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Why is e5?? A blunder

Because it allows white king at black's 3 queenside pawns - the kingside pawn advantage will force the withdrawal of black king, one way or another. To add insult to the injury, black can no longer force trading off white's lone queenside pawn without the help of his king (who must be always ready to prevent white's kingside advance).

Meanwhile, g5 allows black to build a 'wall of fire' white king cannot pass and takes the opposition as well.

If white tries g-pawn advance, black can just trade on b5 and put unstoppable threat on it with king to c5 (which white cannot prevent), then still have time to stop infiltration via ex. f6 and convert.

Meanwhile, black doesn't have to grant passage to white king, as with pawn on e3 attacking white's sole queenside pawn with f-pawn doesn't lose it or force a retreat.

If white trades on f5 after f7f5 push, black can just advance one of the queenside pawn pairs and white would be unable to take the other, even when they infiltrate, as the other would queen. Then black king can take a leisurely stroll to come support a pawn from behind or front, and white king cannot stop a pawn from walking under black's protective coat.

White's best chance might be using b5b6 pawn push to force black king to take on b6, thus allowing white king to threaten to go to e5, where it would place a double attack on f5 square. However, in that case black can just take or advance with the f-pawn; in first case it allows one to lead white king away, thus getting black king time to get on key square for e6 pawn and in second case white king must hurry up in front of f-pawn, which will then make another aforementioned queenside pawn pair with the e-pawn (if white goes after g-pawn via Kf6, the f-pawn will queen before white's g4 pawn can move a single square).
Because now White can play g5, which stops Black's f-pawn from advancing. Black wants to advance his f-pawn to get two connected, passed pawns (e- and f-pawn). If Black had played g5 himself, he could play f5 next. Then gxf5 exf5 and Black has passed pawns. Black could have also played immediately 40. ...f5, with the same idea. If White tries to flank the passed pawns, Black can move either of passed pawns forward protecting the further pawn, and if White takes the back-pawn, the further will escape. White's pawns on the other hand are vulnerable left alone (because of Black's a-pawn) and Black will capture them.
once u push a passed pawn too far it becomes a liability and u have to babysit it by protecting it with your king and the passed pawn is the only advantage u have.

so keep the threat of the passed pawn walking through open until u see a winning line.

f6 instead would have been the picture perfect waiting move and let the opponents king decide if he wants to go right or left, its the zugzwang phenomenon.

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