Position from Chess Mentor on King Pawn Endgame

https://www.chess.com/lessons/view/339

In the lesson above, the description for the first move is "If you understand why this first move needs to be played, then you understand king and pawn endings very well."

Right now, I think the purpose of the move is that pushing the pawn ensures that the white king will be on the 6th rank in front of pawn after capturing the black pawn, so white can win even though black will gain opposition after the black pawn is captured.

Is this reasoning correct? Is there any other idea or reason to consider? Thanks

Sounds exactly right to me.

As bkaifeng indicated, the key issue is where the black pawn is frozen. If White started with any king move, Black would be quite happy to reply by self-freezing the black pawn, playing 1...b5 and achieving a drawn position.

1...Kb8 would be equivalent.

2 Ke4 does not keep the opposition. Anyway, 2 Kf4 would be just as good.

If opposition were the key issue here, Black could play 2...Kc8. If play had started 1 Ke4 b5 2 Kd5 Kb7, it might have continued with 3 Kc5 Ka6 4 Kc6, giving White the opposition and a nevertheless dead drawn position.

If play had gone 1 b5 Kb7 2 Ke4 Kc8 3 Ke5 Kc7, it would have been Black taking the diagonal opposition in a nevertheless lost position.

That is the opposition that matters. Note, however, that, after 1 Kf4 b5 2 Ke4, White would have had the opposition in a drawn position.

Perhaps worthwhile to note that, after 1 b5 Kb7 2 Ke4 Kc7 3 Kd5 Kd7 4 Ke5, it would be a drawn position regardless of whether or not one thought of White as taking "the knight opposition".

Better be careful. After 5...Kd8 6 Kd6 Kc8 7 Kc6 Kb8 8 Kxb6 Ka8 9 Ka6 Kb8 10 b6 Ka8, it would be a draw with the white king on the 6th rank.

Thanks @IMBacon and @kindaspongey for your thoughts

Glad to help.

As far as I can tell, there was not much for me to do for you, apart from confirming that you had the right idea. Anyway, I am glad if I was any help.