user3872: There exists a heuristic that recommends checking from the diagonals (using a queen) in order to get a perpetual. This, I expect, is a rule that is meant for the worse player in queen and pawn endgames. My question is, why does checking from diagonals ensures, or at least raises the probability, for a draw? 

user3270: As you said, this is a very general guideline, but looking back it has served me well in practical play.
Note that by "checking from the diagonals", the pattern I have seen is that the queen maintains a stable circuit on a diagonal but the checks themselves are usually horizontal or vertical.
I think it's because the checks from a diagonal allow the queen to keep the king in a box with only minimal pawn support (a single nearby pawn for either side will usually do it). Checks from a file or rank each allow the king to run across the board in one direction unless there's a pawn directly blocking his path.

3872: <p>There exists a heuristic that recommends checking from the diagonals (using a queen) in order to get a perpetual. This, I expect, is a rule that is meant for the worse player in queen and pawn endgames. My question is, why does checking from diagonals ensures, or at least raises the probability, for a draw? </p>
 3270: <p>As you said, this is a very general guideline, but looking back it has served me well in practical play.</p>

<p>Note that by "checking from the diagonals", the pattern I have seen is that the queen maintains a stable circuit on a diagonal but the checks themselves are usually horizontal or vertical.</p>

<p>I think it's because the checks from a diagonal allow the queen to keep the king in a box with only minimal pawn support (a single nearby pawn for <em>either</em> side will usually do it). Checks from a file or rank each allow the king to run across the board in one direction unless there's a pawn directly blocking his path.</p>
