Re: value of sente; life and death

[David Mechner <mechner@xxxxxxxxxxx>]

Jeremey Thorpe wrote:

> yes, i understand.  however, we are talking about quiet, statically
> evaluable positions, which is to say, positions where there are many
> nearly equally valuable places around the board to play,

If your definition of a quiet position is that there are many
independent places to play that are all as big or nearly as big as the
biggest move, you're right. But by that definition I don't think that
you'll find many quiet positions in the opening or middle game of go.


> [...] your approximation will most of the time (in quiet positions)
> give a value of less than 1.

As my friend Archie would say, "Maybe on Mars." When I'm playing and
get sente, I often have very strong feelings about which move is
biggest - often I'm struggling to get sente for just that reason. The
biggest area is often /substantially/ bigger than the second
biggest. 

On the subject of the distribution of move values, I'd just like to
amplify something I mentioned earlier about them being uneven: They
Are Uneven. There are often "tiers" of values of moves - maybe 1 or 2
or 3 big ones, then a few that are obviously substantially smaller but
similar to each other, then a bunch more that are obviously smaller
still... The situation you're describing just doesn't jibe with my
experience with go.


> this is to say that the remaining terms (3rd-4th, 5th-6th) cannot,
> in general, be ignored.

Agreed. And if you have values for the second, third, etc. independent
pairs of moves you should use them. But it's hard to find and evaluate
so many independent moves. The board usually has a few, and then
things start to interact; to create other moves, etc.

Basically if (as in computer go) you're stuck with making a
simplifying assumption, between assuming:

 1) that moves after the first and second go in pairs of equal size and

 2) that moves are evenly spaced,

I'm not sure which is worse. Clearly neither is true. I'm open to some
kind of demonstration or argument that (2) is better, but a claim that
they're evenly spaced won't do, because they're not.

> but, the value of the next move is not the same as the value of
> sente.  sente means the ability to play the next move far away from
> the current fight.

And why can you play away from the current fight? Because taking the
biggest local move is smaller than taking the biggest move on the
board. That says nothing about the gap between the biggest and the
next-biggest. And the fact that the biggest move is a lot bigger than
the next biggest move doesn't necessarily mean that the opponent 
screwed up - the gote move he just played may have been bigger 
still. This is how games are won.

> The value of sente dosen't actually fluctuate often from move to
> move, and when it does, it's not that much.

What can I say except I couldn't disagree more. 

If you're still not convinced, I propose an experiment. We arrange a
game between a reasonably strong player, say me, and a weak player (I
don't know whether you fit the bill, but that would be the most fun
:). We'll get a 3rd party, a very strong player, to give us their top
10 (or 5) picks for each move. If your assertion is right, the weak
player will be able pick any of them and be ok, by the middle game he
should be trailing by at most a few points. If I'm right, he'll be
crushed.

What do you think? 


WAIT!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

stop the presses. I think I found a solution that will make us
both happy. 

Let the value of sente be the difference of the 1st and 2nd move, plus
1/2 the second (or 1/2 the third, whichever you prefer). If you're
right about the structure of go, counting the 1-2 difference won't
matter much. If I'm right, I still get what I want with a (perhaps
useful) bias term tacked on.

I hope I've averted the international crisis.

-David

-- 
David A. Mechner            Center for Neural Science
mechner@xxxxxxxxxxxxxxxxx         4 Washington Place, New York, NY 10003
212.998.3580                http://cns.nyu.edu/~mechner/