Consider the following position with white to move.
This position is a win for white. White should play either Kc6 or Ke6.
It turns out that white can force mate in one move less with Ke6. If our technique is well-developed or we have excellent calculating skills, we might realize this. Or we might intuit this based on the fact that Ke6 keeps the white king in the center, which is the most flexible in allowing white to chase down black’s king regardless of which side of the board he moves his king.
Suppose that the game proceeds with 1. Ke6 Ke8. Based on rule 1.2, white should play 2. d6. Even if one cannot calculate this, it’s fairly intuitive that this move is the quickest way to win, since d6 must be played in order to win. However, as pointed out in the previous post, we must not only formulate rules that allow us to pick the most optimal move, but also define rules that allow us to rule out sub-optimal moves. In this particular case we formulate two additional rules:
2.1.1 In a won position, don’t make a move that allows your opponent to immediately repeat or force a repeat of the same position with the same side to move. In a lost position, make a move that allows the same position to repeat with the same side to move if given the opportunity.
2.1.2 The above rule also applies when you believe you have a won position, even if this is uncertain.
Rule 2.2 might be referred to as the Principle of Forward Progress. This rules says that if you believe you have a won position, then any move you make should make forward progress.
Based on rule 2.1 or 2.2, we know that after 1. Ke6 Ke8 that the correct move cannot be 2. Kd6 since that allows black to repeat the same position with 2. … Kd8.
We conclude that the optimal move after 1. Ke6 Ke8 is 2. d6.
White now has six possible moves.