user27380: Most drawn endgames where one side is stronger than the other (e.g. has an extra pawn) are drawn because the weaker king can force being stalemated on the rim if the stronger side avoids a repetition.
Let's assume we add an additional rank/file at each side of the board so that the board would have a size of 10x10.
The chess game would be played on the inner 8x8 board just like regular chess. The only exception is, that

a king that is not in check can and must step on the outer area if and only if there are no other legal moves and
must move back into the regular board as soon as it becomes legal.

Would this in effect be equivalent to declaring a stalemate on the board edge a win for the stronger side with perfect play?

user18809: No. Think of a position like White king on f2 versus Black pawn on h2 and Black king on h1. Black is stalemated, but adding the extra outer squares would not turn this into a win for White, but rather into a draw by repetition (...Ki2 Kg3! and now Kh1 is the only legal move

27380: <p>Most drawn endgames where one side is stronger than the other (e.g. has an extra pawn) are drawn because the weaker king can force being stalemated on the rim if the stronger side avoids a repetition.
Let's assume we add an additional rank/file at each side of the board so that the board would have a size of 10x10.
The chess game would be played on the inner 8x8 board just like regular chess. The only exception is, that</p>
<ol>
<li>a king that is not in check can and must step on the outer area if and only if there are no other legal moves and</li>
<li>must move back into the regular board as soon as it becomes legal.</li>
</ol>
<p>Would this in effect be equivalent to declaring a stalemate on the board edge a win for the stronger side with perfect play?</p>
 18809: <p>No. Think of a position like White king on f2 versus Black pawn on h2 and Black king on h1. Black is stalemated, but adding the extra outer squares would not turn this into a win for White, but rather into a draw by repetition (...Ki2 Kg3! and now Kh1 is the only legal move</p>
