John Tromp wrote:
I have computed the game theoretical results of all positions in the gameOk, exactly what I thought. Just depicting the game tree in 2 dimensions. Its a very nice picture though ;)
of connect-4 as played on a 7x6 board, with up to 4 stones. The way I map
this depth-4 game tree into 2 dimensions is to start with a big circle for
the root, and then draw the 7 1-ply positions as subcircles of that one,
and the 7x7=49 2-ply positions as subsubcircles etc. Each circle is colored
in one of 3 shades, represting a loss, draw, or win (but then partly obscured by the smaller circles drawn on top of it).
Nice. So he either means the statement was true, but so obvious its not worth restating, or its false and his postings indicate something else which I/we am/are not able to discern.To me it seems like what your describing would simply be the game tree represented in a 2 dimensional form.
Have you read all my postings? To me it seems you have not read anything I wrote. Listen, I am logging off until 2006.
I was simply reminded of my cover when Frank mentioned fractals, because that's how always talked about it to people: "look at this graphical representation of early connect-4 positions; isn't it fractal like?"
I understand.
But I'm afraid the shortest formula to describe this fractal would be the brute force game tree search:(
Precisely.
For go, a shortcut formula is even less likely, since its PSPACE completeness implies that any fast (subexponential) algorithm for go would translate to
a fast algorithm for *any* problem whatsoever solvable in polynomial space.
Agreed. _______________________________________________ computer-go mailing list computer-go@xxxxxxxxxxxxxxxxx http://www.computer-go.org/mailman/listinfo/computer-go/