optimal decision making in chess – part 6

Consider the following position with white to move.

We need an criterion for determining the most optimal move. What are the objectives of each side? White correctly assesses the game as a draw. His strategic objective is therefore to capture the black pawn and essentially seal the deal on the draw. Black has the same objective. Although black is not the best chess player and he may make some mistakes along the way.

Although the above is a drawn position, white has the advantage since the position is symmetric and it’s white’s move and there is no Zugzwang. It’s just not enough to win.

Every move by white still results in a drawn position. Even after Ka1 the position is still a draw. But based on the principle of forward progress, white should consider either Ka3, Kb3, or Kc3.

Which of those three moves is best? Well white has a possible backup objective – which is the possibility that white could win if black plays badly. To win, white would either need to capture black’s b-pawn and then queen his g-pawn, or queen his g-pawn before black queens his b-pawn in a manner that still allows white to win the game.

We now define the following rule:

4.1 Given a choice between moves that achieve the same objective, choose the move that either most limits your opponent’s objectives or the move that is most flexible with regard to your objectives.

In other words, make moves that give you the flexibility to pursue different objectives, depending on how the game proceeds. This is what is meant by a flexible move. This also implies making the move that gives you the best chances if your opponent messes up.

Now, let’s also consider the move g4. As noted before, we have to define rules that also allow us to rule out moves that are not good. So we add the following rule:

4.2 Don’t make a move that advances your opponent’s plan while sacrificing your own.

Black wants to capture white’s pawn. Playing g4 makes it easier for black to achieve that goal.

If we agree with the above rules, we now know the best move: Kc3. This advances white’s objective of capturing black’s pawn, but also allows flexibility, since this also moves the king closer to the king-side. If black really screws up, white is in a better position to take advantage of that.

Starting off, white can capture the pawn in a maximum of 5 moves. Same for black. For the following, we put in parentheses how many moves it will take each side to capture the opponent’s pawn.

Based on the above, the best variation for both sides is 1. Kc3 (4) Kf6 (4) 2. Kd4 (3) Kf5 (3) 3. Kc5 (2) Kg4 (2) 4. Kb6 (1) Kg3 (1) 5. Kxb7 Kxg2.

We can see the impact of white’s advantage as the king’s approach the center.