A good move for red is a good move for blue?

[Tim Robinson]

Hi! There's a rule of thumb that says you should make the move your opponent would most like to play.
But is it true? Has it been proved?

[Jeff]

On Tuesday, December 31, 2013 5:19:13 PM UTC-8, Tim Robinson wrote:

Hi!   There's a rule of thumb that says you should make the move your opponent would most like to play.
But is it true?   Has it been proved?

My experience says it's true: there are certain places on the board that are saddle points between your pieces' influence and your opponent pieces' influence and a stone put there is key for whoever puts it there.

A similar observation is that you can calculate your move based on attack (how to place a stone to connect your groups) or defense (how to place a stone to keep your opponent from connecting) and you'll end up with the same move. 

[urmaul]

*Maybe* this answer comes a bit late. Based on your question I wondered: Is there a position where both players can win when they move first, and each winning move for blue is not a winning move for red, and vice versa? I conjectured such a position could not exist, but they do, here is an example. Possibly there are even simpler examples. Winning moves for blue are marked with a blue circle, winning moves for red are marked with a red circle.

[OHex]

On Tuesday, February 25, 2014 5:24:11 AM UTC-8, urmaul wrote:

*Maybe* this answer comes a bit late. Based on your question I wondered: Is there a position where both players can win when they move first, and each winning move for blue is not a winning move for red, and vice versa? I conjectured such a position could not exist, but they do, here is an example. Possibly there are even simpler examples. Winning moves for blue are marked with a blue circle, winning moves for red are marked with a red circle.

It appears you attempted to attach an image, but it is not visible to me.  Perhaps the forum stips images from postings -- they do tend to make the postings very large.  You can put images online with an online hosting service like flickr, picasa and imageshack and link to them.

[OHex]

It seems pretty clear that if there's just a single winning move for one player, then taking that move by the other would be a win.  If there are multiple winning moves however, it is not so clear.

On Tuesday, December 31, 2013 5:19:13 PM UTC-8, Tim Robinson wrote:

[urmaul]

Yes, that's the case. Then, I tried to correct it just like I'm trying to correct it right now, but it seems like the correction got lost somehow.
Here is the example I meant: Blue tries to connect from left to right, red tries to connect from top to bottom. Winning moves are colored dots.
  A B C D
 1 . . R .
  2 . . . .
   3 B . . .
    4 B . R .