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.
I played the minimax move 2. f5 yielding
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.
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).
| 3. | g4 | h3 | Again forcing me to reconnect to the top and hence, getting a free hex that could potentially help him connect to the right (h3 provides an escape for ladders up row I). |
| 4. | g3 | f8 | As good of a block towards the bottom that there is. |
| 5. | e8 | Necessary. | |
| 5. | ... | e9 | Essential. Note that this move stops any ladders on row 9 coming from the right and using e8 as an escape. |
| 6. | g7! | Excellent. Reconnecting e8 to the bottom with the d8 or d9 is defeated by e7. I can't stop e7 from connecting to the left because e4-e3 provides enough help (e.g. 6.d8 e7 7.c7 d6 8.b6 c6 9.c7 b5 10.c5 c4) nor could I stop e7 from connecting to the right — e7 is aided by f8, e9, and h3 (e.g. 6.d8 e7 7.f7 f6 8.h5 g6 9.h6 g7 10.h7 h8 11.g8 f10 12.g9 g10 13.i9 h9 14.j7 i7 and the h3 piece provides the ladder escape). 6.g7! may look strange and unconventional but it maintains a very slim advantage. |
| 6. | ... | f7 | The toughest move to meet. Note that 6.... g8 loses quickly to 7.d8 e7 8.f7 f6 9.h5 |
| 7. | e7 | I can't stop f7-f8-e9 from connecting to the right, so I block to the left in the only satisfactory way. I can't allow my opponent to connect from his f7 towards e3-e4. | |
| 7. | ... | d9 | An essential block. |
| 8. | c8 | c9 is no good. I can't allow my opponent to come up row D towards e3-e4. I need to force him as far away from e3-e4 as possible. | |
| 8. | ... | b10 | |
| 9. | a10 | b9 | I've forced my opponent into a second row ladder which is not sufficient because my a3 piece is just barely inside the Vb template. |
| 10. | a9 | b8 | |
| 11. | a8 | f2! | A nice idea. e4-e3-f2 is just strong enough for the second row ladder to work and at the same time, it threatens to cut off my main group of pieces from the top. This looks like it wins but there is a way out! |
| 12. | i2! | A subtle improvement over simply reconnecting with g2 or h2 (both of which are losing). This maintains the connection and i2 interferes with the usefulness of h3. This may seem insignificant but it makes the difference between winning and losing! (In hex, the difference between winning and losing is often very slight) | |
| 13. | ... | c6 | Continuing with his plan to connect to the left which now works due to f2. |
| 14. | h8! | The unique move that stops my opponent from connecting on the right. Note that 14.g8 is not satisfactory. 14.g8 g6 15.i5 h9. h9 is a forking ladder escape that guarantees a connection to the right. | |
| 14. | ... | g6 | |
| 15. | i5 | h7 | Note that h7 is threatens to connect to the horizontal player's main group in two distinct ways, through g8 and through h6, and thus is connected to his main group. |
| 16. | g8 | Not necessary but it doesn't hurt as the reply is forced. | |
| 16. | ... | h6 | |
| 17. | j6 | i9 | |
| 18. | i8 | g10 | |
| 19. | f10 | h4 | |
| 20. | j3 | I now have an unbreakable chain on the right side. |
