, 23. Rxg5+ evaluates slightly lower than 23.hxg3, so your line might be improved for white, too (to +1.31).

However, 22...Kg7 is slightly better for black than 22...Rc6 (yeah, I used 'or' when listing it previously, but it should've been 'and').

All analysis 20 plies deep.

Following this line, I like the position 31 Rf1 Rxg2+ 32 Rf2 for white.

This morning, I’ve played it out when black replies 32 …Rg3, Rg4 or Rg1 and it seems to work out well for white every time.

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I followed your line:

30.b4 Kg6 31 Rf1 Rxg2+ 32 Rf2 Rg4

and then started Hiarcs' autoplay mode, 20 plies per move; this ended up in a draw. Alas, I lost the line after hitting a wrong key, so I am re-running it now, with the idea that once it gets posted, perhaps you or the others can show some improvement for white.

cc: <Terry McCracken> <zb2cr>

White has sacrificed the g pawn to gain tempo and to free up his King and rook. His remaining pawns are connected. (Black cannot swap rooks as this loses every time).

This is the new position.

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An intense endgame ensues with:

33 Rh2 f5 34 Kf3 Rg1 35 a4 Rd1 36 Ke2 Rb1 37 Rg2+ Kf6 38 b5 Rb2+ 39 Kf3 Rb3 40 Rd2 Ra3 41 Kf4 Rxa4 42 Rh2 Ra3 43 Rh6+ Kg7 44 Rd6 Rxd3 45 Kxf5 Rc3 46 Rxd4 a5 47 Rd7+ Kh6 48 Rxb7 Rxc4 49 Rb6+ Kh7 50 Ke5 a4 51 Kd5 Rc3 52 Ra6 a3 53 b6 Rb3 54 Kc6 a2 55 b7 Rb2 56 Kc7 Rc2+ 57 Kb6 Rb2+ 58 Ka7 Kg7 59 b8=Q Rxb8 60 Kxb8 a1=Q 61 Rxa1. The final position is:

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