The stalemate defence
Against a pawn on the seventh the queen wins by forcing the defending king in front of its pawn, then using the free move to bring its own king closer. Against a pawn on the c-file that plan fails.
When the queen checks, the black king goes to a1 instead of c1. If the queen takes the pawn on c2 while the king stands on a1, Black has no legal move and is not in check: stalemate. So the queen never wins the free move it needs to bring its own king closer.
Choose the right square
In the starting position you are in check. Ka1, Ka2 and Ka3 all hold the draw. Kc1, the natural move to block the pawn, loses, and so does Kc3.
The same choice comes back later. In the demonstration, after Qc3+ only Kb1 draws, and after Qb3+ only Ka1 draws. Each time, blocking the pawn on c1 would hand White the free move it needs.
The rook's pawn, and the exceptions
With a rook's pawn the defence is simpler: the king hides in the corner in front of its pawn, and any attempt to take away its last squares gives stalemate.
Both draws rely on the attacking king being too far away to join in. When it is close, the queen often wins, so check the exact position before relying on the corner.
Remember
- Run to the corner, not in front of the pawn
- Qxc2 would be stalemate
- Deny White the free move
- Works when the white king is far away