Glenn C. Rhoads vs. unknown

Comments by Glenn C. Rhoads.

This game of mine illustrates non-parallel mini-max moves. I was the vertical player and opened with 1. a3 and my opponent responded with 1... e4 yielding the following position.

C10 R10 Q1 Va3 He4

I played the minimax move 2. f5 yielding

C10 R10 Q1 Va3 He4    Vf5

By connecting as far away as possible from the top, I increase my strength towards the bottom. (i.e. I am maintaining a minimal strength connection to the top while maximizing my strength towards the bottom). Before playing such a move, I have to verify that my opponent can't stop me from reaching the top. I could meet the attempted block with 2...g4 or 2...h2 by getting a third row ladder (2...g4 3.f4 g2 4.f3, etc. or 2...h2 3.g3 g2 4.f3, etc.), laddering down to e3, and then playing b4 (how to play a third row to a3 is described in a later section). I would be happy with such a line. My opponent however played the excellent e3. This move takes away the ladder, hence forcing me to reconnect to the top, while at the same time increasing his strength to the left.

C10 R10 Q1 Va3 He4    Vf5   He3

Here I played the minimax move g4. g4 has the potential to help block my opponent from going across the bottom of the board (e.g. Blue e7, Red f7, Blue f6, Red h5 and now g4 is helping out) or equivalently helps me to connect downwards on the right. I.e. g4 maintains a minimal strength connection towards the top while maximizing my strength towards the bottom. Note that a stronger move towards the top such as g3 does not have the same potential to help out towards the bottom. This potential may seem remote but in fact I would not have won the game without it! The most important variation is as follows (there were two mistakes in the actual game which took the game out of the path it should have followed into a shorter less instructive branch).

C10 R10 Q1 Va3 He4    Vf5   He3    Vg4 Hh3 Vg3 Hf8 Ve8 He9 Vg7

C10 R10 Q1 Va3 He4    Vf5   He3    Vg4 Hh3 Vg3 Hf8 Ve8 He9 Vg7  Hf7 Ve7 Hd9 Vc8 Hb10 Va10 Hb9 Va9 Hb8 Va8 Hf2

C10 R10 Q1 Va3 He4    Vf5   He3    Vg4 Hh3 Vg3 Hf8 Ve8 He9 Vg7  Hf7 Ve7 Hd9 Vc8 Hb10 Va10 Hb9 Va9 Hb8 Va8 Hf2     Vi2 Hc6 Vh8 Hg6 Vi5 Hh7 Vg8 Hh6 Vj6 Hi9 Vi8 Hg10 Vf10 Hh4 Vj3