Eight pawns vs seven exercise: how to win? I had been thinking about exercises to help players &lt;1400 gain confidence. For instance, they should feel confident they can always win with queen and king vs king, or rook and king vs king, even against Magnus Carlsen. They should also feel confident they can win with a bishop and 8 pawns vs 8 pawns.

So I lazily took all the pieces off the back ranks and removed black's king pawn, to give an exercise with king and 8 pawns vs king and 7 pawns. I figured winning a pawn up in a pawn endgame is a useful skill to know, and it should not be too hard.



[FEN "4k3/pppp1ppp/8/8/8/8/PPPPPPPP/4K3 w - - 0 0"]



However, initial desultory poking around showed Black may be able to sit tight and form a barricade. This could be instructive for a beginning player, but it also might be too intimidating.

While this probably won't happen in actual play (exchanged pieces mean there is probably at least one line open), this is a non-trivial case worth looking at, as Black could quite possibly establish a blockade down two pawns (you can ignore the two backwards pawns--I saw this pawn structure in a recent video of Ben Feingold's, about his 2019 Foxwoods tourney.)



[FEN "8/4k3/1p4p1/p1pPPp1p/P1P2P1P/8/4K3/8 w - - 0 1"]



What is a good strategy for White to minimize the possibility of blockades? Also, what is Black's best strategy to push pawns and maximize the possibility of blockades?
I figured winning a pawn up in a pawn endgame is a useful skill to
  know


It is a useful skill to know and an even more important skill to know is when a pawn-up endgame is a win and when it is a draw and when it could be either depending on who is to move first. This is a vital skill because it stops you from swapping off into a drawn king and pawn endgame when you are a pawn up.


  I had been thinking about exercises to help players &lt;1400 gain
  confidence.


When it comes to building confidence in pawn-up endgames for &lt;1400 players this is where you / they should start. This is a win for white if it is white's turn and a draw if it is black's turn.

[FEN "4k3/8/8/8/8/8/4P3/4K3 w - - 0 0"]


This teaches you the importance of:


The opposition and 
Getting your king in front of your passed pawn not
behind


In terms of preventing (or aiming for) drawing blockades the &lt;1400 player needs to know this position and why it is a win for white if it is white's turn and a draw if it is black's turn.

[FEN "8/ppp3k1/8/PPP3K1/8/8/8/8 w - - 0 0"]


This teaches you that it is the position of the pieces which is key not material balance. White to play wins by sacrificing a pawn or even two depending on black's response.

Finally, Capablanca's Position:

[FEN "6k1/7p/8/8/8/8/6PP/6K1 w - - 0 0"]


It is a win for white but if black knows the ending it is very easy for white to go wrong and end up in a drawn position. Many white players much stronger than 1400 would struggle to win this against a knowledgeable black opponent.

All 3 of the positions above could arise from the position in the question. All 3 have far fewer pieces and so are much simpler but are far from straightforward. Mastering them first would be a good first step.