The Problem Corner #9
Only four pawns and kings on the board. Deep in the endgame it's White to move and win. Knowledge of these types of "fundamental particle" positions will help you win more games.
The fundamental imbalance here is Black's outside passed pawn versus White's protected passed pawn. Other things being equal, the protected passed pawn is more valuable, as this example illustrates.
Note that the Black king cannot leave the square of White's further advanced b-pawn. For example, 1. Kc3 g4 2. Kd3 Kf4? 3. b6! g3 4. b7 g2 5. b8=Q+ queens first and wins easily.
So, the winning plan for White is to capture Black's g-pawn, which the king cannot defend, and then return to the queenside. 1. Kc3 g4 2. Kd3 g3 3. Ke3 g2 4. Kf2 g1=Q+ 5. Kxg1. So far, so good. The dangerous enemy pawn has been eliminated, and White still has a protected passed pawn.
Of course, White has no need to push the b-pawn until the king is in better position. 5. ... Kd5 6. Kf2 Ke5 7. Ke3 Kd5 8. Kd3 Kc5 9. Ke4! Kb6 10. Kd5 Kc7! (diagram).
Now 11. Kc5 Kb7 12. b6? Ka6! 13. Kc6 is stalemate, and 12. Kd6 Kb6 maintains the opposition for Black. 11. Ke6! Kb7 12. Kd7 (now White has the opposition) 12. ... Kb6 (12. ... Kb8 13. Kc6 is similar) 13. Kc8 Ka7 14. Kc7 Ka8 15. Kb6! wins the a-pawn and the game easily.