fredthebear: From general appearance, if properly recorded, the above game should have ended in a draw. Either king should be able to prevent the other from advancing with aid of the blocked pawns, who cannot eliminate each other and cannot be captured by the opposing king. All paths can be blocked; no progress can be made. The rule of opposition applies to king facing king, always separated by at least one square.
The final position on the board is rather quite simple; it's a king and pawns endgame. If it does not seem simple, the reader should borrow some general chess instruction books for beginners from the library and read the endgame chapters again and again. Set up the diagrammed positions on a board and actually move the pieces by hand as the book instructs.
Endgames are tough on a player after a long battle and time running short. Body, mind and spirit can be fatigued. However, common endgame patterns and themes are forcing and repeat themselves often. Once learned, they keep popping up ending after ending after ending year after year after year. Forcing endgames are concrete. Forcing endgames do not change like opening theory does. Endgame studies are highly reliable and keep on rewarding the student time and again. Black should have drawn the final position above.
Experienced masters of the endgame can often play such king and pawn endings quickly, very very quickly (material is greatly reduced, tactics and combinations are much less common so calculation is mostly about counting moves to reach a particular square, such as the promotion square). Endgame masters might not ever run out of time with a 5-second delay feature (it's like having 5 free seconds each and every move). If necessary, masters can make 20 moves or more and never lose a second off their clock by utilizing the time delay feature. It's not so difficult to learn about blocked pawns, pawns majorities, passed pawns, and exceptions to the rule such as the h-pawn... how each pawn will faire compared to his adversary. It becomes a matter of where the king belongs in preventing or aiding passers (or where to prevent the opposing king from entering).
In the above game, 40...Kd6 is next, and the kings are opposed. If White moves a pawn, a properly timed b6 draws for Black because it returns the move to White while it defends the a5 and c5 square from White penetration. On the other hand, b5 would lose the game for Black because it would allow White to advance. That's not so difficult for Black to figure, because it's the only pawn available that can move. Black should be able to shuffle his king back and forth either side of the d-pawn very quickly and not lose on time, assuming there is a time delay feature which is now required at rated tournaments.
Those players who are using the durable old wind-up analogue clocks that do not have the time delay feature need endgame understanding even more so! Their clock starts immediately without delay.
"It cannot be too greatly emphasized that the most important role in pawn endings is played by the king."
-- Dr. Seigbert Tarrasch