Saving half a point is a skill of its own. These two topics show setups that hold against a side with more material: the Vancura defense in rook endings, and a fortress with bishops of opposite colors. Both depend on putting the right piece on the right square and keeping it there.
Verdict Draw. The black rook attacks the pawn from the side.
Hold rook and a-pawn against rook, when the pawn stands on the sixth rank, by keeping the rook on that rank and the king on the far side.
The white pawn stands on a6, and the black rook on c6 attacks it from the side along the sixth rank. The black king stays on the far side of the board, away from the white king. If the white rook leaves the pawn, ... ♜xa6 wins it. If the pawn advances to a7, the rook goes behind it with ... ♜a8, and in the end the rook is given for the pawn and only the kings remain.
1. ♔b5 ♚c7 2. ♖a2 ♜b6+ 3. ♔c5 ♜b8 4. a7 ♜a8 5. ♖a3 ♚b7 6. ♔d6 ♜xa7 7. ♖xa7+ ♚xa7
Putting the rook on the wrong rank. With the rook on c5, one rank lower, the pawn is no longer attacked, and 1. a7 queens.
White to move. Win or draw? (The black rook has moved to the fifth rank.)
White wins. The rook no longer attacks the pawn, so a7 cannot be stopped.
1. a7 ♚e7 2. a8=♕ ♜f5 3. ♕e4+ ♚f6 4. ♖b5 ♜xb5 5. ♔xb5
After 1. a7 ... ♚e7 the pawn queens with a8=♕, and after the rooks are traded the queen wins.
Copy the position into any board or engine to practice it:
3k4/8/P1r5/8/K7/8/1R6/8 w - - 0 1
Verdict Draw. The bishop controls the pawn's path.
Build a position where the stronger side cannot make progress. Here the defender's bishop controls the square in front of the pawn.
The white pawn on g6 is protected by the bishop, but its path goes through g7, a dark square, and the black bishop is dark-squared. The black king attacks the pawn and the bishop controls g7, so the pawn cannot advance. When it does, g7 is met by ... ♝xg7 and the position is a draw. With bishops of the same color, White would win.
1. ♔g8 ♝e5 2. ♔f7 ♚g5 3. ♗f5 ♚h6 4. g7 ♝xg7 5. ♔e6 ♝d4 6. ♔d7 ♚g5 7. ♗b1 ♝h8
Putting the bishop on the wrong color. With the bishop on c8, a light square, the pawn runs: 1. g7 and White wins.
White to move. Win or draw? (Black's bishop is on c8.)
White wins. The bishop is light-squared, so it cannot control g7.
1. g7 ♝e6 2. ♗h7 ♚g5 3. ♗g8 ♝f5 4. ♗d5 ♚f4 5. g8=♕ ♚e5 6. ♕g5 ♚xd5 7. ♕xf5+
g7 cannot be stopped, the pawn queens with g8=♕, and the queen wins the bishop.
Copy the position into any board or engine to practice it:
1b5K/8/6P1/7k/8/8/8/1B6 w - - 0 1