CGT Analysis of Same Small Endgame
For contrast, let's do the analysis of the same small endgame with CGT. Quoting the traditional analysis page:
Suppose 'small' here amounts to: two-point and one-point gote plays and one-point sente plays for Black and for White. We take 'sente' to mean absolute sente: requiring an immediate answer. This takes all the subtlety out of the argument, but means it becomes very clear what should happen.
Translating that into CGT terms, after chilling there are N *s (Stars, or 2 point gote, deiri), M numbers of value 1/2 (1 point gote, deiri), P minies (1 point sente for Black), and Q tinies (1 point sente for White).
As David Wolfe pointed out, if M is odd, it does not matter how we play the infinitesimals, because, even if we get the last play (tedomari) before playing the numbers, our opponent can "round" the 1/2 in his favor, and vice versa. Interestingly, this is in accord with the traditional saying that a tedomari play is worth double.
Another approach is to say, well, getting that last play doesn't hurt, so we might as well ignore the numbers, anyway. Let's do that.
We are left with a position with an atomic weight of zero. The minies are negative, but we can clear them without cost (in sente). (We'll assume that *our* absolute sente are bigger than his. ;-)) Once that is done, we are left with N *s and Q tinies. If N is even, the sum of *s is 0, so we are left with the tinies to consider, and we take one. If N is odd, we know that the sum is fuzzy, a first player win. If we play one of the tinies (reverse sente), we will leave a fuzzy position, which White can win. But if we play one of the *s, we will leave a positive position, since the remaining *s sum to 0 and the tinies are positive. We win a positive position, regardless of who plays first, so that's our play.
Once you get past the terminology, you may notice that there is less reading involved with the CGT approach. Basically, all you need to know is that, in a game of an odd number of *s plus some tinies, by playing one of the *s you reach a positive position, which is a win for you (Black), regardless of who plays first.
-- Bill Spight
Jeff: It seems to me that whether N is even or odd matters a lot! They're the biggest points on the board. My intuition says to play first at my sente points, then the N points, then start playing reverse sente and responding to the opponent's sente plays. Finally, I would play the M points. But that's just intuition, and I don't have tedomari intuitionized. ;-)
Bill: Yes, whether N is even or odd matters a lot. If it is even, after taking your absolute sente, take a reverse sente (tiny). If it is odd, after taking your absolute sente, take one of the gote (star).