Update: I emailed Tim Krabbé, and he agrees that 41. b4 bxa4 draws.
He has posted a PS about this just under his old analysis.
With respect to "Skawinski - Tomczak, European ch rapid, Warsaw 2011",
Tim Krabbé says that "White could have won with 41.b4!".
After 41. b4 bxa4 , they would have reached the position
[Title "The Position I'm Actually Interested In"]
[fen "8/8/2p5/p2k1ppp/pP1P5/3K1PPP/8/8 w - - 0 42"]
with white to move. Stockfish believes that from the above position,
everything other than bxa5 loses outright for white, and that after bxa5, a3 probably
holds for black due to the counter-breakthrough on the kingside. Tim Krabbé does
address that counter-breakthrough, but only for 41. ... axb4 , rather than 41. ... bxa4 .
Here's what I currently believe to be optimal play from the above diagram:
[Title "What I Currently Believe is Optimal Play From That Position"]
[fen "8/8/2p5/p2k1ppp/pP1P5/3K1PPP/8/8 w - - 0 42"]
1.bxa5 a3 2.Kc2 a2 3.Kb2 a1=Q+ 4.Kxa1 g4 5.hxg4 f4 6.gxf4 h4 7.a6 h3 8.a7 h2 9.a8=Q
Proof that white does not have a forced win after that line:
The main line continues 9. ... h1=Q+ 10.Kb2 Qg2+ 11.Kb3 Qxf3+ 12.Kb4 Qxf4 13.Qd8+ Ke4. Playing Ka2 instead of Kb2 doesn't change anything.
If white's king goes back to rank 1 instead of to rank 3 or back to rank 2 instead of to
rank 4, then black checks horizontally from the f-file until white's king goes to rank 4.
Otherwise, black doesn't care how white's king goes from a1 to rank 4.
Let "6ptbd" be short for "6-piece tablebase draw-or-win-for-black".
If white's king goes to a4 instead of b4 then:
Black plays Qd1+. If white plays Ka3 then black plays Qa1+.
If white doesn't play that or doesn't follow it up with Kb3 then Qxd4 followed by Qxf4
yields a 6ptbd, so for the next sentence, assume 12.Ka4 Qa1+ 13.Kb3 Qxa8.
If Kc3 then Qa1+ followed by Qxd4 yields a 6ptbd, else Kxd4 yields a 6ptbd.
Stephen comments that after Qxf4, the position is a finalgen table base draw. Since I already
had a majority of the relevant analysis together before I read that, I'll give analysis which, without relying on finalgen (but still relying on 5&6-piece tablebases being correct about certain positions
not being forced wins for white), shows that white doesn't have a forced win after Qxf4.
After Qxf4, Qd8+ is the only move which doesn't let black immediately
capture on d4 for a 6ptbw. After Ke4, the only moves for white which
don't let black immediately capture for a 6ptbd are Kc3,Qd7,g5 .
After Ke4, if Kc3 then black gets at least a draw as follows:
Black starts with Qc1+, and then black's queen moves as far up as doesn't let white capture
it immediately while still checking from below unless white's king goes to c5 or rank 6.
If Kc5 then Qa3+. Since b5 and and d3 and d5 are covered by black's pawn and king,
the only way out of those checks is going to rank 6, and the only ways for
white's king to get there are a5 and c5, which mean black's queen will be on a3.
In that case, Kxc6 is a 6ptbd, and if Kb6 then Qb4+ followed by Qxd4 is a tablebase draw.
After Ke4, if Qd7 then black gets at least a draw as follows:
Black starts with Qd2+. If Kc4 or Kc5 then black mostly follows the procedure described in the previous paragraph, but if Qb4+ Ka6 then Qa4+ followed by Qxd4 rather than an immediate Qxd4, and if Qb4+ Kxc6 then it's already a 6ptbd which Qxd4 would lose.
Otherwise, Qxd4 gives a 6ptbd.
After Ke4, if g5 then black gets at least a draw as follows:
Until black can check from below in a way that's not Qb1 checking Kb4, black moves so that [white_king's_square,black_queen's_square] is an element of {[a1,d1],[b1,d1],[a2,d2],[b2,d2],[a3,c1],[b3,d1],[b4,d2]}.
Once black can check from below in a way that's not Qb1 checking Kb4, black then does so as close to white's king as doesn't let white capture it immediately, and continues that until white's king reaches rank 6. If Kd6 then Qxd4+ is a 6ptbd. The only other way out of the part of this paragraph that came before this sentence is Kb6. Once white has played that, until white captures c6 or blocks a check or the rest of this sentence calls for Qxg5, black moves so that [white_king's_square,black_queen's_square] is an element of
{[a6,a4],[a7,a4],[a8,a4],[b6,b4],[b7,b5],[b8,b5],[c7,a5],[c8,f5],[d6,d5],[d7,d5],[e7,g5],[e8,g8]}.
White capturing c6 is a 6ptbd, and if white blocks a check then queen-takes-pawn is a 6ptbd.
The sentence two ago only calls for Qxg5 after Ke7, and in that case it's a 6ptbd.
Therefore, none of Kc3,Qd7,g5 keep a forced win for white. QED
Thus, any forced win for white must deviate from that line before h1=Q+.
...Qd2+. Checked with the engine, but even decent human player can realize that. Lines are pretty straightforward in my opinion... – AlwaysLearningNewStuff Sep 12 '15 at 20:22