He should not have pushed to a7. Â There might have been winning chances with the pawn on the sixth rank, as the king could use a7 as a shelter square from checks.
an intresting endgame
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The rook + pawn vs rook endgame was drawn until 52... Kf8?? After that point white could have won by moving his king to the aid the pawn.
On move 53 white made it a draw again by not playing his pawn to a6 or at least getting his king to d6 or e6
on move 53... black loses again with Ra-f1 it would have been better to move the king to e8
Move 54 55 & 56 was winning for white until he pushed the pawn to soon
After 57 the game was correctly determined to be a draw, white should have played on however since black already made numerous endgame errors might get lucky
@JMB2010: 57.Kd7 (instead of a7??) would have won by force. Your line with 57...Rf2  allows the White rook to get out from in front of the pawn with 58.Re8 and relocate to e6. Black's king is too far from the action for Black to hold the draw.
This just goes to show you that well known endgame positions like that actually happen.
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That's a good tactic to welcome critcism.
this has happened to me twice this week these positions really do happen the other time i had 10 sec with 3 sec delay and the opponen also pushed to a7 i was like "thanks" ok im going to learn the vancura position now thank you for your analysis
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heres a game where an intresting endgame occurs of course im also curious about the opening and the middle game so feel free to criticize me